We consider the yield set of a (rigid-perfectly-plastic) polycrystal, where the basic crystal has very few slip systems. One would like to predict whether the effective behavior is ductile or rigid. We address this issue for some model problems of antiplane shear and plane stress. Our main tools are nonlinear homogenization, bounds via compensated compactness, and the elastic comparison method.
ASJC Scopus subject areas
- Applied Mathematics