Topology optimization for maximizing the fracture resistance of quasi-brittle composites

Generating optimal topologies in structural design using a homogenization method

Martin P. Bendsøe, Noboru Kikuchi · Computer Methods in Applied Mechanics and Engineering · 1988 · 7.3K citations · Full text

Engineering, Design, Design Optimization +10

Optimal approximations by piecewise smooth functions and associated variational problems

David Mumford, Jayant Shah · Communications on Pure and Applied Mathematics · 1989 · 5.2K citations · Full text

Natural Sciences, Computational Engineering, Computational Mechanics +13

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