Surface undulation instability of the viscoelastic half-space covered with the stack of layers in bi-axial compression

The near-surface undulation stability loss problems of the viscoelastic half-space covered with the stack of layers in bi-axial compression in the layers’ plane are investigated within the framework of the piecewise homogeneous body model by employing the three-dimensional linearized theory of stability of deformable bodies (TLTSDB). The equations of the TLTSDB are obtained from the three-dimensional geometrically nonlinear exact equations of the theory of viscoelasticity by the use of the boundary-form perturbation technique. By employing Laplace transform, the method for the solution to these problems is developed. It is supposed that the layers in the stack have an insignificant initial imperfection and as a stability loss criterion the case is considered where this imperfection starts to increase and grows indefinitely.The developed method is employed for the investigation of concrete problems. As a result of these investigations the influence of the rheological parameters of the layers and half-space materials on the values of the critical time is studied. The viscoelasticity of the materials is described by the fractional–exponential operator of Rabotnov.