Effective Finite Element Modeling of Layered Honeycomb-Based Composites and Auxetic Materials

The present study addresses two related classes of structures: three-layer plates incorporating a tetrachiral honeycomb core between solid face sheets, and isotropic or orthotropic auxetic plates characterized by a negative Poisson's ratio. Their mechanical response is examined within the framework of linear elasticity using the displacement-based finite element method. Rectangular finite elements with either classical bilinear compatible or quadratic incompatible shape functions are employed. Plane strain is adopted for the composite plates, whereas plane stress is considered for the auxetic plates; three-dimensional finite element calculations provide an additional basis for comparing composite responses. Under static bending, the effects of honeycomb discretization (defined by the number of unit cells per unit area), core relative density, and core thickness are analyzed under different boundary conditions. For static shear and indentation, the study compares the ability of the two shape-function formulations to reproduce the mechanical response of auxetic plates. Analytical relationships for effective material constants are employed to represent tetrachiral, hexachiral, and re-entrant honeycomb structures as homogenized continua. The monograph synthesizes and extends the author's previously published investigations, presenting computationally efficient finite element approaches for the analysis of honeycomb-core composites and auxetic materials, together with revised formulations and updated numerical results.