Understanding how things break and slide is of paramount importance to describe the dynamics of a broad range of physical systems. This includes day-to-day problems such as the breaking of a glass of wine or the sliding of skis on snow, but also engineering systems with, for example, the braking of a car or the failure of a structural component, up to geophysics and earthquake science. These two topics, fracture, and friction, seem unrelated at first but share similar physical characteristics: they are mediated by the propagation of rupture fronts. In both cases, a ruptured state (a crack, or a slipping patch) invades an intact state (the unbroken material, or a sticking interface). While the questions related to fracture and friction are ubiquitous, our physical understanding of these phenomena is far from complete. The Linear Elastic Fracture Mechanics framework describes accurately the stability of defects in materials and their slow growth but fails at describing the unstable three-dimensional dynamics at play in rapid fracture. Concepts from fracture mechanics have been successfully applied to describe the propagation of frictional rupture fronts, but fundamental differences remain due to the complex behavior of the friction coefficient itself, being dependent on the slipping rate and the state of the microcontacts at the interface between two solids. Hence, dynamic rupture exhibits a richness of behaviors. Amongst other things, the interaction between a front and material heterogeneities, boundary conditions, and finite geometry can significantly alter the dynamics of a rupture.

The objective of this work is to explore this richness in dynamic rupture, taking advantage of efficient computational methods that solve the elastodynamic equations. The use of modern computing methods allows modeling ruptures down to the small dissipation length scale near the tip of a rupture, the process zone size. The two software used in this work are open-source codes that were developed in the Computational Solid Mechanics Laboratory at EPFL.

The first part of this work reveals the interactions occurring at the scale of the process zone between a tensile crack and a heterogeneous material in the context of front deformations, which inform on the effective properties of a microstructure. Then, the physical origin of the analogy between frictional rupture and fracture is investigated, demonstrating that the stress drop emerges from the interaction between interfacial and bulk properties. This work also explores the influence of the boundary conditions on the frictional rupture mode, revealing the emergence of a train of self-healing slip pulses under velocity-driven conditions. The study of frictional interfaces is then upscaled by taking a statistical perspective on slip events, demonstrating the emergence of statistical complexity in finite systems even in the absence of material heterogeneities. The last contribution of this thesis is numerical, with a coupling scheme between the two methods used in this work, aiming at providing a better tool for the simulation of complex dynamic rupture problems.

While being rather fundamental, this Ph.D. work offers novel insights into the dynamics of rupture fronts and has direct implications for various domains, ranging from the design of micro-structured materials and interfaces, to the dynamics of earthquakes.