Modeling and numerical investigation of damage behavior in pantographic layers using a hemivariational formulation adapted for a Hencky-type discrete model

In this study, a hemivariational formulation is presented for a Hencky-type discrete model to predict damage behavior in pantographic layers. In the discrete model, elastic behavior of pantographic layers is modeled via extensional, bending and shear springs. A damage descriptor is added for each spring type. Such a damage descriptor is non-decreasing function of time, and therefore, the standard variational formulation of the problem is generalized to a hemivariational one providing not only the Euler–Lagrange equations for the evolution of the displacements of all the standard degrees of freedom but also the Karush–Khun–Tucker condition governing the evolution of damage descriptor. The dissipation energy included in the hemivariational formulation depends upon six additional constitutive parameters (two per each spring type), and the mechanical behavior of layer is simulated with an efficient and smart strategy able to solve the nonlinear equilibrium equations coupled with the evolution of damage variables. A metallic pantographic layer which was experimentally investigated in the literature is considered to test the proposed formulation.