Topological Sensitivity Analysis Applied to the Francfort-Marigo Damage Model

Topological Sensitivity Analysis Applied to the Francfort-Marigo Damage Model

Fancello, Eduardo Alberto; Novotny, Antonio André; Farias, Jan-Michel

Abstract:

The topological sensitivity analysis was formally introduced in 1999, and since then became a rapidly expanding research field. This analysis provides the variation of a given functional when the domain is topologically modified by an infinitesimal perturbation, for example by introducing a hole. The main result of this procedure is a scalar field named Topological Derivative that can be seen as a first order approximation of the value of the functional associated to the perturbed domain. In this paper the topological sensitivity analysis is applied to the Francfort-Marigo damage model, which is used to model brittle materials in quasi-static problems. The expressions for the Topological Derivative are developed and an algorithm is proposed to use this information on the study of damage propagation. Some numerical test cases are evaluated to verify the algorithm''s performance.

The topological sensitivity analysis was formally introduced in 1999, and since then became a rapidly expanding research field. This analysis provides the variation of a given functional when the domain is topologically modified by an infinitesimal perturbation, for example by introducing a hole. The main result of this procedure is a scalar field named Topological Derivative that can be seen as a first order approximation of the value of the functional associated to the perturbed domain. In this paper the topological sensitivity analysis is applied to the Francfort-Marigo damage model, which is used to model brittle materials in quasi-static problems. The expressions for the Topological Derivative are developed and an algorithm is proposed to use this information on the study of damage propagation. Some numerical test cases are evaluated to verify the algorithm''s performance.

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Como citar:

Fancello, Eduardo Alberto; Novotny, Antonio André; Farias, Jan-Michel; "Topological Sensitivity Analysis Applied to the Francfort-Marigo Damage Model", p-35-35. In: Proceedings of the 13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials [=Blucher Material Science Proceedings, v.1, n.1]. São Paulo: Blucher, 2014.
ISSN 23589337, DOI