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| Content Provider | Springer Nature Link |
|---|---|
| Author | Roubíček, Tomáš Mielke, Alexander Bouchitté, Guy |
| Copyright Year | 2007 |
| Abstract | Damage of a linearly-responding material that can completely disintegrate is addressed at small strains. Using time-varying Dirichlet boundary conditions we set up a rateindependent evolution problem in multidimensional situations. The stored energy involves the gradient of the damage variable. This variable as well as the stress and energies are shown to be well defined even under complete damage, in contrast to displacement and strain. Existence of an energetic solution is proved, in particular, by detailed investigating the Γ-limit of the stored energy and its dependence on boundary conditions. Eventually, the theory is illustrated on a one-dimensional example. |
| Ending Page | 236 |
| Page Count | 32 |
| Starting Page | 205 |
| File Format | |
| ISSN | 00442275 |
| e-ISSN | 14209039 |
| Journal | Zeitschrift für angewandte Mathematik und Physik |
| Issue Number | 2 |
| Volume Number | 60 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2007-11-24 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Mathematical Methods in Physics small strain Degenerate parabolic equations Inelastic damage energetic formulation variational inequality Brittle damage Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials) Linear parabolic unilateral problems and linear parabolic variational inequalities Theoretical and Applied Mechanics Variational principles of physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Physics and Astronomy |
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