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A DAE‐approach applied to elastic‐plastic material behavior using FEM
Author(s) -
Ecker Steffen,
Baaser Herbert,
Gross Dietmar
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310407
Subject(s) - discretization , finite element method , nonlinear system , algebraic equation , state variable , mathematics , plasticity , mathematical analysis , computer science , structural engineering , materials science , engineering , physics , quantum mechanics , composite material , thermodynamics
Simulating elastic‐plastic material behavior with the finite element method (FEM), two different types of equations appear. The spatial discretization of the considered domain leads to a system of nonlinear equations for the unknown displacements, whereas the time‐evolution of the internal variables describing the inelastic state is governed by first order differential equations. Altogether a system of differential‐algebraic equations (DAE) has to be solved. In the following, the DAE‐concept is used to describe rate‐independent, associated plasticity, but it can also be applied to visco‐plastic material behavior. The advantage of using a BDF2‐method for time integration of the internal variables is emphasized and the differences between the classical 'elastic predictor – plastic corrector' approach and our method are pointed out. A comparison between both methods in terms of computational efficiency will also be presented. The numerical implementation is done in DAEdalon [2], a free available FEM‐Package.