Balance Laws for the Purely Mechanical Theory

The objective of this chapter is to discuss the balance laws in the purely mechanical theory. Specifically, the conservation of mass and the balances of linear and angular momentum are presented in both global and local forms. The properties of the Cauchy stress tensor are derived and the rate of material dissipation is proposed. Invariance under Superposed Rigid Body Motions (SRBM) is discussed along with the development of the transformation relations for specific tensors. It is shown that the local forms of the balance laws can be derived by using invariance under SRBM of the rate of material dissipation and these transformation relations. Also, linearization of the kinematic quantities and balance laws are discussed.