A method of multiscale modelling considered as a way leading to unified mechanics of materials

Abstract

This paper outlines a development of rational mechanics which may potentially lead to a more unified mechanics of materials. The intention of considerations is to provide in a future a theoretical context for systematic engineering activity in various scales. Methodological considerations leading to a development on the above way are the first aim of this paper. We consider the multiscale method of modelling called collection of dynamical systems with dimensional reduction. Within this approach, the scale of averaging applied in modelling is formalized. Therefore transition between various scale models is possible. In order to make the dimensional reduction procedure realizable, we have to formulate continuum mechanics with finite-dimensional fields in connection with an elementary dynamical system. Such a step is also aimed at obtaining the possibility of the consideration of atomistic and continuum models within one consistent theoretical scheme. One accentuates the particular role of nanoscale models as a bridge between atomistic models and more averaged continuum description. One discusses the methodology of nanoscale modelling accentuating the particular role of the free energy and methodology of defining this function.