Repository: Freie Universit├Ąt Berlin, Math Department

Discrete approximation of dynamic phase-field fracture in visco-elastic materials

Thomas, Marita and Tornquist, Sven (2021) Discrete approximation of dynamic phase-field fracture in visco-elastic materials. Discrete Contin. Dyn. Syst. Ser. S, 14 . pp. 3865-3924.

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Official URL: http://www.DOI.10.3934/dcdss.2021067 .

Abstract

Abstract: This contribution deals with the analysis of models for phase-field fracture in visco-elastic materials with dynamic effects. The evolution of damage is handled in two different ways: As a viscous evolution with a quadratic dissipation potential and as a rate-independent law with a positively 1-homogeneous dissipation potential. Both evolution laws encode a non-smooth constraint that ensures the unidirectionality of damage, so that the material cannot heal. Suitable notions of solutions are introduced in both settings. Existence of solutions is obtained using a discrete approximation scheme both in space and time. Based on the convexity properties of the energy functional and on the regularity of the displacements thanks to their viscous evolution, also improved regularity results with respect to time are obtained for the internal variable: It is shown that the damage variable is continuous in time with values in the state space that guarantees finite values of the energy functional.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2610
Deposited By: Monika Drueck
Deposited On:23 Sep 2021 13:31
Last Modified:23 Sep 2021 13:31

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