Use of the Elastic Predictor-Plastic Corrector Method for Integrating Finite Deformation Plasticity Laws

Abstract

Classical plasticity theories are formulated by means of ordinary differential equations coupled with algebraic equations, so that the whole system of equations governing the material response is highly nonlinear. To integrate these equations, particular algorithms have been developed, the method of elastic predictor and plastic corrector being often used. This method has turned out to be a very efficient tool, when small deformation plasticity is considered. Especially, the usual constraint condition of plastic incompressibility is preserved exactly. However, when nonlinear geometry is involved, there are several possibilities to employ the method of elastic predictor and plastic corrector. Moreover, some effort has to be made, in order to ensure plastic incompressibility. The exponential map approach is one possibility to overcome the difficulties, but this approach is not suitable when deformation induced anisotropy is considered. The present work addresses the numerical integration of finite deformation plasticity models exhibiting both, isotropic and kinematic hardening. The integration of the evolution equations is based on the elastic predictor and plastic corrector procedure, appropriately adjusted to the structure of the adopted constitutive theory. Plastic incompressibility is preserved by introducing a further unknown into the system of equations to be solved numerically.