Young measure flow as a model for damage


Rieger, M. O. and Zimmer, J., 2009. Young measure flow as a model for damage. Zeitschrift für Angewandte Mathematik und Physik, 60 (1), pp. 1-32.

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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.


Item Type Articles
CreatorsRieger, M. O.and Zimmer, J.
Uncontrolled Keywordsfracture,elasticity,continuum mechanics
DepartmentsFaculty of Science > Mathematical Sciences
ID Code15446


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