Comparison of semi and fully-implicit time integration schemes applied to a damage and fatigue phase field model

Free Energy of a Nonuniform System. I. Interfacial Free Energy

John W. Cahn, J. E. Hilliard · The Journal of Chemical Physics · 1958 · 10.3K citations

Natural Sciences, Chemistry, Physics +17

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

Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems

Choice Reviews Online · 2008 · 999 citations

Natural Sciences, Mathematics, Computational Mechanics +16

Phase-field modeling of ductile fracture

Marreddy Ambati, Tymofiy Gerasimov, Laura De Lorenzis · Computational Mechanics · 2015 · 818 citations

Engineering, Materials Engineering, Mechanical Engineering +14