Variational principles of continuum — to the memory of István Gyarmati

Abstract

The variational principle, which allows the deduction of the basic equation system of continuum mechanics from the local form of Gyarmati’s integral principle is presented in this paper. Following the approach of irreversible thermodynamics, the principle the kinetic energy is described like the fundamental equation of thermodynamics as the internal energy change, namely intensive quantity multiplied by the changing of extensive quantity. As the internal energy is objective so that is an independent quantity from the coordinate system, this description to the internal energy can be done. However, the kinetic energy is coordinate-dependent quantity. To resolve this contradiction the stress tensor can be divided into elastic and dissipative stress components by using the laws of thermodynamics.