A nonsmooth Newton method for elastoplastic problems

Abstract

In this work we reformulate the incremental, small strain, J 2-plasticity problem with linear kinematic and nonlinear isotropic hardening as a set of unconstrained, nonsmooth equations. The reformulation is done using the minimum function. The system of equations obtained is piecewise smooth which enables Pang's Newton method for B-differentiable equations to be used. The method proposed in this work is compared with the familiar radial return method. It is shown, for linear kinematic and isotropic hardening, that this method represents a piecewise smooth mapping as well. Thus, nonsmooth Newton methods with proven global convergence properties are applicable. In addition, local quadratic convergence (even to nondifferentiable points) of the standard implementation of the radial return method is established. Numerical tests indicate that our method is as efficient as the radial return method, albeit more sensitive to parameter changes.