A second order scheme for the time discretization of the elasto-plastic or elasto-viscoplastic behavior is proposed, based on a velocity approach. The complete set of equations is given for the evolution problem in the case of small rotations approximation. The method is quite general and may be applied to a large class of constitutive equations. The finite element discretization is briefly outlined and it is shown that the procedure is quite similar to that of previous displacement formulations. A numerical example concerning the sheet metal forming process, with an elasto-viscoplastic behavior and a membrane approximation, is presented. The numerical tests show a considerable improvement in accuracy for a given increment of time.
A Velocity Approach to Elasto-Plastic and Elasto-Viscoplastic Calculation by the Finite Element Method
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Chenot, J. L., and Bellet, M. (May 1, 1990). "A Velocity Approach to Elasto-Plastic and Elasto-Viscoplastic Calculation by the Finite Element Method." ASME. J. Eng. Ind. May 1990; 112(2): 150–154. https://doi.org/10.1115/1.2899558
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