Elastic bars with cohesive energy

Del Piero, Gianpietro; Truskinovsky, Lev
July 2009
Continuum Mechanics & Thermodynamics;Jul2009, Vol. 21 Issue 2, p141
Academic Journal
Most quasi-static variational models of fracture are based on the splitting of the energy functional into the sum of two terms: bulk, depending on the displacement gradient, and surface, depending on the displacement discontinuities. In this paper we consider the simplest one-dimensional problem of this type, a bar stretched by a given axial displacement, and systematically compare two alternative interpretations of the surface energy term. In the first interpretation ( elastic model), the surface energy is viewed as a cohesive energy which is stored and can be recovered. In the second ( inelastic model), it is irreversibly lost. We show that by assuming an evolution scheme based on local minimization and by varying the convexity-concavity properties of the surface energy the elastic model can reproduce a broad class of macroscopic material responses which have been traditionally treated as unrelated. These responses are associated with monotone loading and range from brittle fracture to rate independent plasticity. However, a realistic description for both loading and unloading is achieved only within the inelastic model.


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