Non-local models and length scale effects on metal forming processes

Abstract

The classical theories of plasticity or continuum damage mechanics do not include scale effects associated to a characteristic length of the material, which is often present in deformation processes, and which results in a limitation of the localization of the plastic deformation or damage in narrow bands. The numerical models based in these theories suffer from size and orientation pathological dependence of the geometrical discretization and are unable to accommodate that limitation of the localization. This is true for both the classical finite element method as well as the novel meshless methods, for example. In fact the homogenization hypotheses usually admitted for the continuum and that are the basis of those numerical methods do not accommodate large gradients of the internal variables like the plastic deformation or damage in the localization zones and therefore second order constitutive laws are needed.