Analytical prediction of intrinsic length scales in strain localisation

Abstract
The length scale is not accounted for in classical modelling of strain localisation, either in shear band development or in fracture problems. The length scale can be introduced directly in the constitutive equations (nonlocal models) ; it can also be set by taking into account additional physical phenomena : heat conduction, inertia terms. A general analytical method has been developed to make quantitative analyses of these various approaches for any constitutive relations. It is based on a linear perturbation stability analysis. It is shown that nonlocal models or thermal effects set a minimum thickness of the localisation band. The effect of inertia is contrary to that of thermal conduction and the competition of both effects gives a defined characteristic length of the perturbation.