Theoretical and computational aspects of configurational forces in three-dimensional crack problems

Abstract

Mechanics in material space yields configurational forces (CFs) as an appropriate means to describe driving forces acting at defects or inhomogeneities in magnitude and direction. A thermodynamically based approach to obtain a weak formulation of CFs with virtual defect displacements as test functions is introduced first, starting from a global variational energy balance instead of from the currently employed local configurational balance equation. A theoretical basis and issues of three-dimensional implementation are presented to calculate vectors of CFs along a crack front, providing information on local loading and deflection angles. Spurious nodal CFs are separated from physical ones, inter alia requiring surface integrals along the crack faces. Within a linear elastic framework, these are efficiently replaced by an algebraic expression, providing CFs at crack front nodes in a very good approximation, which is eventually demonstrated by means of analytical and numerical examples.