Energy release rate for non-smooth cracks in planar elasticity
Copyright policy )Energy release rate for non-smooth cracks in planar elasticity
This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with (length) density 1 / 2 at the tip, without further regularity assumptions. First, the blow-up limit of the displacement is analyzed, and the convergence to a (known) positively 1 / 2 -homogenous function in the cracked plane is established. Then, the energy release rate, which is the derivative of the elastic energy with respect to an infinitesimal additional crack increment, is obtained as the solution of a variational problem.
Variational methods for second-order elliptic equations, Methods involving semicontinuity and convergence; relaxation, blow-up limit, singular set, Variational methods for elliptic systems, elliptic problem, 510, 620, Blow-up in context of PDEs, brittle fracture, Mathematics - Analysis of PDEs, Brittle fracture, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], nonsmooth domain, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], PDEs in connection with mechanics of deformable solids, Analysis of PDEs (math.AP)
Variational methods for second-order elliptic equations, Methods involving semicontinuity and convergence; relaxation, blow-up limit, singular set, Variational methods for elliptic systems, elliptic problem, 510, 620, Blow-up in context of PDEs, brittle fracture, Mathematics - Analysis of PDEs, Brittle fracture, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], nonsmooth domain, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], PDEs in connection with mechanics of deformable solids, Analysis of PDEs (math.AP)
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