Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures

The existence and uniqueness of a solution of the first, the second and the third plane boundary value problem are considered for the basic homogeneous equations of statics in the theory of elastic mixtures. Applying the general Kolosov–Muskhelishvili representations from [Basheleishvili, Georgian Math. J. 4: 223–242, 1997], these problems can be splitted and reduced to the first and the second boundary value problem for an elliptic equation which structurally coincides with the equation of statics of an isotropic elastic body.

Stability and Bifurcation of Homogeneous Deformations of a Compressible Elastic Body under Pressure Load

An analysis is given of the stability and bifurcation of homogeneous deformations of a compressible homogeneous isotropic elastic body under pressure loads. The energy minimum principle is used in the stability analysis and singularity theory in the bifurcation analysts. It is found that multiple equilibrium deformations are possible under pressure loads that describe the Cauchy traction over the boundary of the deformed body.