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MiS Preprint

Study of a model for reference-free plasticity

Stephan Luckhaus and Jens Wohlgemuth


We investigate a Kac-type many particle model that allows a reference-free description of plastic deformation. In the framework of the model a solid body is described by a set of particle positions. A lattice is fitted to the particle configuration around each point on a mesoscopic scale. The lattice parameters are used as an argument of a non-linear elasticity energy functional.

There are two main results in this paper. First, we prove an estimate for the difference between the fitted lattice parameters of points of low energy density that are sufficiently close to each other. Sequences of these points can be used for homotopy type arguments. In particular it is possible to identify dislocations as topological defects in this framework. Furthermore, we use the fitted lattice parameters as local Lagrangian coordinates and bound the energy from below with a functional of these coordinates.

MSC Codes:
74G65, 74P10, 70G75
Many-body interactions, Kac-type potentials for plasticity, Lattice-free description of dislocations

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2013 Repository Open Access
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Study of a model for reference-free plasticity

Dissertation, Universität Leipzig, 2013
2013 Repository Open Access
Stephan Luckhaus and Jens Wohlgemuth

Study of a model for reference-free plasticity