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Evolutionary Solid Bodies - Micro-structural rearrangements and design modifications in heterogeneous materials

Structure of the Summer School

The Summer School will start on Sunday evening, October 4, 2015, with a reception and will finish on Saturday afternoon, October 10.


1. Seminar

The lectures will concentrate on the fundamentals, on the linkages of both pillars as well as on selected advanced problems. Special emphasis will be given to discussions between speakers and participants.


2. Workshop

The research field splits up in several branches and representative applications which can hardly be unified. The goal of the Workshop is to let PhD students and post-docs present specific problems related to the core topics. Participants intending to present a talk are asked to register and submit a title and one-page abstract before September 15, 2015.


3. Tutorial

The comprehension of the theoretical contents presented in the seminar lectures will be increased by computing and programming tutorials devoted to the computational details.



Schedule

(23-09-2015)

Seminar and Tutorial

Workshop and Tutorial

Arrival Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

08:30 - 09:15

Introduction to Mechanics
of Materials

Micromechanical Modeling

Hartmaier

Interfacial Fracture

Parry

Homogenization

Ganghoffer

Gradient Plasticity and size effects

Forest

Continuation of tutorials

09:15 - 10:00

Dislocation Dynamics
Fivel

10:00 - 10:30

Coffee break

10:30 - 11:15

Dislocation Dynamics

Fivel

Micromechanical Modeling

Hartmaier

Interfacial Fracture

Parry

Homogenization

Ganghoffer

Phase field modelling

Forest

Continuation of tutorials

11:15 - 12:00

12:00 - 14:00

Questions and Answers / Lunch

14:00 - 14:45

Dislocation Dynamics

Fivel

Material Optimization

Stingl

Shape Optimization

Barthold

Topology Optimization

Sokolowski

Shape optimization

Barthold

Continuation of tutorials

14:45 - 15:30

15:30 - 16:00

Coffee break

Closure & Departure

16:00 - 16:45

Introduction to Optimization

Material Optimization

Stingl

Excursion

Topology Optimization

Sokolowski

Excursion

16:45 - 17:30

Material Optimization
Stingl

17:30 - 19:30

Questions and Answers / Dinner

19:30 - 21:00

Discussions / Tutorials / Social events




Abstracts

Dislocation Dynamics.
Marc Fivel, Grenoble, France


Outline

I:  Discrete dislocation dynamics (DD) simulations in multiscale modeling approaches
    1. Introduction to dislocation concept in crystal plasticity
    2. Identification of single crystal constitutive equations for FEM from DD
    3. Application to nanoindentation simulations: comparison between FEM simulations and experiments

II:  DD investigation of persistent slip band formation and crack propagation in fatigue
    1. DD simulations of persistent slip bands in fatigue
    2. Crack nucleation scenario
    3. Crack propagation in fatigue

III:  DD applications: a review of recent studies
    1. Nanoindentation simulations: from MD to DD
    2. Clear band formation in irradiated fcc crystal
    3. Creep behavior of ice single crystal
    4. Study of the anomalous creep behavior of Ni base superalloy


Abstract

XYZ.


References:

XYZ.

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Micromechanical Modeling - Micromechanical modeling of heterogeneous materials, Microstructure evolution and phase transformations.
Alexander Hartmaier, Bochum, Germany


Outline

I:  Micromechanical modeling of heterogeneous materials
    1. Introduction to micromechanical modeling
    2. Application to polycrystals and multiphase materials
    3. Micromechanical models for damage and fatigue

II:  Microstructure evolution and phase transformations
    1. Phase field models for microstructure evolution
    2. Coupling of phase field and crystal plasticity
    3. Application to grain growth simulations


Abstract

XYZ.


References:

XYZ.

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Material Optimization - Sizing Optimization.
Michael Stingl, Erlangen, Germany


Outline

I:  Introduction to sizing problem
    1. a model state problem
    2. a model design problem
    3. analysis of the model problem
    4. the existence issue
    5. numerical approximation
    6. solving the model problem on a computer

II:
  A) An abstract Sizing Optimization framework
    1. the general setting
    2. an abstract existence theorem
    3. an abstract convergence theorem

  B) Applications: from 1D to 2D - from SO to MO/TO (SO = Sizing optimization, MO = material optimization, TO = topology optimization)
    1. motivation
    2. a general scalar material optimization problem
    3. existence: application of abstract theory
    4. discretization/convergence: application of abstract theory

III: MO/TO models and their solution by the OCM method
  A) Design optimization: the engineering way
    1. several (MO)-type problems in algebraic form
    2. sensitivity analysis
    3. optimality conditions
    4. the Optimality Criteria method (OCM)
    5. extensions
    6. a little demo

  B) From topology optimization to free material optimization (FMO)


Abstract

Concepts of material, sizing and shape optimization are discussed in a unified framework. Starting from a simple sizing example and following the book by Haslinger and Mäkinen, a general framework general framework covering existence and convergence theory is developed, which is then applied to material as well as parametric topology optimization problems. Apart from the analysis of these problems their solution by specialized instruments from the field of mathematical programming is discussed.


References:

"Introduction to shape optimization: theory, approximation and computation". J. Haslinger, R. A. E. Mäkinen. SIAM, Philadelphia, 2003.
"Finite Element Approximation for Optimal Shape, Material and Topology Design". J. Haslinger, P. Neittaanmäki. John Wiley & Sons, 1996.
"Topology Optimization: Theory, Methods and Applications". M. P. Bendsoe, O. Sigmund. Springer, Heidelberg, 2003.

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Interfacial Fracture - Recent advances in thin films buckling delamination.
Guillaume Parry, Grenoble, France


Outline

  Interfacial fracture mechanics, covering three aspects:
    1 Fundamental concepts of linear elastic fracture mechanics at interfaces
      1.1 Stress field at crack tip
      1.2 Mixed mode
      1.3 Energetic approach for interfacial fracture
      1.4 Relationship between K et G
      1.5 Evolution of Gc with mixed mode
    2 Cohesive zone models
      2.1 The concept of cohesive zone
      2.2 Cohesive zone in Materials Sciences
      2.3 Identication of cohesive zone models parameters
    3 Thin films buckling delamination
      3.1 Small state of the art on buckling delamination
      3.2 Illustration of the strong coupling between buckling and adhesion
      3.3 Model for buckling delamination: genesis of the telephone cord buckle
        3.3.1 Model for the coupling between buckling and delamination
        3.3.2 Loading and boundary conditions
        3.3.3 Mechanism for the telephone cord buckle formation
      3.4 A quantitative relationship between morphology and adhesion


Abstract

Thin films and coatings are widely used in many hightech applications such as low emissivity windows, thermal barrier coatings for aeronautical applications , and microelectronic devices. In such systems, large compressive residual stresses often reside in the films, causing buckling and delamination, which is detrimental to the application. Therefore, the buckling and delamination of stressed multilayers have been widely investigated in the framework of material science. The versatile morphologies of buckles, which may appear in a wide variety of shapes, namely, straight, circular, telephone cord (TC), and more, have been the topic of in-depth investigations based on nonlinear thin plate theory. Analytical approaches based on the Von Karman theory of plates have provided valuable insights into straight-sided blisters, for which the coupled post-buckling elastic deformation and delamination problems are analytically tractable. It has been shown that the amount of energy released depends on the blister morphology, while the mode mixity at the crack front determines the energy needed to fracture the interface. Until recently, calculations have only investigated the influence of mode mixity on static, final configurations, although it is precisely the coupling between interface response and transient buckle shapes that accounts for the propagation and, in the end, explains the morphology of the buckles. We propose to present how the coupling between a geometrically nonlinear plate model an a mode dependant cohesive zone model has allowed to gain significant insight into the process of buckling delamination in the last few years.


References:

Audoly, B. (1999). Phys Rev Lett, 83:20.
Barenblatt, G. I. (1962). "The Mathematical Theory of Equilibrium Cracks in Brittle Fracture". Advances in Applied Mechanics, 7:55-129.
Dugdale, D. (1960). "Yielding of steel sheets containing slits". Journal of the Mechanics and Physics of Solids, 8:100-104.
Faou, J. Y., Parry, G., Grachev, S., and Barthel, E. (2012). "How does adhesion induce the formation of telephone cord buckles?" Physical Review Letters, 108.
Faou, J.-Y., Parry, G., Grachev, S., and Barthel, E. (2015). "Telephone cord buckles { a relation between wavelength and adhesion". Journal of the Mechanics and Physics of Solids, 75:93-103.
Gille, G. and Rau, B. (1984). Thin Solid Films, 120.
Gioia, G. and Ortiz, M. (1997). Adv Apl Mech, 33:119.
Hutchinson, J. and Suo, Z. (1992). Adv. Appl. Mech., 29:63.
Liechti, K. M. and Chai, Y.-S. (1992). "Asymmetric shielding in interfacial fracture under in-plane shear". Journal of Applied Mechanics, 59:295-304.
Moon, M., Jensen, H., Hutchinson, J., Oh, K., and Evans, A. (2002). Journal of the mechanics and physics of solids, 50:2355.
Needleman, a. (1987). "A Continuum Model for Void Nucleation by Inclusion Debonding". Journal of Applied Mechanics, 54(September):525.
Needleman, A. (1990). "An analysis of tensile decohesion along an interface". J. Mech. Phys. Solids, 38:289{324.
Rice, J. (1988). "Elastic fracture mechanics concepts for interfacial cracks". J. Appl. Mech., 55:98{103.
Tvergaard, V. and Hutchinson, J. W. (1992). "The relation between crack growth resistance and fracture process parameters in elasticplastic solids". J. Mech. Phys. Solids, 40:1377-1397.
Xu, X.-P. and Needleman, a. (1994). "Numerical simulations of fast crack growth in brittle solids". Journal of the Mechanics and Physics of Solids, 42(9):1397-1434.

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Shape Optimization - Optimization applied to multiscale problems.
Franz-Joseph Barthold, Dortmund, Germany


Outline

I:  Foundations of shape optimization
    1. Continuum mechanics adapted for geometry modifications
    2. Variational shape design sensitivity analysis
    3. Model reduction based on sensitivity information
II:  Numerical aspects of shape optimization
    1. Design velocity fields
    2. Discrete sensitivity analysis
    3. Finite element technology adapted to shape optimization
    4. Singular value decomposition and model reduction
III:  Optimization of multiscale problems using numerical homogenization
    1. Foundations of multiscale analysis adapted for optimization
    2. Model problems for optimization
    3. Sensitivity relations for homogenization techniques


Abstract

Shape optimization is an important concept in structural optimization, i.e. the geometry description is modified in order to obtain improved porperties of the engineering structure. The presentation outlines a concept for the description and variation of geometry fields within continuum mechanics. Based on these funadamentals, the subsequent discrete matrix formulations are derived and implemented in a computaional framework. Here, the parallelisms of structural analysis and structural optimization contributions of the finite elements are highlighted. Last but not least, the methodology is applied to multiscale problems showing that variational sensitivity analysis and structural optimization can be efficiently organized to solve outstanding computational problems.


References:

"Efficient variational design sensitivity analysis". F.-J. Barthold, N. Gerzen, W. Kijanski, D. Materna. MMOM, 2015, accepted for publication.
"Zur Kontinuumsmechanik inverser Geometrieprobleme". F.-J. Barthold. Habilitation, Technische Universität Branschweig, 2002.
"Structural and Sensitivity Analysis for the Primal and Dual Problems in the Physical and Material Spaces". D. Materna. Dissertation, Technische Universität Dortmund, 2009. Published by Shaker Verlag, Aachen, 2010, ISBN: 978-3-8322-8811-2.
"Analysis and applications of variational sensitivity information in structural optimization". N. Gerzen. Dissertation, Technische Universität Dortmund, 2014. Published by Shaker Verlag, Aachen, 2014, ISBN: 978-3-8440-2937-6.

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Homogenization - Discrete homogenization methods towards micropolar and second order grade continua. Applications to architectured and network materials.
Jean-François Ganghoffer, Nancy, France


Outline

I:  Theory: the discrete homogenization method
    1.Small strains framework
    2.Micropolar effective continua
    3.Consideration of plasticity and brittle and plastic collapse

II:   Large strain response

III:   Construction of second order gradient continuum models by homogenization

IV:   Applications: 3D interlocks, trabecular bone, auxetic structures, composite materials, biological membranes


Abstract

Architectured and network materials made of a large collection of repetitive structural beam like elements require suitable homogenization methods to construct effective continua which can be conveniently implemented into structural computations at the macroscopic level. This has both a conceptual interest in terms of the development of new micromechanical schemes, and a numerical one, to circumvent the cost of treating repetitive structures having a huge number of d.o.f. There are numerous examples of such networks, from either artificial or natural origin, like 3D textiles, polymeric foams, repetitive antenna, biological membranes, or trabecular bone. Composite materials based on a 3D fibrous preform impregnated with resin require efficient computational tools to evaluate the effective mechanical properties accounting for size effects. These networks may be prone to complex behaviors, like the development of plastic deformations or large strains; they may further exhibit length scale effects, requiring then appropriate modeling strategies at the continuum level, especially an extension of the Cauchy continuum framework towards appropriate generalized continua.

The foundations and analytical developments of the discrete homogenization method are presented to achieve these objectives, considering successively the small and large strains frameworks, and incorporating scale effects by two alternative strategies for enriching Cauchy continuum: micropolar and second order grade continua. Examples illustrating the construction of the effective responses of architectured materials taken from different fields (aeronautics, biomechanics) are continuously shown to illustrate the methodology of construction of the effective continua.


References:

"Discrete homogenization of architectured materials: implementation of the method in a simulation tool for the systematic prediction of their effective elastic properties". F. Dos Reis, J.F. Ganghoffer. Technische Mechanik, 2010. 30, 1-3, 85-109.
"Equivalent mechanical properties of auxetic lattices from discrete homogenization". F. Dos Reis, J.F. Ganghoffer. Comput. Mat. Science. 2012, 51, 314-321.
"Construction of micropolar models from lattice homogenization". F. Dos Reis, J.F. Ganghoffer. Computers Struct. 2012, 112-113, 354-363.
"Cosserat 3D anisotropic models of trabecular bone from the homogenization of the trabecular structure". I. Goda, M. Assidi, J.F. Ganghoffer. Computer Methods in Biomechanics and Biomedical Engineering, 15:sup1, 288-290, DOI: 10.1080/10255842.2012.713645.
"Homogenized elastoplastic response of repetitive 2D lattice truss materials". F. Dos Reis, J.F. Ganghoffer. Computational Materials Science, 84, 2014, 145-155.
"Enhancement of the mechanical properties of composites made of auxetic inclusions: a micromechanical analysis". M. Assidi, J.F. Ganghoffer. Composite Structures. 2012. 94, Issue 8, 2373-2382.
"Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization". I. Goda, M. Assidi, J.F. Ganghoffer. J. Mech. Phys. Solids, 61, 12, 2013, 2537–2565.

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Topology Optimization - Asymptotic analysis.
Jan Sokolowski, Nancy, France


Outline

I:  Asymptotic analysis for linear problems
    1. model problem in elasticity
    2. topological derivative of energy functional
    3. simplified formulae for the topological derivatives
    4. numerical example

II:  Asymptotic analysis for nonlinear problems
    1. contact problem
    2. crack with unilateral conditions
    3. the second order topological-shape differentiability of the energy functional for control of crack propagation

III:  Asymptotic analysis for multiphysics
    1. thermomechanical problem
    2. piezo mode
    3. algorithm of topological-shape optimization
    4. numerical examples


Abstract

XYZ.


References:

XYZ.

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Gradient Plasticity and Size Effects - The micromorphic approach to gradient plasticity and phase transformation in materials and structures.
Samuel Forest, Paris, France


Outline

I:  Theory

II:  Application to size effects in hardening plasticity and strain localization in softening plasticity and damage

III:  Application to phase transformation: Cahn-Hilliard and Cahn-Allen equations

Abstract

Strain gradient models and generalized continua are increasingly used to introduce characteristic lengths in the mechanical behaviour of materials with microstructure. On the other hand, phase-field models have proved to be efficient tools to simulate microstructure evolution due to thermodynamical processes in the presence of mechanical deformation. It is shown that both methods have strong connections from the point of view of thermomechanical field theory. A general formulation of thermomechanics with additional degrees of freedom is presented that encompasses both applications as special cases. It is based on the introduction of additional power of internal forces introducing generalized stresses. The current knowledge in the formulation of physically non-linear constitutive equations is used to develop strongly coupled elastoviscoplastic material models involving phase transformation and moving boundaries. Simple analytic examples will be provided showing size effect in hardening plastic materials, strain localization in damaging materials and motion of transformation fronts in phase changing materials.


References:

S. Forest, Micromorphic approach for gradient elasticity, viscoplasticity and damage, ASCE Journal of Engineering Mechanics, vol. 135, pp. 117-131, 2009.
S. Forest, Questioning size effects as predicted by strain gradient plasticity, Journal of the Mechanical Behavior of Materials, vol. 22, pp. 101-110, 2013.
S. Forest, K. Ammar and B. Appolaire, Micromorphic vs. phase-field approaches for gradient viscoplasticity and phase transformations. In Advances in Extended and Multifield Theories for Continua , edited by B. Markert, Lecture Notes in Applied and Computational Mechanics 59, Springer, pp. 69-88, 2011.

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