Singular problems for bi-material plane of John's harmonic material

Abstract

The singular plane problems of nonlinear elasticity (plane strain) are considered for bi-material infinite plane of John’s harmonic material. Using model of harmonic material has allowed to apply the theory of complex potentials and to obtain exact analytical global solutions of nonlinear problems. Among them it is problem of bi-material plate with the stresses and strains jumps on the interface. As an application of the problem of jumps, the problem of concentrated force on an interface boundary of two half-planes and the problem of interface crack. Mechanical properties of half-planes are described by the model of John’s harmonic material. Application of this model has allowed to use the methods of a complex functions theory and to obtain exact analytical solution of problems. The values of nominal stresses and displacements are founded. The asymptotic expansions based on the global solutions are constructed for stresses and displacements in a vicinity of a point force and in a vicinity of crack tip. As an example the case of a free crack in plate subjected to constant stresses at infinity is studied.