A phase-field damage model based on evolving microstructure

Article type: Research Article

Authors: Hanke, Hauke | Knees, Dorothee^{; *}

Affiliations: University of Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany

Correspondence: [*] Corresponding author. E-mail: dknees@mathematik.uni-kassel.de.

Abstract: In this paper we discuss a damage model that is based on microstructure evolution. In the context of evolutionary Γ-convergence we derive a corresponding effective macroscopic model. In this model, the damage state of a given material point is related to a unit cell problem incorporating a specific microscopic defect. The size and shape of this underlying microscopic defect is determined by the evolution. According to the small intrinsic length scale inherent to the original models a numerical simulation of damage progression in a device of realistic size is hopeless. Due to the scale separation in the effective model, its numerical treatment seems promising.

Keywords: Two-scale convergence, folding and unfolding operator, Γ-convergence, discrete gradient, state dependent coefficient, damage model

DOI: 10.3233/ASY-161396

Journal: Asymptotic Analysis, vol. 101, no. 3, pp. 149-180, 2017