Abstract
The numerical simulation of elastic-inelastic material behaviour is reviewed and an alternative method, i. e., an augmented Finite Element (FE) formulation is presented. For the augmented FE formulation, the history variables, which provide the information of inelastic deformations from previous time-steps, are represented as FE functions. The discretisation of the augmented system results in additional degrees of freedom (DOF). As a result, generally accepted standard formulations for evaluating inelastic deformations in a numeric sub-step can now be replaced by a fully coupled Newton method. Then, it is not required to solve additional local systems. Both numerical methods are exemplarily applied to a viscoplastic Perzyna-type regularisation of softening material behaviour within a geometrically linear approach in order to simulate the development of shear bands occurring in a tensile bar. Numerical studies prove comparative results, while exhibiting a computational speed-up for the augmented FE formulation.
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Rempler, HU., Wieners, C. & Ehlers, W. Efficiency comparison of an augmented finite element formulation with standard return mapping algorithms for elastic-inelastic materials. Comput Mech 48, 551–562 (2011). https://doi.org/10.1007/s00466-011-0602-9
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DOI: https://doi.org/10.1007/s00466-011-0602-9