This paper deals with the implementation of an anisotropic plasticity constitutive equations exhibiting non-linear isotropic, kinematic hardening and coupled continuum ductile damage models. A fully implicit integration of the coupling constitutive equations is adopted and leads to two non-linear local scalar equations solved using the Newton method. The consistent local tangent modulus is obtained in a closed form by exact linearization of the algorithm. The numerical treatment of the proposed algorithm is implemented on ABAQUS using user interface material subroutines (UMAT and VUMAT). The performance of the present algorithm is assessed and bared out by numerical examples.

This brief note discusses some issues related to the calculation of energy release rate for elliptical cracks in anisotropic solids. By using the Stroh formalism, analytical expressions of the energy release rate are obtained for elliptical cracks in an unbounded anisotropic solid. Because of material anisotropy and geometric asymmetry of the crack, the local energy release rate varies along the crack front. The average energy release rate can be obtained by integrating the local energy release rate over the entire crack front. On the other hand, the total work done by the crack-surface traction on the entire crack opening displacement can be easily evaluated once the crack opening displacement is known. It is shown that the average energy release rate is equal to the rate of change per unit crack area increment of the work done by the external load on the crack opening displacement.

Dynamic propagation of a crack along the interface in an anisotropic material subjected to remote uniform anti-plane shear is studied. The crack is assumed to nucleate from an infinitesimal microcrack and expands with a constant velocity. Explicit expressions for the stress intensity factor and the energy release rate are derived.