Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models

Tianyi Li 1 Jean-Jacques Marigo 2 Daniel Guilbaud 3, 1 Serguei Potapov 4, 1
1 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
2 LMS - Laboratoire de mécanique des solides
3 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
4 EDF R&D MMC - Matériaux et Mécanique des Composants
Abstract : In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results.
Keywords : Finite element implementation Dynamic fracture Variational principles Gradient damage models
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Tianyi Li, Jean-Jacques Marigo, Daniel Guilbaud, Serguei Potapov. Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models. Applied Mechanics and Materials, Trans Tech Publications, 2015, Damage Mechanics: Theory, Computation and Practice, 784, pp. 334-341. ⟨10.4028/www.scientific.net/AMM.784.334 ⟩. ⟨hal-01225237v2⟩

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