Fracture Mechanics of Heterogeneous Materials: A Statistical Approach

This book introduces novel concepts going beyond classical borders in mechanics and physics, bridging material properties at the nano/microscale with mechanical properties at large scales, while addressing cases that go beyond material failure. To begin with, the authors explain how to define the fracture threshold of a material and link it to its microscopic properties, describing the two main families of mechanisms: brittle and ductile. They then go on to show how understanding how materials break extends beyond the prediction of these fracture thresholds, outlining an equation for predicting the path of a fault and the speed at which it spreads. They also discuss the specific geometric properties of networks of cracks, which result from their interaction. Regarding the dynamics of cracks, the book focuses on extreme behaviors: very low and very high speeds. Finally, the authors show that an essential ingredient is lacking in the description of the fracture of materials as it was proposed in the last century: heterogeneities of solids. Readers will learn that the effect of heterogeneities is felt far beyond the fluctuations of speed and trajectory, with recent advances restoring the central role played by the microstructure of materials, and, in so doing, also opening up many perspectives for applications, especially for the design of more efficient heterogeneous materials.