Path-independent Integrals in Finite Elasticity and Inelasticity, with Body Forces, Inertia, and Arbitrary Crack-face Conditions

Abstract-In this paper, certain path-independent integrals, of relevance in the presence of cracks, in elastic and inelastic solids are considered. The hypothesized material constitutive properties include: (i) finite and infinitesimal elasticity, (ii) rate-independent incremental flow theory of elasto-plasticity, and (iii) ratesensitive behaviour including elasto-viscoplasticity and creep. In each case. finite deformations are considered, along with the effects of body forces, material acceleration, and arbitrary traction/displacement conditions on the crack-face. Also the physical interpretations of each of the integrals either in terms of crack-tip energy release rates or simply energy-rate differences in two comparison cracked-bodies are explored. Several differences between the results in the present work and those currently considered well established in literature are pointed out and discussed.