A discontinuous Galerkin formulation for a strain gradient-dependent damage model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2003
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| _version_ | 1866908600087085056 |
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| author | Wells, G. N. Garikipati, K. Molari, L. |
| author_facet | Wells, G. N. Garikipati, K. Molari, L. |
| contents | The numerical solution of strain gradient-dependent continuum problems has been dogged by continuity demands on the basis functions. For most commonly accepted models, solutions using the finite element method demand $C^{1}$ continuity of the shape functions. Here, recent development in discontinuous Galerkin methods are explored and exploited for the solution of a prototype nonlinear strain gradient dependent continuum model. A formulation is developed that allows the rigorous solution of a strain gradient damage model using standard $C^{0}$ shape functions. The formulation is tested in one-dimension for the simplest possible finite element formulation: piecewise linear displacement and constant (on elements) internal variable. Numerical results are shown to compare excellently with a benchmark solution. The results are remarkable given the simplicity of the proposed formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0312002 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | A discontinuous Galerkin formulation for a strain gradient-dependent damage model Wells, G. N. Garikipati, K. Molari, L. Numerical Analysis 65L60, 65M60 The numerical solution of strain gradient-dependent continuum problems has been dogged by continuity demands on the basis functions. For most commonly accepted models, solutions using the finite element method demand $C^{1}$ continuity of the shape functions. Here, recent development in discontinuous Galerkin methods are explored and exploited for the solution of a prototype nonlinear strain gradient dependent continuum model. A formulation is developed that allows the rigorous solution of a strain gradient damage model using standard $C^{0}$ shape functions. The formulation is tested in one-dimension for the simplest possible finite element formulation: piecewise linear displacement and constant (on elements) internal variable. Numerical results are shown to compare excellently with a benchmark solution. The results are remarkable given the simplicity of the proposed formulation. |
| title | A discontinuous Galerkin formulation for a strain gradient-dependent damage model |
| topic | Numerical Analysis 65L60, 65M60 |
| url | https://arxiv.org/abs/math/0312002 |