On configurational forces in the context of the finite element method

摘要

The theory of configurational forces is briefly recast, together with the underlying balance laws. It is shown, that in the case of a homogeneous body without body forces this additional balance laws are identically satisfied if the standard force balance holds. In approximate solutions, for example obtained by finite elements, the equilibrium is not satisfied exactly, thus configurational forces occur on discretization nodes. An implementation of the configurational force balance into the finite element scheme is presented. The use of configurational forces is discussed with three main aspects. It is demonstrated how configurational forces can be used to check and to improve the finite element solution. Examples from fracture mechanics and problems with material inhomogeneities are discussed.