An inspection of the mechanical laws described in the last chapter reveals one scalar equation expressing the conservation of mass, three scalar equations expressing the balance of linear momentum, and three scalar equations expressing the balance of angular momentum, thus giving a total of seven equations in all. If we count the number of unknowns introduced into these equations, we find, however, one scalar density function, three scalar components of displacement or velocity, and nine scalar components of stress, so that, assuming the body forces are given, we thus have 13 unknowns and only seven equations connecting them. To determine the unknowns, it is therefore necessary to employ six additional equations. These equations provide information on the response of the particular material under consideration and are known as constitutive relations.
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- Malvern, L. E., Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs, New Jersey, 1969. Chapter 6 gives a general discussion of constitutive relations. Section 6.7 discusses the principle of material indifference.Google Scholar
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