Assessment of fracture energy of polyethylene

1

Svenska mekanikdagar

Uppsala 12

Svenska mekanikdagar 2017

Svenska mekanikdagar 2017

Uppsala 12-13 juni

FÖRORD

Svenska mekanikdagar arrangerades första gången 1974. Årets arrangemang är det 25:e

i ordningen tillika andra tillfället som mötet hålls vid Uppsala universitet. Konferensen

organiseras av Nationalkommittén för Mekanik som är en underavdelning till Kungliga

Vetenskapsakademien.

2017 års upplaga innehåller 65 presentationer och föreläsningar. En av konferensens

höjdpunkter är Folke Odqvist-föreläsningen som i år ges av Solveig Melin, Lunds

universitet. Vi hoppas och tror att konferensen skall leda till nya insikter och till att nya

kontakter knyts.

Välkomna till Uppsala universitet!

Organisationskommittén,

Per Isaksson, Hållfasthetslära

Kristofer Gamstedt, Tillämpad mekanik

Ett speciellt tack till

Tidigare mekanikdagar

2015, LiU, Linköping

2013, LTH, Lund

2011, Chalmers, Göteborg

2009, KTH/Scania, Södertälje

2007, LTU, Luleå

2005, LTH, Lund

2003, Chalmers, Göteborg

2001, LiTH, Linköping

1999, KTH, Stockholm

1997, LTU, Luleå

1995, LTH, Lund

1993, SP, Borås

1992, KTH, Stockholm

1990, Chalmers, Göteborg

1988, FFA/KTH, Stockholm

1987, SAAB/LiTH, Linköping

1985, LTH, Lund

1983, ASEA, Västerås

1982, UU, Uppsala

1980, LuTH, Luleå

1979, Chalmers, Göteborg

1977, LiTH, Linköping

1976, KTH, Stockholm

1974, KVA, Stockholm

Odqvistföreläsare

Larsgunnar Nilsson

Anders Klarbring

Kenneth Runesson

Henrik Alfredsson

Sture Hogmark

Fred Nilsson

Bo Jacobson

Niels Saabye Ottosen

Peter Gudmundson

Martin Lesser

Bertil Storåkers

Arne Johansson

Viggo Tvergaard

Inge Ryhming

Frithiof Niordson

Sune Berndt

Mårten Landahl

Georg Drougge

Hans-Christian Fischer

Janne Carlsson

Bertram Broberg

Lars Jarfall

Jan Hult

Hus 4 The Svedbergs-laboratoriet Hus 1 Hus 3 Hus 2 Hus 6 Hus 7 Hus 9 Hus 16 Hus Matikum vån 1 Karin Boye bibliotek

Så hittar du: Exempel:

Eng2-1024

Eng = Engelska Parken Alla lokaler inom campus

2 = Hus 2 Se karta för husnummer 10 = Plan 1 20 = Plan 2 10 = Plan 1 K10 = Källarplan/Basement 24 = Rumsnummer 24 De två sista siffrorna är Eng 2-1024 House 2 Floor 1 Room 24 Hus 21 Ihre-salen Intendentur Källare ABM vån 0, Sociologi vån 1, Kulturantropologi vån 2 Musikvetenskap vån 0 Kulturantropologi vån 2 Konstvetenskap vån 0 Ark

eologi och antik vån 2

The Svedberg (kontor) vån 0 Hugo Valentin vån 1 Centrum för Religion och Samhälle vån 2 Språkv erkstaden vån 0, Engelska vån 1, Nor diska vån 2, Moderna vån 3 Geijersalen vån 1 Idé- och lär doms-historia vån 1 Litteratur vet. Källar e – vån 1 Te o lo g i Historia Nordiska Afrikainstitutet Centrum för genusvetenskap Humanistiska teatern 3A 3B 3E 3P 3H 3L 3R 3N 3M 3G Botaniska trädgården 3A = Entrances 3Q 3O Hus 17 5D Hus 5 3S Park ering 5A Hus 7A Fack-villan 11 12 Parkering Park ering Parkering Infar t g ods - The Sv edberg

Engelska parken - Humanisskt centrum

Humanistiska teatern 3C

Svenska mekanikdagar 2017

Villa

v

ä

g

e

n

Thunber

gsväg

_en

PROGRAM

Måndag 12/6

10:30

Registrering

öppnar

Lunch

13:00

Öppnande

Mikael

Jonsson

Upptech, Uppsala universitet

13:15

Odqvistföreläsning

Mechanics at the atomic scale

Solveig

Melin

Lunds

universitet

14:05

Session

1

Kaffe

15:25

Föreläsning

Mechanics at the horizon

Ulf

Danielsson

Uppsala

universitet

16:15

Session

2

17:30

Gustavianum

19:00 Konferensmiddag på Norrlands nation

Tisdag 13/6

08:45

Föreläsning

Non-linear dynamics of the human intervertebral disc

Stephen Ferguson

ETH Zürich

09:35

Session

3

Kaffe

10:55

Session

4

Lunch

13:00

Föreläsning

From fluid to solid mechanics via colloidal chemistry:

hydrodynamic assembly of biomaterials

Fredrik Lundell

KTH

13:50

Session

5

14:50

Avslutning

FÖRELÄSNINGAR

Måndag 12/6, Ihresalen

13:15

Odqvistföreläsning

Mechanics at the atomic scale

Solveig

Melin

Lunds

universitet

15:25

Mechanics at the horizon

Ulf

Danielsson

Uppsala

universitet

Tisdag 13/6, Ihresalen

08:45

Non-linear dynamics of the human intervertebral disc

Stephen

Ferguson

ETH

Zürich

13:00

From fluid to solid mechanics via colloidal chemistry:

hydrodynamic assembly of biomaterials

Fredrik Lundell

SESSION 1 (MÅNDAG 12/6)

Tid Flerskalsmodellering I

Ihresalen Strukturmekanik I Sal: 7-0042 Strömningsmekanik I Sal: 7-0043 Brottmekanik I Sal: 6-0031 14:05 Local microstructure

control by laser annealing

H. Hallberg, F. Adamski, S. Baïz, O. Castelnau Lunds universitet

On a Nash game formulation for robust structural optimization and its numerical solution using a decomposition method C.-J. Thore, H. Alm Grundström, A. Klarbring Linköpings universitet Using magnetic resonance velocimetry to measure turbulence in fibre suspensions M. Leskovec, F. Lundell KTH Kohesiv modellering av brott U. Stigh, D. Svensson, K.S. Alfredsson Högskolan i Skövde 14:25 Computational homogenization of gradient crystal plasticity: mesoscale boundary conditions

K. Carlsson, F. Larsson, K. Runesson

Chalmers

Full-scale finite element modeling of the Vasa ship

R. Afshar, N. Alavyoon, A. Ahlgren, N.P. van Dijk, A. Vorobyev, K. Gamstedt Uppsala universitet

An efficient and systematic study of grid resolution requirements for wall-resolving large eddy simulation of turbulent channel flow

S. Rezaeiravesh, M. Liefvendahl Uppsala universitet

Dynamic crack

propagation in wood fibre composites J. Carlsson, P. Isaksson Uppsala universitet 14:45 Reinforced concrete in two-scale setting A. Sciegaj, F. Larsson, K. Lundgren, F. Nilenius, K. Runesson Chalmers

Risk assessment for buckling of the original foremast of the Vasa ship

N. van Dijk, A. Ahlgren, A. Vorobyev, R. Afshar, K. Gamstedt Uppsala universitet Three-dimensional simulations of dispersed cellulose nanofibrils in microfluidic channels K. Vijayakumar, L.D. Söderberg, F. Lundell KTH Fatigue strength predictions of gears combining heat treatment simulations and material fatigue testing

E. Olsson, N. Melin, M. Henriksson

SESSION 2 (MÅNDAG 12/6)

Tid Flerskalsmodellering II

Ihresalen Strukturmekanik II Sal: 7-0042 Strömningsmekanik II Sal: 7-0043 Brottmekanik II Sal: 6-0031 16:15 An xfem-based two-scale fracture model E. Svenning, F. Larsson, M. Fagerström Chalmers Multibody dynamic modelling of a wind turbine direct drive train

S. Asadi, H. Johansson Chalmers

The fluid mechanics of rotor-stator mixers–the effect of stator slot width

A. Håkansson, H.H. Mortensen, F. Innings Högskolan i Kristianstad

Dislocation based fracture mechanics within generalized continua M. Mousavi Karlstads universitet 16:35 Effect of boundary conditions in numerical homogenization of three dimensional lamina and laminated composites

J.J Espadas Escalante, N. van Dijk, P. Isaksson Uppsala universitet

An Eulerian-based thermo-flexible multi-body approach for simulating rig testing of disc brakes

N. Strömberg Örebro universitet LDV-measurements behind a rectangle cylinder S.M. Sayeed-Bin-Asad, T. S. Lundström, A.G. Andersson, J.G.I. Hellström

Luleå tekniska universitet

Creep failure of fibre network: the origin of uncertainty A. Mattsson, T. Uesaka Mittuniversitetet 16:55 Numerical model reduction in computational homogenization of transient heat flow

F. Ekre, F. Larsson, K. Runesson Chalmers Selftuning energy harvester by sliding weight H. Staaf, E. Köhler, P. Folkow, P. Enoksson Chalmers Formulation Of An Efficient And Accurate Method For Reliability Assessment Using Conditional Probability

R. Mansour, M. Olsson KTH

SESSION 3 (TISDAG 13/6)

Tid Biomekanik I

Ihresalen Materialmekanik I Sal: 7-0042 Strömningsmekanik III Sal: 7-0043 Brottmekanik III Sal: 6-0031 09:35 Validation of a parameter

identification method for the human abdominal aorta

J.-L. Gade, C.-J. Thore, J. Stålhand

Linköpings universitet

Implementation of an adaptive shell element for modelling laminated composites in LS-dyna

J. Främby, M. Fagerström Chalmers

Modal instability of the flow in a toroidal pipe J. Canton, P. Schlatter, R. Örlü KTH Assessment of fracture energy of polyethylene M. Kroon, E. Andreasson, P. Olsson Linnéuniversitetet 09:55 On the necessity of muscle contraction dynamics for athletic movements

L.J. Holmberg Linköpings universitet

Modeling metallic glass formation using the phase-field method

A. Ericsson, M. Fisk, H. Hallberg

Lunds universitet

Influence of velocity sampling point location on the accuracy of wall-modelled large-eddy simulation

T. Mukha, M. Liefvendahl Uppsala universitet

Fracture mechanics evaluation of the influence of loading rate and temperature on environmentally assisted cracking in high strength steels

A.E. Halilovic, P. Efsing, T. Narström, R. Pettersson KTH 10:15 Mechanics of pressure ulcer: particle-based approach S. Sarangi, T. Uesaka Mittuniversitetet Energy harvesting by viscoelastic soft dielectric elastomers

R. Denzer, E. Bortot, M. Gei, A. Menzel Lunds universitet

Validation of the explicit algebraic reynolds-stress model in transitioning atmospheric boundary layer

V. Zeli, G. Brethouwer, S. Wallin, A.V. Johansson KTH

Damage tolerance of solid foams

S. Chen, P. Isaksson Uppsala universitet

SESSION 4 (TISDAG 13/6)

Tid Biomekanik II

Ihresalen Materialmekanik II Sal: 7-0042 Pedagogik Sal: 7-0043 Experimentell mekanik I Sal: 6-0031 10:55 On soft tissue modelling

J. Stålhand,B. Sharifimajd, J.-L. Gade, A. Klarbring, J. Karlsson, T. Länne

Linköpings universitet

Modelling of cyclic and viscous behaviour of pearlitic steels-application to tread braked railway wheels

A. Esmaeili Chalmers

Project examination in the course rigid body dynamics

A. Boström Chalmers

Full-field grain-strain mapping of sand using neutrons

S.D. Athanasopoulos, S.A. Hall, T. Pirling, J. Engqvist, J. Hektor Lunds universitet 11:15 Elastic modulus of human

single trabeculae estimated by synchrotron CT experiments and numerical models D. Wu, T. Joffre, S. Gallinetti, C. Öhman Mägi, S.J. Ferguson, P. Isaksson, C. Persson Uppsala universitet

Case hardening steels modelled by thermo-viscoplasticity over a wide range of temperature P. Oppermann, R. Denzer, A. Menzel Lunds universitet Learning-by-doing fluid mechanics M. Liverts, A. Hyvärinen, S. Sembian, K. Vijayakumar, T. Rosén, B. Fallenius, A. Talamelli, J. Fransson KTH Mechanical characterization of thin metal oxide coatings on polymer films by fragmentation analysis M.V. Tavares da Costa, J. Bolinsson, P. Fayet, K. Gamstedt Uppsala universitet 11:35 A review of the relationships between density and mechanical properties of vertebral trabecular bone C. Öhman-Mägi, O. Holub, R.M. Hall, C. Persson Uppsala universitet Thermomechanical capacity of railway wheel treads M.S. Walia, A. Esmaeili, T. Vernersson, R. Lundén Chalmers Constructive alignment by use of project assignments in solid mechanics courses M. Ander, J. Brouzoulis, F. Larsson Chalmers

Material models for structural adhesive tapes

A. Biel, U. Stigh Högskolan i Skövde

11:55 Automated examination in

statics and dynamics through individualized home assignments

S.B. Lindström, L.J. Holmberg Linköping university

SESSION 5 (TISDAG 13/6)

Tid Mjuka material

Ihresalen Materialmekanik III Sal: 7-0042 Farkost Sal: 7-0043 Experimentell mekanik II Sal: 6-0031 13:50 A mixed finite element

formulation for slightly compressible finite elasticity with fibre reinforcement

A. Zdunek, W. Rachowicz FOI Stockholm

Effects of delamination on guided wave propagation in laminated composite beams – numerical simulation S. Shoja, V. Berbyuk, A. Boström Chalmers

Active flow control for trucks: from theory to practice

G. Minelli, S. Krajnovic, L. Hjelm, B. Bergqvist Chalmers

Differential aperture x-ray microscopy (DAXM) applied to tin whisker growth J. Hektor, J.-B. Marijon, M. Ristinmaa, S. A. Hall, H. Hallberg, S. Iyengar, J.-S. Micha, O. Robach, O. Castelnau Lunds universitet 14:10 Non-affine deformation of

soft fibre network

S. Hossain, P. Bergstrom, T. Uesaka

Mittuniversitetet

On the hierarchical structure of wood and its mechanisms providing high tensile strength

O. Marthin, K. Gamstedt Uppsala universitet Verification of a transmission synchronization model M. Irfan, V. Berbyuk, H. Johansson Chalmers Determination of mechanical properities by nanocutting F. Sun, K. Gamstedt Uppsala universitet 14:30 The effect of geometry

changes on the mechanical stiffness of fibre-fibre bonds A. Brandberg, A. Kulachenko KTH Variability of nominally identical components and their influence in an assembly – application to a Volvo XC90 G. Dorendorf, M. Gibanica, T. Abrahamsson Chalmers, Volvo Evaluation of displacements of a wooden hull section of the Vasa ship by means of 3D laser scanning

A. Vorobyev, F. Garnier, N. P. van Dijk, R. Afshar, O. Hagman, K. Gamstedt Uppsala universitet

MECHANICS AT THE ATOMIC SCALE

Solveig Melin

Division of Mechanics, Lund University, Lund, Sweden solveig.melin@lth.se

Nano-sized structures are today found in a variety of everyday products such as mobile phones or medical sensors. For such small structures, with at least one linear measure below 50-100nm, it is well-known that the mechanical response differs from what is found at the macroscopic scale, and sometimes non-intuitive behaviors are reviled. One aspect that makes nano-structures special is that the number of surface atoms no longer can be neglected as compared to the number of bulk atoms. Since the surface atoms are lacking some neighbors they are left in an energy state differing from the bulk atoms. This, in turn, gives a clear surface effect directly influencing the mechanical response. This is illustrated in Figs 1 and 2 which show the uneven axial stress distribution at the same strain level over the cross sections of two Cu beams under tensile loading. The calculations are molecular dynamic simulations using the free-ware Lammps [1]. The figures are produced using the post-processor Ovito by Stukowski [2]. The cross sections have a side length of 6a0, with a0

=3.615Å denoting the lattice constant of Cu. Other important factors at the nanoscale are the lattice structure and the crystallographic orientation of the lattice. The structure is inherently non-isotropic. This can also be seen from Figs 1 and 2, where two different orientations are at hand at otherwise identical conditions.

Figure 1: Cu-beams with orientation x=[100], y=[010] and z=[001] under tensile loading. x in the axial direction. Individual atoms shown.

Not only crystal structure features are important at the scale. Also the geometry of the nano-structure influences the results. This is seen in Figs 1 and 2 in that the atoms close to the corners of the cross sections show stresses that differ from what is found for atoms more centrally placed along the sides of the beams.

In this talk the behavior of nano-sized beams and plates will be presented and discussed with results retrieved foremost from molecular dynamic simulations. But such simulations are computationally demanding, limiting the problem size and simulation time. One approach to reach larger systems is to continualize the molecular dynamic models. This non-local continuum conceptconcept, called peri-dynamics, was developed by Silling [3] and has also been investigated here to determine to what extent features from the nano-scale can be preserved by the peridynamic approach.

References

[1] LAMMPS http://lammps.sandia.gov

[2] Stukowski A, Visualization and analysis of atomistic simulation data with OVITO–the

Open Visualization Tool. Modelling Simul.

Mater. Sci. Eng. 18 (2010).

[3] Silling S A, Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces, J. Mech. Phy. of Solids, vol 48, p 175—209 (2000).

Figure 2: Cu-beam with orientation x=[110], y=[-110] and z=[001] under tensile loading. x in the axial direction. Individual atoms shown.

MECHANICS AT THE HORIZON

Ulf Danielsson

Department of physics and astronomy Uppsala University

The collision of black holes is the most violent phenomenon that we know in the universe. During a brief instant the power of the emitted gravitational waves exceeds the combined power of all stars in the visible universe. But space time is stiff, the waves are tiny, and their successful detection takes mechanical engineering to its very limits. How can one measure the motion of a mirror with an accuracy much better than the size of a proton? The lecture explains the physics behind one of the most exciting discoveries of all times, as well as the technology that made it possible, and gives a glimpse of the physics of tomorrow.

Figure 1: Colliding black holes, courtesy LIGO/Caltech.

NON-LINEAR DYNAMICS OF THE HUMAN INTERVERTEBRAL DISC

Stephen J. Ferguson

Institute for Biomechanics, ETH Zurich, Zurich, Switzerland

Introduction

Accurate predictions of the dynamic response of the intervertebral disc to vibration are highly relevant for studies of disc injury, degeneration and ergonomics. Lumped parameter models of the spine have been developed to investigate its response to whole body vibration. However, these models assume the behavior of the intervertebral disc to be linear-elastic. Recently, the authors have reported on the unique nonlinear dynamic behavior of the human lumbar intervertebral disc [1]. This response was shown to be dependent on the applied preload and amplitude of the stimuli, and we hypothesize that this cannot be described by linear-elastic models.

Methods

A simulation model was implemented, with the quasi-static, asymmetric tension- compression behavior of the disc described with a polynomial function, fitting both axial states independently while maintaining continuity across the transition. The dissipative properties of the disc were described by an additional term incorporating the strain rate. For validation, our prior base- excitation experiments of human discs were simulated with the model, and for comparison with a model incorporating conventional linear elastic material properties, over a frequency sweep from 1 – 60 Hz and back down.

Results

The model incorporating non-linear elastic properties, with a tension-compression asymmetry, was able to capture the unique dynamic characteristics observed in our prior experimental study, such as softening or hardening behavior of the tissue with increasing

frequency, and most importantly, a non-uniform "jump" phenomena in the oscillation, whereby the disc enters and exits resonance at different frequencies on the upwards and downwards frequency sweep. Furthermore, hardening or softening behavior, and the characteristic resonance ranges, were predicted well by a model with properties fit only to a priori quasi- static tension-compression data. In contrast, a conventional linear elastic model predicted only a single, symmetric resonance point at one characteristic frequency, independent of sweep direction.

Discussion

Linear elastic material models fail to adequately capture the non-linear dynamic response of the disc to vibration. For dynamic analysis, the use of standard linear-elastic models should therefore be avoided, or restricted to study cases where the amplitude of the stimuli is relatively small. For a biofidelic and accurate simulation of the vibrational response of the disc, the tension-compression asymmetry of the disc should be incorporated.

Acknowledgements

Funding for this research project was provided by the European Union through a Marie Curie action (FPT7-PITN-GA- 2009-238690-SPINEFX).

References

1. Marini, G., Huber, G., Püschel, K., Ferguson, S.J., "Non-linear dynamics of the human lumbar intervertebral disc", J. Biomech, 2015, 48(3): 479-88

FROM FLUID TO SOLID MECHANICS VIA COLLOIDAL CHEMISTRY:

HYDRODYNAMIC ASSEMBLY OF BIOMATERIALS

Fredrik Lundell (1),(2)

1. Linné FLOW Center, KTH Mechanics, Royal Institute of Technology, 100 44 Stockholm, Sweden; 2. Wallenberg Wood Science Center, KTH Mechanics, Royal Institute of Technology, 100 44 Stockholm,

Sweden;

Introduction

Many materials found in nature demonstrate impressive material properties such a strength-at-break and stiffness. The key to achieve good properties lies in the material structure from the molecules, via structures on nano- and microlevels to the macroscopic material. One example is a wood fiber in a tree, where cellulose molecules are organised in cellulose nanofibrils that are organised into fibres that eventually build up the tree. Recently, it has been demonstrated that disintegration of pulp fibres into typically 4 nm wide and micrometer long cellulose nanofibrils (CNF) can be industrially viable. Such fibrils have many appealing properties: they are strong and stiff (138 GPa) and are biodegradable. However, it is not straightforward to assemble such fibrils into larger structures. In this talk, I will first describe how we have used hydrodynamic assembly to synthesize nanostructured filaments from CNF and protein nanofibrils (PNF). From this work, some fundamental aspects regarding the behaviour of fibrils in flows have been identified and these aspects will be discussed in the second part.

Hydrodynamic Assembly and beyond

Flow-focusing utilises multiple flows to focus a central flow to the centre of a channel. Conservation of mass causes an acceleration of the central flow during this process and as a result, elongated particles dispersed in flow will be aligned in the flow direction.

If the colloidal behaviour of these particles in suspension is such that there is a chemically (e.g. by pH) controlled transition from dispersion to gel, this transition can be used to lock the structure in the aligned state. This is achieved by letting the focusing streams contain ions that can diffuse into the central flow and trigger the dispersion to gel

transition. As a result, the central flow is transformed to a gel thread that can be ejected from the channels and dried so that filaments are obtained. The filaments can then be evaluated in terms of mechanical properties by tensile testing and nanostructure by X-ray scattering.

As expected, the alignment of the fibrils controls the strength and stiffness of the filaments. Stiff and string filaments are obtained if the fibrils are aligned to a higher degree whereas less aligned fibrils give more elastic and weaker filaments. Scattering studies with X-ray makes it possible not only to study the fibril alignment in the final filament, but also in-situ in the flow channel. In combination with polarized light studies, this has revealed how the fibrils first align thanks to the extensional flow and then de-align due to Brownian diffusion.

The possibilities and limitations of hydrodynamic assembly are investigated by a combination of simulations and experiments.

Acknowledgments

This work has been performed within Wallenberg Wood Science Centre. I am grateful for great collaborations with, in particular, Daniel Söderberg, Lars Wågberg, Karl Håkansson, Nitesh Mittal, Tomas Rosén and Stephan V. Roth.

References

Håkansson, K. M. O., Fall, A., Lundell, F., Yu, S., Krywka, C., Roth, S. V., Santoro, G., Kvick, M., Prahl-Wittberg, L., Wågberg, L. & Söderberg, L. D. (2014) Hydrodynamic alignment and assembly of nanofibrils into strong cellulose filament Nature

Communications 5 4018

FULL-SCALE FINITE ELEMENT MODELING OF THE VASA SHIP

R. Afshar (1), N. Alavyoon (1), A. Ahlgren (2), N.P. van Dijk (1), A. Vorobyev (1) , K. Gamstedt (1)

1. Applied Mechanics, Department of Engineering Sciences, Uppsala University, Uppsala, Sweden; 2. Swedish National Maritime Museums, the Vasa Museum, Stockholm, Sweden

Abstract

A full-scale model of the 17th century Vasa shipwreck has been developed to assess its current and future structural stability as well as design an improved support structure. A wireframe model, consisting of only lines, points and curves to describe the geometry of the ship, has been provided by the Vasa museum. It has been developed based on geodetic measurements using a total station. From this wireframe model, a three-dimensional (3D) model comprising solid bodies for solid-like parts (i.e. hull and keel), surfaces for the shell-like components (deck planks) and lines for beam-like constituents (deck beams) has been developed in Creo Parametric 3D software. This geometric model has been imported in finite-element software, Ansys, for further development of the stiffeners (knees, riders, columns, masts, etc.), adjustment of the correct location of deck beams and, finally, structural analyses of the entire ship (Figure 1).

Figure 1. (a) The full-scale FE model of the Vasa ship; (b) a longitudinal section of the ship model and the corresponding von-Mises stresses in all of the timber members (units in MPa); (c) a transverse cross-section, showing the summation of displacements (units in mm).

It can be seen from Fig.1 (b) that the level of stresses in the most members is less than 1MPa and appear to be in columns and deck beams. The stresses in hull is relatively lower that the other members. Considering the displacements at a transvers section of the ship, as shown in Fig. 1 (c), the displacement distribution is towards the port side. In fact, this is expected due to the asymmetry of the ship (about 72 mm) towards the port side. The maximum displacements are relatively small and are at the deck planks [1]. In addition, some efforts have been made to calculate the stiffness parameters at the joints of the ship, which play an important role in the structural integrity of the ship [2-5]. Although, there are still some members at the bow and aft side that need to be added to complete the model. Nevertheless, the current model can be used as a starting tool to assess the structural integrity of the ship and study the support structure concepts. During development of the FE model other similar historical shipwreck projects, in particular [6-8], have been used.

References

[1] R. Afshar, N. Alavyoon, A. Ahlgren, N.P. van Dijk , A. Vorobyev and K. Gamstedt, A full-scale finite-element model of the Vasa ship, Computational Methods in Wood Mechanics-from Material Properties to Timber Structure, 7-9 Jun 2017, Vienna, Austria.

[2] D. Wu, R. Afshar, K. Gamstedt, Calculation of Joint Stiffness Parameters of the Section Replica of the Vasa Ship, International Conference on Experimental Mechanics and Applications, 26-27 March 2017, Madrid, Spain.

[3] R. Afshar, N.P. van Dijk, I. Bjurhager, E.K. Gamstedt, Comparison of experimental testing and finite element modelling of a replica of a section of the Vasa warship to identify the behaviour of structural joints, Journal of Engineering Structure (Submitted). [4] E. Kristofer Gamstedt, Reza Afshar, Nico van

Dijk and Alexey Vorobyev, Development of a Numerical Model to Simulate the Effect of new Support Designs for a Wooden Shipwreck, Analysis and Characterization of Wooden Cultural Heritage by means of Scientific Engineering Methods, 28-29 April 2016, Halle, Germany.

[5] I. Hassel, R. Afshar, A. Vorobyev, F. Bommier, E. K. Gamstedt, Towards determination of local and overall

 

(b)

(c) (a)

displacements of the Vasa ship structure: Effect of its mechanical connections, Historic Ships, 25-26 November 2014, London, UK. [6] Fenton R.F., Fowles R.J. HMS victory:

modelling and structural analysis: how this contributes to the conservation of Nelson’s famous flagship. Historic Ships, 25-26 November 2014, London, UK.

[7] Invernizzi S., et al. Numerical modelling and assessment of the Ebe schooner-brig., International journal of Architectural Heritage: Conservation, Analysis and Restoration, 6:5, 453-477, 2012.

[8] Stoyanov S., Mason P.Bailey C. Smeared shell modelling approach for structural analysis of heritage composite structures – An application to the Cutty Sark conservation. Computers and Structures 88 (2010) 649– 663.

CONSTRUCTIVE ALIGNMENT BY USE OF PROJECT ASSIGNMENTS IN

SOLID MECHANICS COURSES

Mats Ander, Jim Brouzoulis, Fredrik Larsson

Div. of Material and Computational Mechanics, Chalmers University of Technology, 412 96 Göteborg

Constructive alignment

Constructive alignment [1] has during the last fifteen years been an increasingly popular method to design, develop and improve undergraduate courses. The key feature of the method is to clearly define the learning outcomes of the course, to align assessment as well as the learning activities to support the students own learning to reach the outcomes.

Project assignments

As a part of the new curriculum at the school of Civil engineering at Chalmers two new courses in solid mechanics,TME295 [2] and TME300 [3], have been developed for the academic year 2016/17.

In fact the curriculum is also designed according to Constructive alignment on a higher level. As a measure to align the new courses we have introduced compulsory project assignments for the students. We use a real structure, a pedestrian and bicycle bridge as a core project, Figure1. The analysis of this bridge will stepwise introduce the students into the different topics of the course. The tasks connected to the bridge covers, when they are accomplished, about 70% of the course learning outcomes. The remaining 30% is covered by other assignments within the project.

Organisation and assessment

There are 200-230 students attending the courses. Students are working in pairs. The project is handed in at three occasions during the course and are corrected within 4-5 days for reasonable quick feedback. The project scheduled learning activities comprises weekly consulting classes, three computer workshops and one session with physical experiments. We also use traditional lectures and problem solving classes in the course. The course is assessed by the project assignment 2.0 hp and by a graded final written exam 4.0 hp consisting of both theory questions and problems to solve.

Course evaluation

At the first written exam after the course 75 % of the students passed the exam. In the previous course it used to be 55-65%. Yet it is too early to draw some general conclusion from this, but it is promising. The student experienced a lot of work and they felt that the project ‘’forced them in a

good way’’ to follow the course tempo as well as preparing them for the final exam. The physical experimenting with tensile tests and the analysis of a real bridge structure was highly motivating. Also the commitment of the teaching team was appreciated. On the down side was that the students sometimes felt that their assignments were not judged and corrected equally by the teachers. One of the nicest quotes we have got from a colleague teacher in the structural engineering course; ‘’I have never experienced a group of students from the solid mechanics course in the first quarter, that are so skilled and well prepared for my course in the second quarter’’.

Figure 1: The pedestrian bridge with support detail

Acknowledgements

We would like to acknowledge the project planning guidance from Magnus Gustafsson at the division of Engineering Education Research, Chalmers.

References

[1] J-.Biggs (1999) Teaching for quality learning at university, Open university press, McGraw-Hill.

[2]https://student.portal.chalmers.se/en/chalmerss tudies/courseinformation/Pages/SearchCourse.as px?course_id=25582&parsergrp=3 [3]https://student.portal.chalmers.se/en/chalmerss tudies/courseinformation/Pages/SearchCourse.as px?course_id=25583&parsergrp=3

MULTIBODY DYNAMIC MODELLING OF A WIND TURBINE DIRECT

DRIVE TRAIN

Saeed Asadi, Håkan Johansson

Div. Dynamics, Mechanics and Maritime Sciences, Chalmers University of Technology

Abstract

Wind turbines normally operate under long time and experience a wide range of operating conditions. A representative set of these conditions is considered as part of a design process, as codified in standards [IEC 61400]. However, operational experience shows that failures occur more frequent than expected, among the more costly are the failures in the main bearings and gearbox.

As modern turbines are equipped with increasingly sophisticated diagnostics systems, an important task is to evaluate the drive train dynamics from online measurement data. In particular, internal forces leading to fatigue can only be determined indirectly from sensors at other locations.

In this contribution, a direct wind turbine drive train is modelled using the floating frame of reference formulation [1] for flexible multibody dynamics system, cf Fig. 1. The purpose is to evaluate drive train response based on blade root forces and bedplate motions. The dynamic response is evaluated in terms of main shaft deformation and main bearing forces under different operational conditions (normal operation at different wind speeds, extreme turbulence, start-up-shut down, etc.). The model was found to agree well with a commercial wind turbine system simulation software.

Using system simulation data, different model simplifications was studied to investigate the trade-off between simulation time and accurate capture of dynamic performance. Operating conditions as stipulated in [IEC 61400] are evaluated in terms of drive train performance. Ultimately, global sensitivity analysis [2] is used assess the sensitivity of the blade root forces and bedplate motion on predicted main bearing life. Future work will be devoted to evaluate drive train performance for real measurement data.

Figure 1: Illustration of studied direct drive wind turbine (above) engineering model (below).

Acknowledgements

This project is financed through the Swedish Wind Power Technology Centre (SWPTC). SWPTC is a research center for design of wind turbines. The purpose of the center is to support Swedish industry with knowledge of design techniques as well as maintenance in the field of wind power. The Center is funded by the Swedish Energy Agency, Chalmers University of Technology as well as academic and industrial partners.

References

[1] Shabana A. Dynamics of Multibody Systems, Cambridge Press, New York, 4th edition, 2013. [2] Zhang, X. Pandey, M. D., Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method, Structural Safety, 2013, 43:28-40.

FULL-FIELD GRAIN-STRAIN MAPPING OF SAND USING NEUTRONS

S. D. Athanasopoulos (1), S. A. Hall (1), T. Pirling (2), J. Engqvist (1), J. Hektor (1)

1. Division of Solid Mechanics, Lund University, Lund, Sweden; 2. Institut Laue Langevin, Grenoble, France

Granular media are highly complex materials since they are characterised by the mobility and interaction of their constituent particles. Under the effect of loading certain areas carry the load while other, neighbouring areas, fall into a less or even completely unloaded state. This inhomogeneous behaviour, which might also exhibit significant variations as the loading develops (i.e., loaded clusters of grains might shift into an unloaded state and vice versa), is associated with the existence of force-chains [1]; a micro-scale network of spatially continuous lines of forces between grains that are constantly readjusting throughout the grain skeleton as the deformation evolves. To this end, understanding the (micro-) mechanisms associated with the distribution and evolution of forces/stresses through granular assemblies will provide significant insight of the overall behaviour of granular matter during deformation, until mechanical failure of the material is reached.

In recent years neutron diffraction scanning has been successfully used as a new experimental tool for studies on granular materials under load, inferring force/stress distribution from crystallo-graphic (grain) strains [2,3]. In this work the use of the neutron diffraction technique has provided the opportunity to measure the "grain strains" in a quartz sand specimen (i.e., the strains in the crystal lattices of the constituent non-bonded elastic-brittle grains of a sand sample) during mechanical loading, as a function of an applied boundary load. Through the elastic properties of averaged gauge volumes of grains, full-field mappings of the grain-strain distribution evolution were produced (Fig.1)

Figure 1: Macroscopic axial displacement as a function of the deviatoric axial force. Outset: 2D grain-strain mappings (white being less compressed and black being more) per load step.

The experimental method involves prismatic samples of sand (D50 = 210 μm) loaded in a specially designed plane-strain cell (experiments performed at the neutron diffraction instrument SALSA, at the Institut Laue-Langevin, France). The loading was realised in steps over a load-unload cycle (Fig.1) with a confining pressure of 3 MPa. At each load step the loading was paused with a fixed piston displacement while scanning diffraction measurements were made over a 2D grid of 50 points, using rows of five 2x2x2 mm3 gauge-volumes through the thickness of the sample. The 2D diffraction mappings of crystal strains at each load step show a spatially structured grain-strain distribution, based on the averaging of the sum of the 5 small volumes at each point of the 2D grid.

Further experiments are underway with a new version of the loading device, which allows simul-taneous Digital Image Correlation (DIC) measure-ments to take place. As a result, a multiscale characterisation of the total, “macroscopic” strain field (DIC) and the force transmission (neutron diffraction) in the sample will be possible.

References

1. J. F. Peters, M. Muthuswamy, J Wibowo, and A. Tordesillas, Physical Review E72, 041307 (2005).

2. S. A. Hall, J. Wright, T. Pirling, E. Andò, D. J. Hughes, and G. Viggiani, Granular Matter 13, 251-254 (2011).

3. C. M. Wensrich, E. H. Kisi, V. Luzin, U. Garbe, O. Kirstein, A. L. Smith, and J. F. Zhang, Physical Review E90, 042203 (2014).

MATERIAL MODELS FOR STRUCTURAL ADHESIVE TAPES

Anders Biel, Ulf Stigh

University of Skövde, SE-541 28 Skövde, Sweden

Background

The fracture toughness of a structural adhesive tape is comparable to that of a structural adhesive. However for a structural adhesive tape the maximum stress is lower and the deformation before fracture is larger. From a designers point of view the large flexibility gives new possibilities. Deformations up to 1000% are possible, [1,2]. In a numerical simulation is it convenient to represent the tape with a cohesive zone; sometimes denoted a cohesive layer model.

Experiments and evaluation

In this study, material data for a 0.5 mm thick transparent acrylic foam adhesive tape (3M VHB-4905F) is determined experimentally. The J-integral approach is used with the double cantilever beam specimens (DCB). In order to study the fracture process, the specimens are manufactured of transparent polymethylmeth-acrylate (PMMA), [3]. During the experiments images are taken of the fracture process zone. All experiments are quasi-static.

Results

Figure 1 shows the experimentally determined cohesive law. It includes two stress peaks. At the first, σ ≈ 0.4 MPa, cavities nucleate in the tape and increase in size. At a deformation about, w ≈ 1 mm the cavities completely fill the tape. Any further elongation is mainly related to elongation of the walls between the cavities and the stress increases slightly to, σ ≈ 0.35 MPa. At the end, the walls between the cavities fracture and the stress decrease abruptly.

Figure 1: Cohesive law for the pressure sensitive tape 3M VHB-4905F.

One example of the images taken during the experiments is shown in Figure 2A where the crack front is located at the lower end of the image. The cavities and the walls formed between them are clearly visible. At the upper part of the image, newly nucleated cavities are shown as bright dots.

The images are analyzed in Matlab using the

Image Processing Toolbox. In Figure 2B, the

remaining acrylate is shown in black and cavities in green. The stress state in the walls between the cavities is similar to the one in a macroscopic study [4]. An evaluation shows similar stresses in the walls as in that study.

Consecutive images from the fracture process of the walls between the cavities indicate that the pressure inside the cavities is smaller than the ambient air-pressure. Thus, the ambient pressure should be considered in extreme applications of with pressure sensitive adhesives.

Figure 2: Cavities in the adhesive layer; (A) Image from the experiment and (B) corresponding Image analyzed with Matlab.

References

[1] Biel A., Alfredsson K.S. and Carlberger T., (2014) Proc Mater Sci, 3, 1389

[2] Hayashida S., Sugaya T., Kuramoto S., Sato C., Mihara A. and Onuma T., (2015) Int J Adhes Adhes, 56, 61

[3] Biel A. and Stigh U., (2017) Int J Fract, 204, 159

[4] Pharr M, Sun J-Y, Suo Z (2012) Rupture of a highly stretchable acrylic dielectric elastomer. J Appl Phys 111:104114

PROJECT EXAMINATION IN THE COURSE RIGID BODY DYNAMICS

Anders Boström

Chalmers University of Technology, Department of Applied Mechanics, Göteborg

Introduction

A course in Rigid body dynamics has been given at Chalmers for many years, since 2008 it is given in English on the master program in Applied mechanics and also to other programs and Erasmus students. The number of students is usually 40-50.

Course aim

The course is a continuation of the basic course in dynamics given to second year undergraduates. The main aim of the course is to treat rigid body motion in 3D. Important aspects include advanced kinematics (3D rotations, Euler angles, rotation matrices, general relative motion, constraints, rolling), general Newtonian equations in 3D, Lagrange’s equations, and coupled oscillations. The goal is that the students should be able to solve larger dynamic problems in 3D with typical applications to vehicles, robots, etc.

Course structure

The course is traditional in many ways with lectures and problem-solving sessions. To fulfill the goal of treating larger systems in 3D the course also includes a large project, typically some sort of vehicle or robot. The project is in three parts: kinematics, Newtonian equations, and Lagrange’s equations, usually including some calculations with Matlab for kinematics, eigen-frequencies, or stability. The project is not mandatory, but it gives a pass on the whole course with the lowest grade and a bonus to the exam for a higher grade. If the project is not passed, the student must do the exam, but can still have a bonus from passed part(s) of the project. Almost all students get a pass by doing the project. The course also includes a mandatory lab in commercial software (ADAMS) for modelling rigid body dynamics, it is the same system as in the project that is modelled.

Some examples of systems that have been used in the projects through the years are a tricycle, a Segway, a delta robot, and a car suspension. Figure 1 shows a photo of the delta robot. It is a pick-and-place robot that has a very ingenious construction. The three identical, very light, arms are connected at the tool and through the construction the tool is not rotated at all when the arms are moving. The robot can lift 1 kg and make two operations per second.

Figure 1: The delta robot.

Discussion

There are a number of pros and cons with the possibilities for the students to pass the course without doing the exam. The main reason for giving the project is that its solution corresponds very well to the main aim of the course (that is to solve larger 3D problems for rigid body dynamics). At the exam the given problems are much smaller and only check some aspect of the course. Another advantage with the project is that the students are forced to work actively with the course material from the very beginning. The students are generally very satisfied with the course structure.

There are also some disadvantages with the possibility to skip the exam. The project must be done individually, although some cooperation is of course allowed and even encouraged. Still, there is of course a risk that some students get away without a proper understanding by mostly copying some friend. There have been some recognized instances of this and also a few who have been failed for this reason. Another drawback is that only about a third of the students write the exam, thus the grades are generally low on the course. The presentation will concentrate on the project and its rules and the positive and negative aspects of passing the course on the project.

THE EFFECT OF GEOMETRY CHANGES ON THE MECHANICAL

STIFFNESS OF FIBRE-FIBRE BONDS

August Brandberg, Artem Kulachenko

KTH Royal Institute of Technology

Having control over the strength and foldability of paper produced from a given paper pulp is valuable in all manufacturing involving paper. Mechanical response obtained from experiments on the macroscopic scale are a function of many coupled parameters and in situ testing of microscopic network constituents is generally not possible.

Fibre networks have been modelled using methods ranging from two dimensional line surfaces to fully resolved 3-D geometries captured using micro-tomography [1,2]. By modelling individual fibres as beams the depth of the sheet and non-linear material behavior can be retained when working with large, representative segments. However, beams cannot capture the deformation of individual fibre cross-sections and this deformation mode may store a significant amount of elastic energy. If the contact between fibres is modelled through a penalty-based beam-to-beam contact formulation, the finite stiffness and strength of the bond region can be incorporated with a directional contact stiffness and cohesive fracture.

Method

A FEM model of a bond is constructed by isolating the segments of two fibres that form a contact (see Figure 1) that are then pressed together. The model contains the essential characteristics of fibres including helically wound fibrils and independently resolved cellulose and lignin/hemi-cellulose.

Figure 1: The experimental setup with two fibre segments and two rigid plates where the load is applied.

Results

The effect of increased compression is shown in Figure 2. The increase in stiffness stems mainly from fibre collapse.

Figure 2: Force-displacement response as the amount of compression is increased. Stiffness extracted from the linear part of the lines with markers.

Conclusions

The crossing angle of the fibres in the bond region does not affect the normal stiffness but has a strong influence on the tangent stiffness, which increases rapidly as the angle between the fibres decreases. The response of the bond region is a strong function of pressing conditions, in particular the closing of the fibre lumen.

Furthermore, while the residual stress state of the fibre-fibre bond may be important in predicting the ultimate strength of the bond, the test of the bond with and without the residual state shows that it has only a moderate effect on the fibre bond stiffness, which means the stiffness of the bond can be assessed through its final geometrical configuration.

References

[1] Cox, H.L., The elasticity and strength of paper and other fibrous materials. British Journal of Applied Physics, 1952. 3:72.

[2] Targhagh, M., Simulation of the mechanical behaviour of low density paper and an individual inter-fibre bond. 2016, University of British Columbia.

MODAL INSTABILITY OF THE FLOW IN A TOROIDAL PIPE

Jacopo Canton, Philipp Schlatter, Ramis Örlü

Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, Stockholm

Introduction

While hydrodynamic stability and transition to turbulence in straight pipes — as one of the most fundamental problems in fluid mechanics — has been studied extensively, the stability of curved pipes has received less attention. In the present work, the first (linear) instability of the flow inside a toroidal pipe is investigated as a first step in the study of the related laminar-turbulent transition process. The impact of the curvature of the pipe (defined as the ratio between the radius of the pipe and that of the torus) on the stability properties of the flow is studied in the framework of classical linear stability analysis.

We focus on an idealised toroidal geometry which, albeit rarely encountered in industrial applications, is representative of a canonical flow and is relevant in the context of the research on the onset of turbulence. Moreover, the toroidal pipe constitutes the common asymptotic limit of two important flow cases: the curved pipe and the helical pipe. The technical relevance of these flows is apparent from their prevalence in industrial appliances, such as in heat exchangers, exhausts and other devices; for a comprehensive review of the applications, see Vashisth et al. [1]. The study of the flow in curved pipes has been the subject of several papers over the last decades: theoretical, experimental and numerical results have been presented [2-4], however, a thorough analysis of the causes and mechanisms of hydrodynamic stability and transition to turbulence in this flow is still missing.

Base flow

In order to determine the linear stability of the toroidal pipe flow, we investigate the growth of infinitesimal disturbances around a basic state. This base flow, i.e. the solution to the steady, incompressible Navier–Stokes equations, is invariant with respect to the axial pipe direction and is maintained in motion by a constant volume force. The base flow is characterized, as first discovered by Dean [5], by the presence of two counter-rotating vortices, so-called Dean vortices in his honour. These two primary vortices are present at every Re and for any value of δ (different from zero), and are located symmetrically with respect to the equatorial plane of the torus. The shape of the vortices and the position of their centres depend on both Re and δ.

Figure 1: Critical mode for δ =0.3, Re=3379

Stability analysis

Results show that the flow is linearly unstable for all curvatures investigated between 0.002 and unity, and undergoes a Hopf bifurcation at Re of about 4000. The bifurcation is followed by the onset of a periodic regime, characterised by travelling waves with wavelength O(1) pipe diameters. The neutral curve associated with the instability is traced in parameter space by means of a novel continuation algorithm, which provides a complete description of the modal onset of instability as a function of the two governing parameters. Several different modes are found, with differing properties and eigenfunction shapes. Some eigenmodes belong to groups with a set of common characteristics, deemed ‘families’, while others appear as ‘isolated’. Comparison with nonlinear DNS shows excellent agreement, confirming every aspect of the linear analysis, its accuracy, and proving its significance for the nonlinear flow. Experimental data from the literature are also shown to be in considerable agreement with the present results [6].

Acknowledgements

Financial support by the Swedish Research Council (VR) is gratefully acknowledged. Computer time was provided by the Swedish National Infrastructure for Computing (SNIC).

References

[1] Vashist, S., Kumar, V. & Nigam, K. D. P. 2008 Ind. Eng Chem. Res. 47, 3291–3337.

[2] Ito, H. 1987 JSME Intl J. 30, 543–552. [3] Kühnen, J., Holzner, M., Hof, B. & Kuhlmann,

H. C. 2014 J. Fluid Mech. 738, 463–491. [4] Di Piazza, I. & Ciofalo, M. 2011 J. Fluid Mech.

687, 72–117.

[5] Dean, W. R. 1927 Phil. Mag. 4, 208–223. [6] Canton, J., Schlatter, P., Örlü, R., J. Fluid

DYNAMIC CRACK PROPAGATION IN WOOD FIBRE COMPOSITES

Jenny Carlsson, Thomas Joffre, Per Isaksson

Applied Mechanics, The Ångström Laboratory, Uppsala University

Introduction

Dynamic crack propagation has, partly due to the complexity of the field, primarily been studied on relatively homogenous materials such as steel, glass and amorphous polymers. There is a need to understand also the dynamic failure process in heterogeneous and anisotropic materials. This presentation aims to provide a link between dynamic crack propagation in homogenous materials and that in heterogeneous. This is done by comparing crack propagation in strip specimens [1] in a short fiber composite, to that of its pure matrix material. The work has been focused on wood pulp based bio-composites with a degradable PLA matrix. As both PLA and wood fibers are hydrophilic, experiments are performed for both wet and dry material. The experiments are compared to numerical results obtained using a dynamic phase field model [2] where a crack is represented by a diffuse fracture phase field. The phase field method is based on the principle of energy minimization, and the governing equations are obtained from variation of the Lagrangian,







































Results and Discussion

Crack tip velocities up to 0.5–0.7 times the Rayleigh velocity (cR) are measured from image analysis of high-speed camera footage. The different materials have slightly different limiting crack tip velocities, specifically wet PLA had the lowest limiting velocity (0.5cR), while wet wood fiber PLA composite had the highest (0.7cR). A decrease in critical fracture toughness occurs for the wet samples of both materials, compared to the dry samples. The analytical solution, obtained from the phase field model correlates satisfactory with both wet and dry PLA and wood fiber PLA composite with respect to fracture energy and crack tip velocity, Fig. 1.

In the PLA material, branching occurs, to some extent, in all samples. The branching pattern correlates reasonably well with respect to simulations (Figs. 2-3). The dry wood fiber PLA composite shows some branching, but the wet wood fiber PLA composites show no apparent branching.

Figure 2: Branching pattern in dry PLA.

Figure 3: Branching pattern predicted for dry wood fiber PLA composite using a dynamic phase field finite element model.

Comparison of experimental and simulation results show interesting differences. Firstly, the wet wood fiber PLA composite samples do not branch. Secondly, although there was no significant change in stiffness between dry and wet PLA, the limiting velocity was lower for the wet samples. These differences are possibly due to the microstructure of the material. A wet material could also be more ductile, indicating that plasticity behavior may have to be included in the models. Thus, there is a need for further development of fracture models to better capture the behavior of heterogeneous and/or anisotropic materials.

Acknowledgements

The Swedish Energy Agency and The Swedish Research Council Formas are acknowledged for the financial support of this project.

References

[1] Nilsson, F. (1974). Crack propagation experiments on strip specimens. Eng. Frac. Mech., 6, 397-403.

[2] Borden, M. et al. (2012). A phase-field description of dynamic brittle fracture. Comp. Methods in Appl. Mech. Eng., 217-220, 77-95.

0 100 200 300 400 500 600 700 800 900 1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 γ [N/m] WFC dry sim WFC wet sim PLA sim WFC dry exp WFC wet exp PLA dry exp PLA wet exp

COMPUTATIONAL HOMOGENIZATION OF GRADIENT CRYSTAL

PLASTICITY: MESOSCALE BOUNDARY CONDITIONS

Kristoffer Carlsson, Fredrik Larsson, Kenneth Runesson

Chalmers University of Technology – Department of Industrial and Materials Science

By incorporating gradient effects in crystal plasticity models, it is possible to account for the experimentally observed length-scale dependency in the inelastic response of polycrystals, e.g. the Hall-Petch effect. In this contribution, we consider variationally consistent selective homogenization (as described by Larson et al.[1]_{) applied to a}

polycrystalline material modeled by gradient crystal plasticity. Thereby, the (homogenized) macroscale problem becomes that of a local continuum, while the internal variables “live” only on the underlying mesoscale.

We perform a set of numerical investigations on three-dimensional polycrystalline Statistical Volume Elements (SVE’s) of different size (i.e. number of crystal grains), where each grain has an fcc lattice structure. The orientation of the slip systems, as well as the shape and position of the crystal grains, are randomly generated to mimic an isotropic polycrystal. Several realizations are generated for each SVE-size, whereby statistical analysis of the homogenized response is allowed for. Of particular interest is the influence that SVE boundary conditions has on homogenized quantities, in particular, the macroscale stress. In a similar fashion as presented by Runesson et al.[2], we consider different combinations of Dirichlet/Neumann boundary conditions on the displacement and microstress fields, and investigate the convergence of the response with increasing size of the SVE and number of random realizations in order to validate bounding characteristics.

Figure 1: Resulting mesoscale stress fields from imposing a macroscopic strain strongly (left) and weakly (right) to an SVE.

Figure 2: Shear components of homogenized stress vs. strain for a single SVE-realization with 10 grains using different combinations of SVE boundary conditions.

Acknowledgements

Financial support from the Swedish Research

Council (VR), grant no. 621-2013-3901, is gratefully acknowledged.

References

[1] F. Larsson, K. Runesson and F. Su, Variationally consistent computational homogenization of transient heat flow, Int. J. Num. Meth. Engng, 2010; 81:1659–1686 [2] K. Runesson, M. Ekh, F. Larsson,

Computational homogenization of mesoscale gradient viscoplasticity, Comput. Methods Appl. Mech. Engrg. 2017; 317:927-951

DAMAGE TOLERENCE OF SOLID FOAMS

Shaohui Chen, Per Isaksson

Applied Mechanics, The Ångström Laboratory, Uppsala University

Solid polymer foams are used in a variety of applications in modern world, e.g. as biomedical implants, energy absorbing or insulation materials, packages or sandwich structures [1]. Foams and other materials having relatively large voids/pores are insensitive to small defects [2,3]. This interesting fracture phenomenon, typical for discontinuous materials, is not well understood or thoroughly analyzed. In this study, mode I fracture experiments and numerical analyses were conducted on PVC foams to reveal the fracture behavior.

Both the experimental and numerical results show that for sufficiently small defects (initial cracks), the continued fracture process occur through breakage of cell edges located relatively far away from the defect while the global fracture load is fairly constant and hence unaffected by the small defects, Fig. 1. At larger defects than about 4 cells, however, the continued cell edge fractures are localized to the vicinity of the initial defect, resulting in a decreasing global fracture load, in accordance with classical linear elastic fracture mechanics (LEFM), Fig. 2. This is in strong disagreement to classical fracture theories developed for more continuous materials such as glass or steel. Also, the critical defect size is affected by the regularity -or randomness- of the cellular structure: the critical defect size is smaller for more ordered cell structures than for those having larger variances in cell sizes, even though their average cell size is similar.

A key conclusion is that for brittle foams having defects smaller than roughly 4 cells, other fracture theories than the classical LEFM have to be applied when analysing fractures.

Figure 1: Left: failure load at various crack length ratios (crack length a, average cell size d). Right: CT image showing a growing crack in a solid foam.

Figure 2: The final fracture is localized to the initial large defect, but not to the smaller defect.

References

[1] Gibson LJ, Ashby MF. Cellular solids: structure and properties. Cambridge univ. press, 1999. [2] Fleck NA, Qiu XM. The damage tolerance of

elastic–brittle, two-dimensional isotropic lattices. J Mech Phys Solids 2007, 55:562-588. [3] Symons DD, Fleck NA. The imperfection

sensitivity of isotropic two-dimensional elastic lattices. J Appl Mech 2008, 75: 051011.

ENERGY HARVESTING BY VISCOELASTIC SOFT DIELECTRIC

ELASTOMERS

Ralf Denzer (1), Eliana Bortot (2), Massimiliano Gei (3), Andreas Menzel (4),(1)

1. Division of Solid Mechanics, Lund University, Sweden 2. Technion, Israel Institute of Technology, Haifa, Israel 3. Applied and Computational Mechanics, Cardiff University, UK

4. Institute of Mechanics, TU Dortmund University, Germany

Introduction

In this paper we propose a numerical framework for reliable simulations of soft energy harvesters. In particular, a simple electrical circuit is realised by connecting the capacitor, stretched periodically by a source of mechanical work as depicted in Figure 1, in parallel with a battery through a diode and with an electrical load consuming the energy produced, see Figure 2.

Figure 1: The dielectric elastomer generator in its reference configuration.

Figure 2:.Scheme of the electrical circuit in which the dielectric elastomer generator operates.

As these devices undergo a high number of electro-mechanical loading cycles at large deformation, the time-dependent response of the material must be taken into account as it strongly affects the generator outcome. To this end, the viscoelastic behaviour of the polymer and the possible change of permittivity with strains are

analysed carefully by means of a proposed coupled electro-viscoelastic constitutive model, calibrated on experimental data available in the literature for an incompressible polyacrylate elastomer (3M VHB4910). Numerical results showing the importance of time-dependent behaviour on the evaluation of performance of DEGs for different loading conditions, namely equi-biaxial and uniaxial, are reported in the final section, see [1].

Results

As a result we show the simulated efficiency of the energy harvester taking a large strain electro-viscoelasticity model and electrostriction into account, see Figure 3. It turns out that depending on the excitation frequency
and the external ohmic electric load we can reach efficiencies up to 49%.

Figure 3: Efficiency of the energy harvester under equi-biaxial loading depending on excitation frequency and external ohmic electric load.

References

[1] E. Bortot, R. Denzer, A. Menzel and M. Gei. Analysis of viscoelastic soft dielectric elastomer generators operating in an electrical circuit. International Journal of Solids and Structures, 78-79, 205-215, 2016.