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.
Highlights
Contemporary engineering is developed in many directions and in relation to various scales
The method of theoretical description discussed in this paper is considered as a way of development of rational mechanics towards incorporation of discrete models related to atomic scale and averaged continuum models into one theoretical framework
We introduce the following assumptions which represent general properties of the collection of dynamical systems distinguished within the elementary dynamical system [9]: 1. Subsystems are distinguished by the determination of groups of variables φh = {φhα}, where α ∈ IAh, IAh is a finite set related to the separate hth subsystem and h ∈ IP
Summary
Contemporary engineering is developed in many directions and in relation to various scales. The state of theory determines the possibility of automatizing processes of design by means of computers We observe such a situation in case of engineering related to scale corresponding to traditional constructions in our environment where the theory applied is predominantly well developed. Theory and numerical simulations have rather auxiliary character This means that we have not sufficient confidence in models of mechanics of materials when more complex phenomena based on less clear physical processes appear. The method of theoretical description discussed in this paper is considered as a way of development of rational mechanics towards incorporation of discrete models related to atomic scale and averaged continuum models into one theoretical framework. We promote the interdisciplinary character of mechanics of materials
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