# Steady-state propagation of a mode II crack in couple stress elasticity

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## Abstract

The present work deals with the problem of a semi-infinite crack steadily propagating in an elastic body subject to plane-strain shear loading. It is assumed that the mechanical response of the body is governed by the theory of couple-stress elasticity including also micro-rotational inertial effects. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. It is assumed that the crack propagates at a constant sub-Rayleigh speed. An exact full field solution is then obtained based on integral transforms and the Wiener–Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the propagation velocity and the characteristic material lengths in couple-stress elasticity. The present analysis confirms and extends previous results within the context of couple-stress elasticity concerning stationary cracks by including inertial and micro-inertial effects.

## Keywords

Dynamic fracture Couple-stress elasticity Microstructure Mode-II crack Micro-rotational inertia Complex materials## Notes

### Acknowledgments

Panos A. Gourgiotis gratefully acknowledges support from the European Union FP7 project “Modelling and optimal design of ceramic structures with defects and imperfect interfaces” under contract number PIAP-GA-2011-286110-INTERCER2. Andrea Piccolroaz would like to acknowledge the Italian Ministry of Education, University and Research (MIUR) for the Grant FIRB 2010 Future in Research “Structural mechanics models for renewable energy applications” (RBFR107AKG).

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