Abstract: This paper discusses the fundamental assumptions, the differential equations, and the variational principles of discontinuous form belonging to a new developing branch of science-the solid mechanics of discrete form.The solid mechanics of discrete form belongs to the branch of science of discrete medium mechanics which is the developing direction of the mechanics for the present. Based on the solid system with discretization and separability, the unknown functions with discontinuity in defined regions and the defined regions with variable boundaries, the mechanics systems to solve the solid displacements,strains and stresses in various cases are called the solid mechanics of discrete form.When the unknown functions are sufficiently smooth functions in the whole defined region and the effects of the variable boundaries are disregarded,the solid mechanics of discrete form will degenerate into the classical solid mechanics belonging to continuum.mechanics: Its variational principles will degenerate into the classical variational principles with the same cases.

Key words: piezoelectric ceramics, electroelastic field, anti-plane shear problem, impermeable crack