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Error estimation and adaptivity in elastoplasticity

Abstract : In this paper, a method is developed to control the parameters of a finite element computation for time-dependent material models. This method allows the user to obtain a prescribed accuracy with a computational cost as low as possible. To evaluate discretization errors, we use a global error measure in constitutive relation based on Drucker's inequality. This error includes, over the studied time interval, the error of the finite element model and the error of the algorithm being used. In order to master the size of the elements of the mesh and the length of the time increments, an error estimator, which permits estimating the errors due to the time discretization, is proposed. These tools are used to elaborate two procedures of adaptivity. Various examples for monotonous or non-monotonous loadings, for 2-D or axisymmetric problems, show the reliability of these procedures.
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L. Gallimard, P. Ladevèze, J. Pelle. Error estimation and adaptivity in elastoplasticity. International Journal for Numerical Methods in Engineering, Wiley, 1996, 39 (2), pp.189-217. ⟨10.1002/(SICI)1097-0207(19960130)39:2<189::AID-NME849>3.0.CO;2-7⟩. ⟨hal-01689591⟩

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