Viscoplasticity

Quasistatic problems in viscoplasticity theory

We study the existence theory to quasistatic initial-boundary value problems with internal variables, which model the viscoelastic or viscoplastic behavior of solids at small strain. In these problems a system of linear partial differential equations coupled with a nonlinear system of differential equations or differential inclusions must be solved. The solution theory is based on monotonicity ...

Viscoplasticity : from Theory to Application 15 – 18 October 2007 Monte

Mathematical and numerical model for nonlinear viscoplasticity.

A macroscopic model describing elastic-plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In additio...

Geometric integrators for multiplicative viscoplasticity: analysis of error accumulation

The inelastic incompressibility is a typical feature of metal plasticity/viscoplasticity. Over the last decade, there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve this geometric property. In this paper we examine, both numerically and mathematically, the excellent accuracy and convergence characteristics of such geometric...

Numerical Analysis of a Contact Problem in Rate-Type Viscoplasticity

In this paper, we consider numerical approximations of a contact problem in rate-type viscoplasticity. The contact conditions are described in term of a subdiierential and include as special cases some classical frictionless boundary conditions. The contact problem consists of an evolution equation coupled with a time-dependent variational inequality. Error estimates for both spatially semi-dis...