Gradient material mechanics: Perspectives and Prospects

Abstract

This is a modest contribution dedicated to the work and virtue of George Weng, a prominent figure in material mechanics and a dear intellectual friend. The paper starts with the basics of gradient theory as applied to elasticity, plasticity and dislocation dynamics by introducing weak non-locality in the constitutive equations through Laplacian terms and corresponding deterministic internal lengths (ILs) characterizing the dominant deformation mechanisms. It then considers the interaction of such deterministic ILs with surface effects associated with internal or external surfaces, as well as stochastic effects associated with pre-existing or deformation-induced random microstructures. Experimentally observed stress drops and strain bursts are interpreted through combined gradient-stochastic models. Statistical features of corresponding deformation processes that cannot be fitted with Boltzmann–Gibbs–Shannon entropy statistics are interpreted by Tsallis q-entropy statistics. Some benchmark novel experiments for the direct determination of ILs for plasticity (by testing bulk specimens with gradient grain size) and dislocation dynamics (by testing thin films in TEM with gradient dislocation density) are proposed.