Title: Instabilities in dynamic fracture

Speaker: Yuri Lubomirsky (Weizmann Institute)

Abstract:

Cracks, the major vehicle for material failure, undergo various dynamic instabilities in brittle materials. Despite their fundamental importance, these instabilities are not explained by the classical theory of cracks, which is based on the linearized field theory of elasticity. We develop a 2D theoretical-computational framework capable of predicting arbitrary paths of dynamic cracks, incorporating small-scale, near crack-tip elastic nonlinearity and dissipation. We show that cracks undergo a high-speed oscillatory instability controlled an intrinsic length, either nonlinear elastic or dissipative, in quantitative agreement with experiments. The instability is shown to exist, with the same salient properties, in materials exhibiting widely different near crack-tip elastic nonlinearity (including no crack-tip nonlinearity), highlighting its universal character. We further show that upon increasing the driving force for fracture, a tip-splitting instability emerges, as experimentally demonstrated. The theory culminates in a comprehensive stability phase diagram of 2D brittle fracture. Ongoing efforts in 3D dynamic fracture will be briefly presented (time permitting).

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