Adaptive solution of problems modeled by unified state variable constitutive equations
Abstract
The objective of the work was an efficient, numerical implementation of one of the unified, internalstate-variable constitutive models. Such models are general and convenient in numerical applications since they describe elastic, plastic, viscous, damage phenomena and they do not require neither yielding condition nor loading/ unloading criterion. However, they result in so called stiff initial-boundary value problems. Therefore, an efficient numerical implementation demand adaptive techniques, both in space and in time. The paper presents application of such an adaptation approach. It uses an improved version of the semi-implicit Euler method with automatic time step control and the h refinement of the FEM meshes based on the interpolation error estimate and on the reliable, selfequilibrated, implicit, a posteriori estimate. Selected problems were solved and both the efficiency and reliability of the unified model were confirmed.
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References
[1] M. Ainsworth, T.J. Oden. A unified approach to a posteriori error estimation using element residual methods. Numer. Math., 65: 23-50, 1993.[2] I. Babuska, T. Strouboulis, C.S. Upadhyay. A model study of the quality of a posteriori error estimators for linear elliptic problems. Comp. Meth. Appl. Mech. Engng., 114: 307-378, 1994.
[3] J.M. Bass, J.T. Oden. Adaptive finite element methods for a class of evolution problems in viscoplasticity. Int. J. Engng. Sci., 25: 623-653, 1987.
[4] M.A. Biot. Theory of stress-strain relations in anisotropiic viscoelasticity and relaxation phenomenon. J. Appl. Phys., 25: 1385-1391, 1954.
[5] S.R. Bodner. Review of a unified elasto-viscoplastic theory. In: A.K. Mille, ed., Unified Constitutive Equations for Plastic Deformation and Creep of Engineering Alloys. Elsevier and Applied Science, London, 1985.
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