Calculus of Variations and Geometric Measure Theory

H. Hanke - D. Knees

A phase-field damage model based on evolving microstructure

created by knees on 27 May 2016
modified on 19 Dec 2017


Published Paper

Inserted: 27 may 2016
Last Updated: 19 dec 2017

Journal: Asymptotic Analysis
Volume: 101
Number: 3
Pages: 149-180
Year: 2017


In this paper we discuss a damage model that is based on microstructure evolution. In the context of evolutionary Gamma-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. This motivates the derivation of an effective macroscopic evolution model.