Finite elastoplastic transformations of transversely isotropic metals

A finite strain theory for transversely isotropic elastic-plastic materials is developed. The formulation is based on a multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts. The axis of transverse isotropy at each material point is assumed to “follow” the deformation of the continuum. We derive a constitutive equation for the plastic spin Wpi, which is the average spin of the continuum as seen by an observer spinning with the substructure (e.g. the fibers in a metal-matrix composite). It is shown that Wpi = mm Dpi - Dpi mm, where Dpi is the plastic part of the deformation rate and m is the unit vector in the direction of transverse isotropy in the intermediate (isoclinic) configuration. The numerical implementation of the developed model in a finite element program as well as an algorithm for the numerical integration of the elastoplastic equations are discussed in detail. The problem of plane strain extrusion of a metal-matrix composite reinforced by short aligned fibers is solved using the finite element method.