On numerical solution of elastic–plastic problems by using configurational force driven adaptive methods

Abstract

In this paper, the concept of configurational forces is introduced in the context of finite element mesh refinement for elastic–ideally plastic problems. This paper also includes the numerical computation of configurational forces in the elastic and plastic domains. Methods are demonstrated on three plane problems where the analytical solution is available. The first example is a thick-walled tube loaded by internal pressure. This simple, one dimensional problem allows computation of configurational volume forces analytically to validate the finite element (FE) results. The second example is Galin׳s problem that involves an infinite plate with a circular hole loaded by biaxial tension at the infinity. This is a two dimensional problem for which the analytical solution is known with some restrictions for elastic–ideally plastic case when Tresca yield criterion is considered. The last example introduces another plane problem that follows Naghdi׳s solution on infinite wedges. For this, a new analytical solution is presented for plane stress state using von Mises yield criterion with a uniform shear loading along the boundary. R-, h-, and combined adaptive procedures are demonstrated on the above examples. Since exact stress fields are known, the norm of the difference between numerical and analytical solutions is used as the measure of error.