Nonlinear Elastic Constitutive Relations of Auxetic Honeycombs

When designing a flexible structure consisting of cellular materials, it is important to find the maximum effective strain of the cellular material resulting from the deformed cellular geometry and not leading to local cell wall failure. In this paper, a finite in-plane shear deformation of auxtic honeycombs having effective negative Poisson’s ratio is investigated over the base material’s elastic range. An analytical model of the inplane plastic failure of the cell walls is refined with finite element (FE) micromechanical analysis using periodic boundary conditions. A nonlinear constitutive relation of honeycombs is obtained from the FE micromechanics simulation and is used to define the coefficients of a hyperelastic strain energy function. Auxetic honeycombs show high shear flexibility without a severe geometric nonlinearity when compared to their regular counterparts.