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Phase-field modeling of rapid fracture in linear and nonlinear elastic solids Karma, Alain


This talk will discuss phase-field modeling of dynamic instabilities of fast moving cracks in brittle solids. Experiments in thin gels have shown that cracks can attain extreme speeds approaching the shear wave speed when micro branching, which limits propagation to smaller speeds in thick samples, is suppressed. Furthermore, they have revealed the existence of an oscillatory instability with an intrinsic system-size-independent wavelength above a threshold speed. In apparent contradiction with experimental observations, the commonly used phase-field formulation of dynamic fracture yields crack that branch by tip splitting at roughly half the shear wave speed. A phenomenologically based phase-field formulation is proposed that can model crack propagation at extreme speeds by maintaining the wave speed constant inside the microscopic process zone. Simulations of this model for linear elasticity outside the process zone produce crack that tip split above a high threshold speed but no oscillations. In contrast, simulations for nonlinear neo-Hookean elasticity yield crack oscillations above a ultra-high speed threshold. Those oscillations have an intrinsic wavelength that scale with the size of the nonlinear zone surrounding the crack tip, which can be much larger than the process zone scale, and bear striking similarity with observed oscillations in thin gels.

This work was carried out in collaboration with Chih-Hung Chen and Eran Bouchbinder and his supported by a grant from the US-Israel Binational Science Foundation.

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