Table of Postulates in Continuum Mechanics and Principles of Forming its Lines
D. V. Georgievskii
Lomonosov Moscow State University, Moscow, Russia
Keywords: postulate, axiomatics, conservation laws, integral form, local equation, source, flux, production, internal energy, energy conjugacy, entropy
Abstract
A single integral form of the postulates of continuum mechanics in the form of laws of change (conservation) of certain quantities is represented as a table of postulates. It is assumed that in a continuous medium, both purely mechanical and various non-mechanical interactions occur, which are described by scalar, vector, and second-rank tensor energetically conjugate pairs of quantities, one of which characterizes a process and the other defines the response of the environment to this process. The first three rows of the table of postulates are used to construct the fourth and fifth rows corresponding to the laws of change in internal energy and the quantity that, in the case of the thermodynamic pair “temperature-entropy” coincides with entropy. It is shown that the assignment of sources, flows through the boundary, and productions in the fourth and fifth rows of the table of postulates actually makes these rows definitions. The principles used in nonisothermal mechanics to construct constitutive relations linking dependent and independent state variables for each type of interaction are generalized.
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