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.
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|
|Creators||Rieger, M. O.and Zimmer, J.|
|Uncontrolled Keywords||fracture,elasticity,continuum mechanics|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||riegerzimmer.pdf: The final publication is available at Springer via http://dx.doi.org/10.1007/s00033-008-7016-3|
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