Multiscale Modeling in Continuum Mechanics and Structured Deformations
Invited Lecturers
- Gianpietro Del Piero (Univ. d. Studi di Ferrara, Ferrara, Italy)
6 lectures on:
Foundations of the theory of structured deformations: kinematics, simple deformations, structured deformations, approximation theorem, energetics, stress. The “strong” formulation of Del Piero and Owen, versus the “weak” formulation of Choksi and Fonseca.- Luca Deseri (Università di Ferrara, Ferrara, Italy)
3 lectures on:
Crystalline plasticity and structured deformations; geometry of single crystals undergoing single or multiple slip; energetics in the setting of two-level shears; loading and unloading without dissipation; yielding; non-smooth hardening.- Khan Chau Le (Ruhr-Universitaet Bochum, Bochum, Germany)
6 lectures on:
Variational problems of crack equilibrium and crack propagation; governing equations and boundary conditions; equilibrium criterion at the crack tip; motion of an elastic body with a propagating crack; asymptotic behavior of the near-crack tip field.- Jean-Jacques Marigo (Laboratoire de Mécanique des Solides , Palaiseau Cedex, France)
6 lectures on:
An evolution scheme and numerical approximation techniques for fracture mechanics; the evolutional scheme of Francfort and Marigo within the Griffith scheme for brittle fracture; solution techniques based on the concept of Gamma-convergence.- David R. Owen (Carnegie Mellon University, Pittsburgh Pennsylvania, USA)
5 lectures on:
Field theories for bodies undergoing disarrangements; structured motions; refined description of contact and body forces; balance laws; dissipation; a theory of elasticity with disarrangements.- Roberto Paroni (Università di Sassari, Alghero, Italy)
3 lectures on:
Second-order structured deformations; approximation theorem and energetics in different settings: classical, SBV2, SBH.- Miroslav Silhavy (Academy of Sciences, Prague 1, Czech Rep.)
6 lectures on:
Energy minimization for isotropic nonlinear elastic bodies; quasiconvexity, polyconvexity, rank-one convexity of isotropic functions; differentiability; formulas for the first and second differentials; relaxation of invariant functions; relaxation of invariant sets.