Jump Conditions

Abstract

In the preceding chapter we derived the differential equations for the time evolution of certain physical variables. For those derivations we assumed that all field quantities are continuously differentiable within the body, i.e., within _{ß R} and ß _t , (the reference and present configurations), respectively. These assumptions were also implemented for the application of the Reynolds transport theorem and the Divergence Theorem. The derivation of the local balance equations, as demonstrated in the last chapter, is no longer possible in those forms if the associated field variables are not continuously differentiable in the whole domain. When the variables do not satisfy the continuity conditions at a surface of a body then the global balance laws imply the so called jump conditions that must hold on surfaces across which certain field variables are not continuous. These jump conditions can be interpreted as boundary or transition conditions at boundary surfaces. Particular surfaces are:

Material Surface A material surface (or also a material line), analogous to a material body, is defined as a surface (line) within a body which is formed by the same material elements or particles at all times.

Singular Surface A surface within a material body across which a physical quantity experiences a discontinuity is called a singular surface.