Nine circles of elastic brittle fracture: A series of challenge problems to assess fracture models

Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of fracture in materials subjected to mechanical, thermal, and/or other types of loads. By and large, each new proposal focuses on a particular aspect of the problem, while ignoring others that have been well-established. This approach has resulted in a plethora of models that are, at best, descriptors of fracture only under a restricted set of conditions, while they may predict grossly incorrect and even non-physical behaviors in general. In an attempt to address this predicament, this paper introduces a vetting process in the form of nine challenge problems that any computational model of fracture must convincingly handle if it is to potentially describe fracture nucleation and propagation in general. The focus is on the most basic of settings, that of isotropic elastic brittle materials subjected to quasi-static mechanical loads. The challenge problems have been carefully selected so that: $i$) they can be carried out experimentally with standard testing equipment; $ii$) they can be unambiguously analyzed with a sharp description of fracture; and, most critically, $iii$) in aggregate they span the entire range of well settled experimental knowledge on fracture nucleation and propagation that has been amassed for over a century. For demonstration purposes, after their introduction, each challenge problem is solved with two phase-field models of fracture.