2011•Mathematics and Mechanics of SolidsRequires access

A Priori Inequalities between Energy Release Rate and Energy Concentration for 3D Quasistatic Brittle Fracture Propagation

Marius Buliga

Abstract

We study the properties of absolute minimal and equilibrium states of generalized Mumford—Shah functionals, with applications to models of quasistatic brittle fracture propagation. The main results, theorems 7.3, 8.4 and 9.1, concern a priori inequalities between energy release rate and energy concentration for 3D cracks with complex shapes, seen as outer measures living on the crack edge.

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Key concepts: Quasistatic process, Brittleness, Quasistatic loading, Strain energy release rate, A priori and a posteriori, Fracture mechanics, Quasistatic approximation, Brittle fracture