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When a tensor-valued function σ(x) is continuous in regions ∑0 and ∑1, but has a finite jump across the interface Γ01 between ∑0 and ∑1, then Γ01 is referred to as singular surface relative to the field σ (x). In this paper, it is intended to give a general treatment of three-dimensional static and free vibration analysis of bodies composed of multi-phase elastic and/or piezoelectric bodies with electro-mechanical singular surfaces. The geometry of the medium, boundary conditions, and the geometry of the singular surfaces may be arbitrary. The displacement field and the electric potential in each region are expressed in terms of functions composed of 3-D series and special 3-D functions. The... 

In this paper, the method of additive plasticity at finite deformations is generalized to the micropolar continuous media. It is shown that the non-symmetric rate of deformation tensor and gradient of gyration vector could be decomposed into elastic and plastic parts. For the finite elastic deformation, themicropolar hypo-elastic constitutive equations for isotropicmicropolar materials are considered.Concerning the additive decomposition and the micropolar hypo-elasticity as the basic tools, an elastic-plastic formulation consisting of an arbitrary number of internal variables and arbitrary form of plastic flow rule is derived. The localization conditions for the micropolar material obeying...