A nonlocal formulation based on a novel averaging scheme applicable to nanostructured materials

A novel averaging process for modeling the mechanical behavior of heterogeneous fine grained or nanostructured materials is presented. The representative volume element (RVE) is considered as an assembly of heterogeneous system of grains which are assumed to be small. Heterogeneity may have different origin; they can be isotropic with different mechanical properties, they can be a collection of the same crystal structure with different orientation or they can be a collection of grains with radically different material properties and different crystal structures. The averaging process is explained for an RVE which consists of two isotropic materials with different material properties, for the sake of simplicity. The resulting constitutive equation is of nonlocal character, and it is shown that the equation can be reduced to a gradient type. Opening of Mode III crack in small scale yielding condition within the framework of gradient elasticity is summarized. Further, single-grit scratching experiments on a range of metals and ceramics are considered. Finally, it is indicated that the results of the analysis of a groove created in a scratch test can be used to determine the material parameters in the constitutive equations of gradient dependent elasticity, and the advantages of gradient dependent theories in understanding material removal mechanisms is outlined. © 2002 Elsevier Science Ltd. All rights reserved