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Phase field modelling of crack propagation

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The phase field method for fracture has emerged as a promising numerical framework to model crack nucleation and growth. Among other possibilities, the method has proven to be capable of capturing complex crack propagation paths, crack branching, crack nucleation from arbitrary locations, and merging of two or more cracks. All of these features can be modelled within the original finite element mesh and in complex 3D topologies, overcoming some of the limitations intrinsic to discrete computational fracture methods. Not surprisingly, the phase field fracture method has gained immediate traction in the computational mechanics community and it has been applied to model numerous brittle and ductile damage phenomena, including hydraulic fracturing, fibre cracking, composites delamination and stress corrosion cracking, to name a few.

In the talk, I will: (i) introduce the basic theoretical foundations of the method and its connections to Griffith’s fracture framework, (ii) outline the implementation in a finite element context, and (iii) showcase its potential by addressing several engineering applications. Specifically, I will show how we have extended the method to capture brittle fracture in functionally graded composites [1], and present a novel multiphysics framework to predict hydrogen assisted cracking in a coupled deformation-diffusion-phase field fracture fashion [2]. The finite element codes developed are available for download in


[1] Hirshikesh, S. Natarajan, R.K. Annabattula, E. Martínez-Pañeda. Phase field modelling of crack propagation in functionally graded materials (in review)

[2] E. Martínez-Pañeda, A. Golahmar, C. F. Niordson. A phase field formulation for hydrogen assisted cracking. Computer Methods in Applied Mechanics and Engineering 342, 742-761 (2018)

About the speaker:

Emilio Martínez Pañeda is an 1851 Research Fellow at the University of Cambridge and a Junior Research Fellow at Wolfson College. His current research interests lie in the field of applied mechanics; more specifically in plasticity, fracture mechanics, coupled diffusion-deformation theories, and mechanism-based models for damage. His work on the mechanics of solids has been disseminated in numerous journal publications and has been recognized through several awards, including the Acta Student Award, the Springer PhD Thesis Prize and the Extraordinary Doctoral Prize for the Best PhD Thesis in Engineering. More info:

This talk is part of the Engineering - Mechanics and Materials Seminar Series series.

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