Relaxation of an optimal design problem in fracture mechanic: the anti-plane case
Arnaud Münch, Pablo Pedregal (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In the framework of the linear fracture theory, a commonly-used tool to describe the smooth evolution of a crack embedded in a bounded domain Ω is the so-called energy release rate defined as the variation of the mechanical energy with respect to the crack dimension. Precisely, the well-known Griffith's criterion postulates the evolution of the crack if this rate reaches a critical value. In this work, in the anti-plane scalar case, we consider the shape design problem which consists...