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A Time Adaptiv Finite‐Element Procedure Applied to Creep and Relaxation Processes
Author(s) -
Hartmann S.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200008014128
Subject(s) - relaxation (psychology) , finite element method , creep , euler method , diagonal , operator (biology) , algebraic equation , mathematics , tangent , block (permutation group theory) , interpretation (philosophy) , algebraic number , euler's formula , mathematical analysis , computer science , geometry , structural engineering , physics , engineering , repressor , chemistry , psychology , social psychology , biochemistry , quantum mechanics , transcription factor , programming language , nonlinear system , gene , thermodynamics
In this paper we interpret the finite‐element method applied to constitutive models with internal variables as the solution of differential algebraic equations (DAE). With this interpretation we can utilize Diagonal Implicit Runge‐Kutta methods (DIRK) as well as a corresponding step‐size control and a special solution technique for block‐structured systems of equations. This proceeding doesn't affect already developed FE‐implementations which are based on the Backward Euler method. Furthermore, the meaning of the consistent tangent operator becomes more obvious. The paper ends with some examples in creep and relaxation tests, where step size control should always be used conditioned by the different time scales.