Computational studies on path independent integrals for non-linear dynamic crack problems

Abstract

Recently the authors have derived various new types of path independent integrals in which the theoretical limitations of the so-calledJ integral are overcome. First, for elastodynamic crack problems, a path independent integralJ′ which has the physical meaning of energy release rate was derived. Later, more general forms of path independent integralsT * andT were derived, which are valid for any constitutive relation under quasi-static as well as dynamic conditions. This paper presents the theoretical and computational aspects of these integrals, of relevance in non-linear dynamic fracture mechanics. An efficient solution technique is also presented for non-linear dynamic finite element method in which a factorization of the assembled stiffness matrix is done only once throughout the computation for a given mesh pattern. Finite element analyses were carried out for an example problem of a center-cracked plate subject to a uniaxial impact loading. The material behavior was modeled by three different constitutive relations such as linear-elastic, elastic-plastic, elastic-viscoplastic cases. The applicability of theT * integral to non-linear dynamic fracture mechanics was shown with the numerical results.