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SUMMARYThe theory of conÿgurational forces is brie y 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 satisÿed if the standard force balance holds. In approximate solutions, for example obtained by ÿnite elements, the equilibrium is not satisÿed exactly, thus conÿgurational forces occur on discretization nodes. An implementation of the conÿgurational force balance into the ÿnite element scheme is presented. The use of conÿgurational forces is discussed with three main aspects. It is demonstrated how conÿgurational forces can be used to check and to improve the ÿnite element solution. Examples from fracture mechanics and problems with material inhomogeneities are discussed.

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The theory of material forces for a hyperelastic material is briefly presented using the translational invariance of the control volume. The theory is derived for the dynamical setting, while the numerical implementation is limited to the static case. The finite element (FE) method is used to solve the standard field equations. After obtaining the solution the material force balance is consistently discretized with FE. As a result of this postprocessing discrete material forces are obtained. They are then used to set up an adaptive scheme, in which the magnitude of the material forces acts as an indicator for mesh refinement. Special consideration is given to the boundary, where two different refinement strategies are proposed. The two strategies are compared by studying the refinement process for three examples.