On configurational forces in short-time dynamics and their computation with an explicit solver

Abstract

A theoretical description and a computational method to calculate configurational forces in the context of the finite element (FE) method is presented. With respect to problems in short-time dynamics, the fully 3D-case and large deformations in hyper-elastic materials are taken into account. The FE implementation and numerical analysis of different structures demonstrates the applicability of this field of mechanics. In the chosen derivation, the Lagrangian depends on the deformation gradient and on the position (in the reference configuration) explicitly, which accounts for inhomogeneous materials, e.g. materials with phase boundaries, voids or cracks. Analogous to the local balance of linear momentum, the so-called Eshelby stress satisfies a configurational force balance (balance of momentum for the material motion problem), where configurational (or material) forces appear as volume forces in the physical space. A consistent FE description is obtained by formulating the weak form of the configurational force balance. Thus, the configurational forces acting on the finite element nodes may be computed after the physical boundary value problem is solved. For the static case and small deformations, the configurational force is strongly related to the well known J-integral in fracture mechanics.