Adaptive return mapping algorithms for J2 elasto-viscoplastic flow

In this paper a new class of integration algorithms for elasto-viscoplastic constitutive equations is proposed. It is based on the generalized trapezoidal rule, which is a weighted combination of the start and end of the increment. But instead of taking constant weights, the weights are a function of the plastic multiplier. In this way the magnitude of the plastic-strain increment determines the way the integration is performed. The stress update and consistent tangent are derived for the case of J2 flow. Several candidates within the class of adaptive return mapping algorithms are investigated. It is shown numerically that some of the proposed algorithms are more accurate than commonly used algorithms such as mean normal and radial retur