Young measure flow as a model for damage |
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Authors: | Marc Oliver Rieger and Johannes Zimmer |
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Institution: | (1) Mathematical Institute, University of Utrecht, Budapestlaan 6, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands |
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Abstract: | 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. |
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