An existence result for a model of complete damage in elastic materials with reversible evolution
In this paper, we consider a model describing evolution of damage in elastic materials, in which stiffness completely degenerates once the material is fully damaged. The model is written by using a phase transition approach, with respect to the damage parameter. In particular, a source of damage is represented by a quadratic form involving deformations, which vanishes in the case of complete damage. Hence, an internal constraint is ensured by a maximal monotone operator. The evolution of damage is considered “reversible”, in the sense that the material may repair itself. We can prove an existence result for a suitable weak formulation of the problem, rewritten in terms of a new variable (an internal stress). Some numerical simulations are presented in agreement with the mathematical analysis of the system.
KeywordsComplete damage Phase transition Non-smooth PDE system Existence result for weak solutions
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- 1.Bangerth, W., Heister, T., Heltai, L., Kanschat, G., Kronbichler, M., Maier, M., Turcksin, B., Young, T.D.: The deal.II library, version 8.2. Arch. Numer. Softw. 3, 1–8 (2015)Google Scholar
- 10.Evans, L.C.: Partial Differential Equations. American Mathematical Society, Providence (1997)Google Scholar