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The variational approach to fracture. (English) Zbl 1176.74018
The paper summarizes the work of the authors and related groups of the last decade and reports new results on “a very classical introduction to brittle fracture within a rational mechanical framework”. The paper is based on Griffith’s hypothesis that “crack propagation results from the competition between bulk energy away from the crack and surface energy on the crack”. The so-called Griffith’s surface energy is generalized to a “Griffith-like” surface energy, and the problem is reformulated in a variational light. The paper is a “must” for every scientist which is interested to apply engineering concepts on the basis of rigorous mathematical formulations. The potential readers, however, should be familiar with the basics of continuum mechanics in the sense of Truesdell and should be equipped with a thorough education in calculus. Some of the necessary mathematical prerequisites are provided by the authors in an appendix.

MSC:
74A45 Theories of fracture and damage
74R10 Brittle fracture
74G65 Energy minimization in equilibrium problems in solid mechanics
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