Multiscale approaches : from the nanomechanics to the micromechanics

Computational modelling of materials behaviour is becoming a reliable tool to underpin scientific investigations and complement traditional theoretical and experimental approaches. In cases where an understanding of the dual nature of the structure of matter — continuous when viewed at large length scales and discrete when viewed at an atomic scale — and its interdependencies are crucial, multiscale materials modelling (MMM) approaches are required to complement continuum and atomistic analyses methods. At transitional (or microstructure) scales — in between continuum and atomistic — continuum approaches begin to break down, and atomistic methods reach inherent time and length-scale limitations (Ghoniem et al., 2003). Transitional theoretical frameworks and modelling techniques are being developed to bridge the gap between length scale extremes. The power of analytical theories lies in their ability to reduce the complex collective behaviour of the basic ingredients of a solid (e.g. electrons, atoms, lattice defects, single crystal grains) into insightful relationships between cause and effect. For example, the description of deformation beyond the elastic regime is usually described by appropriate constitutive equations, and the implementation of such relationships within continuum mechanics generally relies on the inherent assumption that material properties vary continuously throughout the solid