Approaches to Finite-strain Elastoplasticity
Elastoplastic material models involve a decomposition of the strain tensor into an elastic and a plastic part. The latter is driven by a nonsmooth evolution law, the flow rule. Small-strain elastoplasticity, which is based on the additive decomposition of the strain tensor, has developed significantly over the last decades, since techniques from convex analysis and variational inequalities are applicable.
For finite-strain elastoplasticity, convexity is unacceptable because of physical requirements like objectivity and plastic indifference. The latter leads to the multiplicative decomposition of the strain tensor and asks to consider the plastic tensor as elements of multiplicative matrix group, which leads to strong geometric nonlinearities. We show how polyconvexity and time-incremental minimization can be used to establish global existence for elastoplastic evolutionary systems.
Alexander Mielke, WIAS Berlin, Germany
