Unilateral problems for laminates: a variational formulation with constraints in dual spaces

In this paper, models for laminated composite plates accounting for elastic bimodular constitutive behavior and frictionless unilateral contact conditions are established and rationally deduced from the three-dimensional elasticity by means of a variational constrained approach. Consistent internal constraints on both stress and strain dual fields are enforced through a modified Hu-Washizu-type functional, defined on the convex set of the compatible displacements. A bimodular strain energy density is adopted and for the first-order shear-deformable (Reissner-Mindlin type) laminate model a variational formulation of Signorini's problem is recovered. The rational deduction of a Lo-Christensen-Wu-type model for bimodular laminate on unilateral support is also outlined and briefly discussed.