On the dynamics of moving singularities in solids under the use of the level-set method and the configurational force concept

摘要

In this paper we examine the motion of a moving singularity within a continuum body under the use of the level-set method and the material force concept. The level set method introduces an implicit representation of a singular surface where it transforms into a thin transition layer of non-zero thickness where all quantities take inhomogeneous expressions within the body. The existence of an inhomoge-neous energy of the material predicts inhomogeneity forces which drive the singularity. The driving force is in fact a material force entering the canonical momentum equation (pseudo-momentum) in a natural way. The kinetic relation is produced by invoking relations that can be considered as the regularized versions of the Rankine-Hugoniot jump conditions combined with non-equilibrium jump relations at the singularity. The effectiveness of the method is illustrated by the use of two examples: (1) propagating phase-transition front that corresponds to a stress-induced martensitic transformation in an elastic bar and (2) propagation of a straight brittle crack.