Efficient time integration in multiplicative inelasticity |
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| Authors: | Ralf Landgraf Alexey V Shutov Jörn Ihlemann |
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| Institution: | 1. Professorship of Solid Mechanics, Faculty of Mechanical Engineering, Technische Universität Chemnitz, Reichenhainer Straße 70, 09126 Chemnitz, Germany;2. Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia |
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| Abstract: | In Shutov et al. (Comput Methods Appl Mech Eng 265:213–225, 2013), the numerical time integration of a famous large strain model of Maxwell fluid type has been considered. The underlying model is based on the multiplicative decomposition of the deformation gradient and includes a Neo-Hookean hyperelasticity relation as well as an incompressible viscous flow rule. Shutov et al. presented a time stepping algorithm for implicit time integration of the inelastic flow rule, which is based on Euler backward time discretisation, prevents error accumulation and is iteration free. In this contribution, the basic idea of the this approach is applied to more general models of multiplicative viscoelasticity. Here, extended hyperelastic relations including general functions of the first principal invariant of deformation tensors are regarded. An efficient time stepping algorithm is derived, where only one scalar equation for one scalar unknown has to be solved within every time step. The approach is applied to a specific viscoelastic model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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