Configurational-force-based finite element mesh refinement for elastic-plastic problems

Abstract

In this paper the computation of configurational forces in case of elastic-ideally plastic material will be examined. Numerical computation of the error in configurational forces will also be introduced in elastic and plastic domain. It will be shown that the so-called r-adaptive mesh refinement procedure \cite 1 is also applicable for elastic-plastic problems as well as the configurational force driven h-adaptive scheme. In some special examples configurational forces are computable in analytic way. This is useful to compare the solution with numerical results, therefore validating the finite element procedure. Two plane problems will be considered where analytical solutions are known. The first one is the thick walled tube model loaded by internal pressure. Second one is an artificial problem where the displacement field assumed to be known in every point of the domain considered. According to the papers Krieg \cite 5 and Szabó \cite 8 analytical solution is obtainable for stress and strain distributions, if the time derivative of the strain is constant. R- and h-adaptive procedures will demonstrated on these two examples.