Asymptotic homogenization analysis for damage amplification due to singular interaction of micro-cracks

• Published in: Journal of the mechanics and physics of solids Vol. 60; no. 8; pp. 1478 - 1485
• Main Authors: Markenscoff, Xanthippi, Dascalu, Cristian
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-08-2012; Elsevier
• Subjects: Amplification; Asymptotic properties; Coalescence; Damage; Damage amplification; Effective coefficients; Engineering Sciences; Homogenization; Homogenizing; Ligaments; Mathematical models; Mechanics; Micro-crack interaction; Microcracks; Microstructure; Micro-crack interaction; Homogenization; Effective coefficients; Coalescence; Damage amplification
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2012.04.004

The paper investigates the overall damage amplification effect due to micro-crack interaction in a framework of two-scale modeling. A homogenization method based on asymptotic expansions is employed to deduce the macroscopic damage equations. The damage model completely results from energy-based micro-crack propagation laws. We consider a locally periodic microstructure with periods containing pairs of micro-cracks separated by small ligaments. The asymptotic solution in the ligament region allows the study of the effect of micro-crack interaction on the effective coefficients. The local macroscopic response expresses the collective coalescence of a periodic microstructure with interacting micro-cracks. We show that the slope of the homogenized coefficients is inversely proportional to the square root of the distance between the tips of the interacting micro-cracks, accounting for the singularity in the stress fields as the micro-cracks approach each other. This leads to damage amplification as the result of the interaction of micro-cracks.