Two stress update algorithms for large strains: accuracy analysis and numerical implementation
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 n...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1997 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/8448 |
| Acceso en línea: | https://hdl.handle.net/2117/8448 https://dx.doi.org/10.1002/(SICI)1097-0207(19971215)40:23<4363::AID-NME263>3.0.CO;2-Z |
| Access Level: | acceso abierto |
| Palabra clave: | Solids--Mechanical properties Numerical analysis Large strains Stress update Error analysis Convected frames Nonlinear computational mechanics Finite element method Mecànica dels sòlids -- Mètodes numèrics Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Àrees temàtiques de la UPC::Física::Física de l'estat sòlid |
| Sumario: | 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 unified derivation of both algorithms in spite of their inherent differences. Then the two algorithms are adapted from convected frames to a fixed Cartesian frame and implemented in a small-strain finite 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. |
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