We discuss a recent approximation result for Barenblatt's cohesive fracture energies in the case of antiplane shear. The regularized functionals are damage energies of Ambrosio-Tortorelli type and the approximation is obtained in the sense of Gamma-convergence. The extension to the general case of linearized elasticity in dimension n is still an open problem. To prepare for this extension we study the structure of a subclass of functions of bounded deformation.
Some recent results on the convergence of damage to fracture
Iurlano F
2016-01-01
Abstract
We discuss a recent approximation result for Barenblatt's cohesive fracture energies in the case of antiplane shear. The regularized functionals are damage energies of Ambrosio-Tortorelli type and the approximation is obtained in the sense of Gamma-convergence. The extension to the general case of linearized elasticity in dimension n is still an open problem. To prepare for this extension we study the structure of a subclass of functions of bounded deformation.
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