Poly-, Quasi- and Rank-One Convexity in Applied Mechanics
Invited Lecturers
- John Ball (University of Oxford, Oxford, Great Britain)
5 lectures on:
Outstanding open problems of nonlinear elasticity; existence, singularities and asymptotic behaviour of solutions, status of elasticity with respect to atomistic models, understanding of microstructure induced by solid phase transformations, and fracture.- Antonio De Simone (SISSA, Trieste, Italy)
5 lectures on:
Liquid Crystal Elastomers (LCEs): nematic and smectic phases and their response to external loads. Variational models of the quasistatic response of LCEs. Soft deformation paths as quasi-convex hulls of the sets of spontaneous strains. Quasi-convex envelope of the energy density and its use in finite-element simulations.- Patrizio Neff (Techn. Univ. Darmstadt, Darmstadt, Germany)
5 lectures on:
Polyconvexity: Coercivity and growth conditions for anisotropic energies used in biomechanics, tensile instabilities for fiber reinforced solids, dimensional reduction of generalized continuum models and their relation to classical shell models.- Annie Raoult (Univ. René Descartes Paris 5, Paris Cedex 06, France)
5 lectures on:
Network modeling: adapted principle of frame indifference, existence results, homogenization. Mechanical applications in biomechanics and carbon nanotube modeling. Adapted convexity conditions for director models in thin structure. theories.- Joerg Schroeder (University of Duisburg-Essen, Essen, Germany)
5 lectures on:
Representation theorems for isotropic tensor functions, continuum mechanical interpretation of generalized convexity conditions, construction of anisotropic polyconvex functions. Applications: Modeling of arterial walls and hyperelastic thin shells.- Miroslav Silhavy (Academy of Sciences, Prague 1, Czech Rep.)
5 lectures on:
Semiconvexity of isotropic functions, rank 1 convexity and phase equilibria in general materials, phase equilibria in isotropic materials, explicitly solvable models: e.g., Hadamard material, a class of energies related to nematic elastomers.- David J. Steigmann (Berkeley University of California, Berkeley, CA, USA)
5 lectures on: Polyconvexity conditions in terms of the right stretch tensor, gradient formulae for the rotation and stretch factors in the polar decomposition combined with convexity properties of certain stretch invariants.