Crack nucleation in variational phase-field models of brittle fracture 

Corrado Maurini
d’Alembert Institute
Sorbonne Université
Paris, France


Phase-field approaches model sharp cracks as the localisation of a smooth damage field. Their success is due to their ability to predict the nucleation and propagation of complex crack patterns without ad-hoc hypotheses. My talk will focus on the problem of crack nucleation. First, I will introduce the variational formulation of phase-field models as the quasi-static evolution of softening gradient damage models including an internal length-scale. In this framework, I will show how crack nucleation can be understood as the results of a structural instability and present the methods to study it theoretically and numerically. I will argue that classical phase-field model can correctly predict the material strength and toughness in the case of almost uniaxial loadings. Hence, I will discuss the difficulties in the case of multi-axial loadings, where the strength is a hyper-surface in the stress space.

Speaker Biography

Corrado MauriniDr Corrado Maurini is a Full Professor of Solid Mechanics in the d’Alembert Institute ( at Sorbonne Université in Paris, France. He earned a Ph.D. degree in Mechanics from University of Rome La Sapienza and Paris 6 – Pierre and Marie Curie University in 2005, after Master degrees from La Sapienza and Virgina Tech. His research interests are in theoretical and computational nonlinear solid mechanics and instabilities, and in particular on fracture and damage, phase-field models of fracture, nonlinear elasticity, plates and shells, morphing structures and active materials. His current work on crack nucleation in variational models of fracture is partially founded by the European Commission under the Marie Skłodowska-Curie Action Newfrac, Grant Agreement n° 861061ITN (

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