The basic problem in Continuum Mechanics may be stated as follows: Given the initial or the undeformed state of the body, its material, and the loads applied to it, find the deformed shape at any time t. That is, for every material point of the body, find the time history of the mass density ?, the displacement u, the velocity v, and the temperature ?. Thus there are five unknowns (either three components of displacement or velocity, ? and ?) at each material point of the body. As summarized in Sec. 4.11, these are to be determined by solving the eight Eqs. (3.124), (4.28), (4.29), and (4.88) subject to the given initial and boundary conditions. A solution of equations (3.124), (4.28), (4.29), and (4.88) satisfying the prescribed initial and boundary conditions is called a thermomechanical process. Only those thermomechanical processes that satisfy the entropy inequality (4.109) are admissible in a continuous body.
A difficulty with the aforestated problem formulation is that the system of equations is highly indeterminate; there are 8 equations and 18 unknowns ( ?, u i, 
iL, e, Q L, ?). This is to be expected as the balance laws are applicable to every continuous medium. However, identical bodies made of different materials deform differently when subjected to the same initial and boundary conditions. The remaining 10 equations characterize the material of the body and are known as constitutive relations.
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