Vol. 11, No. 3, 2016

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A phase-field model of quasistatic and dynamic brittle fracture using a staggered algorithm

Hamdi Hentati, Marwa Dhahri and Fakhreddine Dammak

Vol. 11 (2016), No. 3, 309–327
Abstract

Fracture mechanisms in solids are governed by complex fracture phenomena such as crack initiation and multiple crack branching. Recently, the numerical modeling of dynamic fracture mechanisms has been based on the introduction of a crack phase field. Following our recent works on phase-field modeling of quasistatic brittle fracture, a numerical method is presented to investigate the dynamic failure mechanisms in brittle solids using the phase-field model and a staggered algorithm. For that, numerical experiments of a brittle piece under tensile loading are performed. Based on these numerical results, the importance of developing a numerical method to optimize the computation time is shown. The optimized method is presented in a linear (P1) finite elements case in elasticity. We then show the results of using the optimized method in the case of dynamic fracture mechanics in brittle materials, and we analyze when the dynamic solution converges to the quasistatic one. We also investigate the influence of the numerical parameters $h$ (mesh size) and $\eta$ (regularization parameter) on the evolution of energies, displacements and crack location. The influence of exerted loading $\delta$ and transverse wave speed ${C}_{T}$ is also elaborated.

Keywords
brittle fracture, staggered algorithm, phase field