As an example the case of a free crack in bi-material plane subjected to constant stresses at infinity is studied. Based on the global solutions the asymptotic expansions are constructed for stresses and displacements in a vicinity of crack tip. The values of nominal (Piola) and Cauchy stresses and displacements are founded. As an application of the problem of jumps, the problem of interface crack is solved. Among them the problem of bi-material plane with the stresses and strains jumps at an interface is considered. Using model of this harmonic material has allowed to apply the theory of complex functions and to obtain exact analytical global solutions of some nonlinear problems. Mechanical properties of half-planes are described by the model of semi-linear material. The singular plane problems of nonlinear elasticity (plane strain and plane stress) are considered for bi-material infinite plane with interface crack. Bi-material plane with interface crack for the model of semi-linear materialÄomanskaya, T.
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March 2023
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