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Models for hysteresis in continuum mechanics are studied that rely on a time-discretised quasi-static evolution of Young measures akin to a gradient flow. The main feature of this approach is that it allows for local, rather than global minimisation. In particular, the case of a non-coercive elastic energy density of Lennard-Jones type is investigated. The approach is used to describe the formation of damage in a material; existence results are proved, as well as several results highlighting the qualitative behaviour of solutions. Connections are made to recent variational models for fracture.
- Continuum mechanics
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- 1 Finished
MATHEMATICAL ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF MATERIALS WITH PHASE TRANSITIONS AND MICROSTRUCTURES
18/03/05 → 17/03/08
Project: Research council