Journal article
Computation in finite strain viscoelasticity: finite elements based on the interpretation as differential-algebraic equations
Publication Details
Authors: | Hartmann, S. |
Publication year: | 2002 |
Journal: | Computer Methods in Applied Mechanics and Engineering |
Pages range : | 1429-1470 |
Volume number: | 191 |
ISSN: | 0045-7825 |
Abstract
In this article the interpretation of current non-linear finite element calculations applied to constitutive equations of evolutionary type as a system of differential-algebraic equations is continued [P. Ellsiepen, S. Hartmann, Int. J. Numer. Methods Engrg. 51 (2001) 679]. This procedure is applied to a model of finite-strain viscoelasticity which incorporates a particular model of non-linear rate dependence. Three specific topics are studied: firstly, we investigate a possible treatment of the interpretation in view of mixed finite elements. Secondly, the application of stiffly accurate diagonally implicit Runge-Kutta methods, which yield on element level the same Structure as a Backward-Euler-based integration step, is analysed. It is shown that the resulting stress algorithm is reducible to the solution of only three non-linear equations at each Gauss point (one Maxwell element). Lastly, the effect with respect to expense and achievable accuracy of a time-adaptive procedure is focused, which is necessary in the case of different time scales such as relaxation or creep dominated processes. (C) 2002 Elsevier Science B.V. All rights reserved.
In this article the interpretation of current non-linear finite element calculations applied to constitutive equations of evolutionary type as a system of differential-algebraic equations is continued [P. Ellsiepen, S. Hartmann, Int. J. Numer. Methods Engrg. 51 (2001) 679]. This procedure is applied to a model of finite-strain viscoelasticity which incorporates a particular model of non-linear rate dependence. Three specific topics are studied: firstly, we investigate a possible treatment of the interpretation in view of mixed finite elements. Secondly, the application of stiffly accurate diagonally implicit Runge-Kutta methods, which yield on element level the same Structure as a Backward-Euler-based integration step, is analysed. It is shown that the resulting stress algorithm is reducible to the solution of only three non-linear equations at each Gauss point (one Maxwell element). Lastly, the effect with respect to expense and achievable accuracy of a time-adaptive procedure is focused, which is necessary in the case of different time scales such as relaxation or creep dominated processes. (C) 2002 Elsevier Science B.V. All rights reserved.
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