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Variational approach to dynamic cohesive fractures
key words : variational methods, phase-field models, cohesive fracture, damage-plasticity models, dynamics
Gradient damage models (aka phase-field models) are widely used to predict the nucleation and propagation of cracks. Recently, a novel class of phase-field models based on coupled damage-plasticity models have been developed. Their capabilities to predict the nucleation and propagation of cracks in brittle and ductile materials under complex stress states has been validated in a quasi-static regime.
When the load varies slowly with time, the quasistatic approach is preferred to the dynamic approach for its simplicity. However, when that is not the case, one important challenge is to extend these models in a dynamical setting.
In this work, we present a variational approach to model the dynamics of cohesive fractures. In particular, we show some analytical and numerical results of such approach by studying the behavior of a homogeneous one-dimensional bar. At difference with respect to the quasi-static case, the variational approach no longer uses the energetic stability criterion, but is formulated in terms of the principle of least action. A Lagrangian is thus defined and given by the difference between the potential energy and kinetic energy of the body. Irreversibility and energy balance, as in the quasi-static case, are then used to complete the variational formulation of the problem.
Preliminary results obtained in the antiplane case suggest that this approach can potentially unify within a single consistent variational theory key concepts developed to predict or prevent material failure: Griffith and cohesive crack models, damage models, plasticity, strength criteria, and limit analysis. This work would contribute in this direction by extending the framework to include dynamical problems.