Calculus of Variations and Geometric Measure Theory

R. Ballarini - G. Royer Carfagni

Closed-Path J -Integral Analysis of Bridged and Phase-Field Cracks

created by royercarfagni on 25 Apr 2016


Published Paper

Inserted: 25 apr 2016

Journal: Journal of Applied Mechanics
Volume: 83
Pages: 06-1008-1/13
Year: 2016
Doi: 10.1115/1.4032986


We extend the classical J-integral approach to calculate the energy release rate of cracks by prolonging the contour path of integration across a traction-transmitting interphase that accounts for various phenomena occurring within the gap region defined by the nominal crack surfaces. Illustrative examples show how the closed contours, together with a proper definition of the energy momentum tensor, account for the energy dissipation associated with material separation. For cracks surfaces subjected to cohesive forces, the procedure directly establishes an energetic balance a la Griffith. For cracks modeled as phase-fields, for which no neat material separation occurs, integration of a generalized energy momentum (GEM) tensor along the closed contour path that traverses the damaged material permits the calculation of the energy release rate and the residual elasticity of the completely damaged material.

Keywords: phase field model, fracture, cohesive fracture, J-integral, Eshelby tensor, energy release rate, small scale brdiging limit