A multiscale Griffith criterion

Abstract

In this letter, a compatibility-momentum tensor is proposed based on the strain compatibility condition of continuum mechanics. By rescaling the compatibility-momentum tensor, we construct a so-called multiscale energy-momentum tensor and the corresponding L-integral, which is path-independent if the interior region of the integration contour is dislocation-free. By applying the invariant L-integral to the field of a mode III elastoplastic crack under small-scale yielding condition, we derive a multiscale criterion for macroscopically brittle fractures.

Acknowledgements

The author thanks the anonymous referees for helpful comments and suggestions. This work is supported by a grant from NSF (Grant No. CMS-0239130), which is greatly appreciated.