Beams comprising unilateral material in frictionless contact: a variational approach with constraints in dual spaces

In this paper, beam models accounting for non-linear elastic bimodular constitutive behavior and frictionless unilateral contact conditions are rationally deduced from 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 functional, obtained by a non-standard application of Lagrange multipliers and constrained in the convex set of the admissible contact displacements. A bimodular strain energy density is adopted and for both no-shear and first-order shear deformable beam models a generalized variational formulation of Signorini's problem is recovered. Finally, several simple study cases are investigated, highlighting the influence of the bimodular constitutive law.