Review of continuum mechanics and its history. Part II: The mechanics of thermoelastic media. Perfect fluids. Linearly viscous fluids

Abstract

This paper is the second of a series of two articles reviewing the contributions of continuum mechanics and its history. The review is written for the mathematician who is not a specialist in this field, and aims to give an in-depth overview of the mathematics as well as a historical perspective of this field. The first of the two papers [10], Part I. "Deformation and Stress. Conservation Laws. Constitutive Equations'', starts at the very origins of continuum mechanics and brings the reader up to the 1820's when Navier publishes the system of the general equations of linear elasticity in 1821. The present paper continues, discussing the consequences of this system, some of its simplifications and approaches for solution. It also gives a perspective of how waves propagate in continuous media. Reviewed are also perfect fluids and linearly viscous fluids. At the end, the paper discusses the conditions for compatibility of the stresses.