ANALYSIS OF FINITE ELASTOPLASTIC DEFORMATION USING A NEW FINITE-ELEMENT METHOD

A direct finite element scheme based on a variational method of the least squares type is used to analyze large deformation of dilatant solids. The approach is incremental in nature. The scheme treats both Cauchy stress rates and velocities as dependent variables, and provides the requisite computational basis for mixed problems, that is, problems with combined elliptic and hyperbolic character. There are two unique features of the method, which distinguish the scheme from that based on the conventional displacement and the mixed formulations. One is that the method is insensitive to the type of the governing field equations, that is, the computational algorithm is the same in both elliptic and hyperbolic regions. The other is that the method is insensitive to the absence of work hardening, that is, the resulting matrix system is always symmetric and positive definite. Numerical results for a number of fundamental deformation problems demonstrate that the onset of progressive damage of the deforming material, either due to dilational cracking or the formation of shear bands, can emerge as the natural outcome of the analysis. The analysis predicts various failure modes as they are embedded in the governing field equations and does not employ any additional failure criterion. The results also demonstrate the significance of the infinitesimal assumption of the elastic component of the deformation rate in choosing time-step sizes during numerical implementation. © 1990.