Nonlinear elasticity in nanostructured materials

We elaborate on a blended continuum/atomistic theoretical picture of the nonlinear elastic properties of nanostructured materials, looking at diverse aspects such as dispersions of inhomogeneities within a matrix, random or graded nanograined materials, two-dimensional atomic sheets. In particular, we discuss the possible onset of length-scale effects and we establish the limits and merits of continuum versus atomistics. While most situations here discussed correspond to model systems, the main conclusions have a paradigmatic relevance and indeed apply to most nanomaterials of current interest.