Abstract
In this paper, the elastic region model of continuous medium is established, and their constitutive relations are determined in mathematical form. The geometric properties of the deformation of the continuous medium are studied, and the spatial position and direction of each part of the continuous medium caused by the deformation are determined. We emphasize that the thermodynamic basis of the displacement concept is a finite size equilibrium region and a quasi-static process. Just from the macro point of view, the main mechanical problem of continuous medium should be how to find out its stress-strain relationship reasonably within the framework of the ancient elastic theory. This complex mesoscopic analysis will help to understand the size and constitutive relation of materials parameters, but it will not change the basic structure of elastic theory.
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