FINITE-STRAIN ANISOTROPIC PLASTICITY AND THE PLASTIC SPIN

A detailed analysis of the kinematics of anisotropic elastoplastic solids under finite isothermal deformations is presented. The formulation is based on a multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts. Emphasis is placed on the proper definition and the physical meaning of the so-called 'plastic spin', which is the spin of the continuum relative to the material substructure. Constitutive equations for the plastic spin are derived for three different material systems: (i) a fibre-reinforced metal-matrix composite, in which the local axis of transverse isotropy is defined by the local orientation of the fibres, (ii) polymeric materials, in which the anisotropy is deformation induced, and (iii) an elastoplastic material which yields according to a yield condition of the kinematic hardening type. The numerical implementation of the elastoplastic equations in a finite element programme, as well as an algorithm for their numerical integration, are briefly discussed. The choice of the intermediate unstressed configuration and the proper definition of the plastic spin in 'non-isoclinic' configurations are also discussed.