Linear continued fracture mechanics

Linear elastic fracture mechanics is no longer valid for dynamic fracture mechaiusms since continuous crack propagation addresses time dependent boundary conditions. The energy balance for the dynamic conditions can be written as... 

The application of fracture mechanics to concretes, which was proposed in the early 1960s, was an important attempt to avoid the contradictions of homogeneity and continuity of cement-based composites, by Kaplan (1961, 1968). At the beginning, only linear elastic fracture mechanics (LEFM) was considered. The principal relations and formulae were taken from papers and studies concerning metals, and their application to concrete-like composites was attempted. It appeared obvious that the most direct and natural representation for the behaviour of brittle matrix composites should be based on the examination of the crack opening and propagation processes. 

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