Stability of Nonlinearly Elastic Sandwich Plates with Highly Porous Core and Prestressed Uniform Coatings

The present paper is dedicated to studying the stability of nonlinearly elastic sandwich plates, which are common structural elements. The bifurcation of equilibrium is considered for a three-layer circular plate under radial compression and a three-layer rectangular plate under biaxial tension and compression. It is assumed that the middle layer of plates (core) is made of a highly porous material, while the top and bottom layers (coatings) are homogeneous, prestrained and contain internal stresses. An original approach is taken when modeling them in this study: to describe the behavior of the porous core, the governing equations of a nonlinear micropolar body are used, and the behavior of the coatings is studied within the framework of the classical elasticity. This allowed us to take into account in detail the effect of material microstructure on buckling. Using representations of constitutive relations for different reference configurations, in the case of a physically linear material model, linearized equilibrium equations were derived that describe the behavior of sandwich plates with a highly porous core and prestressed uniform coatings in a perturbed state. Using special substitutions, the stability analysis of three-layer circular and rectangular plates was reduced to solving linear homogeneous boundary value problems for systems of ordinary differential equations. As a result of the numerical analysis for plates with a core of dense polyurethane foam and polycarbonate coatings, it was determined that preliminary tension of the coatings stabilizes the considered deformations of the plates as a whole, while the effect of preliminary compression of the coatings is negative.

nonlinear elasticity, deformation stability, micropolar medium, internal stresses, sandwich plate, porous core, prestressed coatings