Formulation of the Material Force Approach for Finite Inelasticity

Abstract

The material forces represent the thermodynamically driving forces on any kind of inhomogeneity and discontinuity. For comprehensive investigations, the balance of the inverse motion problem has to be formulated and evaluated to separate different portions of the material forces arising from different inhomogeneities and discontinuities. This paper presents a general approach for inelastic material models based on the multiplicative split of the deformation gradient in order to calculate the J ‐integral of an inelastic crack tip. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Material parametrization of natural rubber based compound and characterization of crack propagation under consideration of dissipative effects

“…( 12) is simplified to a path independent vectorial J-integral. A prerequisite for the use of this concept is that the constitutive material laws are derived from the Helmholtz free energy and that a change in non-elastic strains is accompanied by a dissipative potential [19].…”

“…In a later work [9], he recognizes that the material forces on a crack in a purely elastic body under quasi-static load correspond to the well-known J-integral. The concept of material forces offers a more general interpretation of the J-integral and thus a unified approach to the description of cracks in complex materials such as hyperelastic [29], viscoelastic/elastoplastic [19,20] ,or magnetoelasticity [12].…”