Two stress update algorithms for large strains: accuracy analysis and numerical implementation
✍ Scribed by Antonio Rodríguez-Ferran; Pierre Pegon; Antonio Huerta
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 415 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0029-5981
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✦ Synopsis
Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a uniÿed derivation of both algorithms in spite of their inherent di erences. Then the two algorithms are adapted from convected frames to a ÿxed Cartesian frame and implemented in a small-strain ÿnite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis.