Investigation on crack initiation and propagation in hydraulic fracturing of bedded shale by hybrid phase-field modeling

Revisiting brittle fracture as an energy minimization problem

Gilles A. Francfort, Jean‐Jacques Marigo · Journal of the Mechanics and Physics of Solids · 1998 · 3.4K citations

Engineering, Materials Engineering, Materials Science +13

A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

Christian Miehé, Martina Hofacker, Fabian Welschinger · Computer Methods in Applied Mechanics and Engineering · 2010 · 2.9K citations

Engineering, Computational Engineering, Materials Engineering +16

Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations

Christian Miehé, Fabian Welschinger, Martina Hofacker · International Journal for Numerical Methods in Engineering · 2010 · 2.8K citations

Engineering, Materials Engineering, Mechanical Engineering +17

A phase-field description of dynamic brittle fracture

Michael J. Borden, Clemens V. Verhoosel, Michael A. Scott et al. · Computer Methods in Applied Mechanics and Engineering · 2012 · 1.8K citations

Engineering, Materials Engineering, Materials Science +12

The Variational Approach to Fracture

Blaise Bourdin, Gilles A. Francfort, Jean‐Jacques Marigo · Journal of Elasticity · 2008 · 1.8K citations · Full text

Engineering, Computational Engineering, Applied Mechanics +11