Failure induced by a dynamic anti-plane slip pulse in flexoelectric materials

Failure models related to dynamic slip pulses have been extensively used in seismology as for example the models of Yoffe (1952), Freund (1979) and Rice et al (2005). The models of Freund and Rice et al. describe a finite mode III crack of constant length that propagates at constant (subsonic) rapture velocity whereas the trailing edge leaves behind a dislocation as a permanent irreversible deformation. The driving forces of such models are far field shear tractions, whereas at the same time a frictional traction acts along the crack line due to the contacting crack surfaces that allow only shear slip. Yoffe’s model on the other hand assumes a complete healing and thus rendering the trailing edge to behave as a crack-tip, just as the leading edge does. An important difference between Freund’s and Rice et al.’s models is that Rice et al.’s model includes additionally the effect of the static friction, whereas Freund’s model incorporates only the kinetic friction. The present work extends the models of Freund and Rice et al. to flexoelectric materials under steady state anti-plane loading. The problem is formulated so that the mechanical problem is casted as a strain gradient elasticity problem. Our analytical results point out that the well known influence of the cohesive zone in classic dynamic fracture can be established in the context of flexoelectricity (and strain gradient elasticity) without the need for a cohesive zone. An interesting analogy with the Rice et al. analysis can be established and, in this way, a flexoelectric material can be used for laboratory work in earthquake and friction studies. • FEM analysis of dynamic slip pulses • Flexoelectric dynamic slip pulse • Asymptotic analysis for Flexoelectric dynamic slip pulse • Energy Release Rate for Flexoelectric slip pulse • Flexoelectric slip pulse analogue with cohesive zone model