Computation in finite-strain viscoelasticity: finite elements based on the interpretation as differential–algebraic equations

✍ Scribed by Stefan Hartmann

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 435 KB
• Volume: 191
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00332-2

✦ Synopsis

In this article the interpretation of current non-linear ®nite element calculations applied to constitutive equations of evolutionary type as a system of dierential±algebraic equations is continued [P. Ellsiepen, S. Hartmann, Int. J. Numer. Methods Engrg. 51 (2001) 679]. This procedure is applied to a model of ®nite-strain viscoelasticity which incorporates a particular model of non-linear rate dependence. Three speci®c topics are studied: ®rstly, we investigate a possible treatment of the interpretation in view of mixed ®nite elements. Secondly, the application of stiy 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 eect with respect to expense and achievable accuracy of a time-adaptive procedure is focused, which is necessary in the case of dierent time scales such as relaxation or creep dominated processes.