ABSTRACT
The prediction of material response requires the combination of several elements. In general, these elements include mathematical models describing the material’s response characteristics (constitutive equations), specific conditions describing the initial state of the matter (initial conditions), conditions describing how the specific body is being influenced by its surroundings (boundary conditions), and laws describing how to combine these elements (balance laws). The focus of this chapter will be on the balance laws. These laws have a special place in the theory of material response since they are the same for all materials, while other equations, such as the constitutive equations, change from material to material. This chapter also will look at the jump conditions, which are a specific form of the balance laws that hold across a discontinuity, such as a shock wave. The jump conditions relate variables on two sides of a discontinuity.
