• Lebihain, Mathias

Abstract

Being able to predict the macroscopic response of a material from the knowledge of its constituent at a microscopic or mesoscopic scale has always been the Holy Grail pursued by material science, for it provides building bricks for the understanding of complex structures as well as for the development of tailor-made optimized materials. The homogenization theory constitutes nowadays a well-established theoretical framework to estimate the overall response of composite materials for a broad range of mechanical behaviors. Such a framework is still lacking for brittle fracture, which is a dissipative evolution problem that (ii) localizes at the crack tip and (iii) is related to a structural one. In this work, we propose a theoretical framework based on a perturbative approach of Linear Elastic Fracture Mechanics to model (i) crack propagation in large-scale disordered materials as well (ii) the dissipative processes involved at the crack tip during the interaction of a crack with material heterogeneities. Their ultimate contribution to the macroscopic toughness of the composite is (iii) estimated from the resolution of the structural problem using an approach inspired by statistical physics. The theoretical and numerical inputs presented in the thesis are finally compared to experimental measurements of crack propagation in 3D-printed heterogeneous polymers obtained through digital image correlation.

Topics

• impedance spectroscopy
• polymer
• theory
• crack
• composite
• homogenization