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 / E. Bonetti, F. Freddi, A. Segatti. - In: CONTINUUM MECHANICS AND THERMODYNAMICS. - ISSN 0935-1175. - 29(2017 Jan), pp. 31-50. [10.1007/s00161-016-0520-3]

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

E. Bonetti;
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.
complete damage; existence result for weak solutions; non-smooth PDE system; phase transition
Settore MAT/05 - Analisi Matematica
gen-2017
13-lug-2016
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/424500
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