The exact solutions of the stability problem for two different half-planes compressed along the cracked interface are considered within the framework of the three-dimensional linearized theory of stability of deformable bodies. The exact analytical solutions are constructed in a form common for finite (large) and small strains as applied to compressible and incompressible, isotropic and orthotropic, and elastic and plastic models. The solutions are derived using complex potentials of the above-mentioned theory and the Riemann-Hilbert problem methods. Mechanical effects are analyzed. This article is a complete report read at the ICTAM 2000 (Chicago, USA). An abstract was included in the ICTAM-2000 Abstract Book.
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