Variational methods beyond the elastic threshold

Activities will focus on the inelastic response of complex solids, with the following goals:

• to review recent progress in the theoretical and computational modeling of plastic behavior, both at the macroscopic scale and at the level of dislocation structures. In these areas, variational methods have provided a valuable framework for the formulation of sound models and for the implementation of efficient strategies for their numerical solution.
• to identify promising areas for further applications of variational techniques by analyzing the inelastic response of emerging complex systems
• to identify material systems whose mechanical response requires the development of mathematical tools outside the reach of variational methods

Among the topics to be covered, we expect the following:

• mechanics of crumpled membranes,
• numerical implementation of models in associative and non-associative elasto-plasticity,
• mechanics of foams and powders,
• constitutive models for granular materials and for the weathering of soft rocks,
• modeling of polymers and rubber-like materials,
• macroscopic and atomistic models of dislocation structures,
• variational methods in fracture mechanics.

The format will be such as to favor contacts and exchange of ideas among participants, with few invited lectures and ample time for discussion (with both thematic sessions and informal gatherings).
This workshop is part of the <link internal>period of concentration on the mechanics of complex solids at the Max Planck Institute for Mathematics in the Sciences.