Balance Equations

Abstract

In the preceding chapter, we focussed on (some of the) kinematic aspects related to the motion of a continuous body. In particular, the motion x(X,t) was treated as a given function. However, it is in fact one of the main tasks of continuum mechanics to calculate the motion of the particles forming continuous bodies and, along with it, the evolution of the associated fields such as e.g. density and temperature. This can be done, once the relevant equations — usually functional differential equations — will have been established together with sufficient initial and/or boundary conditions. These equations comprise two sets of statements, the so-called balance equations of mass, momenta, energy and entropy and the constitutive relations describing the material behaviour of the body for which the spatial and temporal evolution of the field quantities, such as motion, density and temperature are sought. The balance equations have fairly general character and, in particular, contain no material specific information. The present section is devoted to the derivation of the global forms of the balance laws.