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.

An existence result for a model of complete damage in elastic materials with reversible evolution / Bonetti, Elena; Freddi, Francesco; Segatti, Antonio. - In: CONTINUUM MECHANICS AND THERMODYNAMICS. - ISSN 0935-1175. - 29:1(2017), pp. 31-50. [10.1007/s00161-016-0520-3]

An existence result for a model of complete damage in elastic materials with reversible evolution

FREDDI, Francesco;
2017

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2823615
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