Nucleation and propagation of brittle fracture as a constrained energy minimization problem

Abstract

This paper presents a macroscopic, or continuum, theory aimed at describing when, where, and why cracks nucleate and propagate in nominally elastic brittle materials under monotonic, quasi-static, but otherwise arbitrary mechanical loads. Motivated by recent insights, the proposed sharp theory posits that: \emph{cracks nucleate and propagate exclusively in regions where the strength surface of the material is exceeded, with their evolution dictated by the minimization of the sum of the potential --- the elastic energy minus the work done by the externally applied forces --- and surface energies.} While the theory applies to materials with any elasticity (linear or nonlinear) and any material symmetry (isotropic or anisotropic), attention is restricted here to the most basic case of isotropic elastic brittle materials. For demonstration purposes, the theory is confronted with a set of nine tests that span the entire range of well-settled experimental knowledge on fracture nucleation and propagation --- the so-called ``Nine Circles of Elastic Brittle Fracture''--- on both a hard material (a silicate glass) and a soft material (a synthetic rubber).