The Variational Approach to Fracture

2008/03/14 by Blaise Bourdin, Gilles A. Francfort, Jean-Jacques Marigo +1 · 14 citations
Engineering · #Numerical methods in engineering #Fatigue and fracture mechanics #Rock Mechanics and Modeling

paper · doi:10.1007/s10659-007-9107-3

Citations

• Optimal approximations by piecewise smooth functions and associated variational problems
• Approximation of functional depending on jumps by elliptic functional via t‐convergence

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• Gamma convergence for a phase-field cohesive energy
• Curvature penalization of strongly anisotropic interfaces models and their phase-field approximation
• Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane
• Phase-field and lip-field approaches for fracture with extreme mesh deformation (X-Mesh): a one-dimensional study
• A unified phase-field model of fracture in viscoelastic materials
• Homogenisation of phase-field functionals with linear growth
• Effective toughness estimation by FFT based phase field fracture: application to composites and polycrystals
• A GPU-Accelerated Three-Dimensional Crack Element Method for Transient Dynamic Fracture Simulation
• Fracture propagation by using shape optimization techniques based on outer Riemannian metrics