Kinematics of Singular Surfaces and Jump Equations of Balance

A continuous medium (or continuum) is the idealized model of a material body as observed at the macroscopic level and regarded as a continuous distribution of matter in which physical quantities (mass, velocity, internal energy, etc.) are distributed throughout the body and mathematically described as fields. The physical laws, or balance laws, are then formulated as integral equations for fields defined in regions of space occupied by the continuum. Phenomena with singularities can be described as discontinuities or concentrations of a field on a surface within the body. In the first case, we have propagating wave fronts (simply waves) and, in the second, interfaces, where physical properties different from the surrounding media are carried. Interfaces may model the direct interaction between two different phases of a material. Here and in Section [1] of this encyclopedia, we study mainly the theory of singular surfaces related with wave fronts. The general conditions of propagation and the jump equations of balance are written here, independently from the material constitutive class, whereas in [1], such conditions are developed for some classes of constitutive equations. Ref. [1]. Montanaro A (2012) Propagation of wavefronts in thermoelastic media. In: Hetnarski R (ed) Encyclopedia of thermal stresses. Springer, Berlin, Heidelberg/ New York, this volume