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SUMMARYIn 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 J 2 ow. 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 return.

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A new integration algorithm is described for large strain plastic deformations. The algorithm degenerates to the Euler forward elastoplastic-plastic model for small strain increments and to the rigid-plastic model for large strain increments. The model benefits from the advantages of both models: accuracy and fast convergence over a large range of strain increments.