A numerical homogenization approach to characterize in-plane anisotropic hyperelastic responses of a non-metallic honeycomb core

Abstract

In this research, a numerical homogenization approach to predict the experimentally observed nonlinear elastic, orthotropic and asymmetric responses of non-metallic honeycomb cores under large in-plane deformations is presented. A pragmatic approach to simulate the general in-plane and/or flexural loading of the bulk core is to homogenize the core behavior using a nonlinear equivalent-continuum (effective) constitutive model. To accomplish this, an anisotropic hyperelastic constitutive model was developed to capture the effective constitutive relations of the bulk honeycomb core. The hyperelastic constitutive model was assembled using data obtained from an experimentally validated Finite Element model of the Representative Volume Element or unit cell of the honeycomb core microstructure using curve-fitting methods. The hyperelastic material model was first evaluated using a single element model, which represented the unit cell of the honeycomb core, in a commercial nonlinear finite element program on which simple states of loading such as uniaxial tension and compression were imposed. After validation of the model using elementary simulations, it was employed for nonlinear finite element simulations of the bulk honeycomb core using simple continuum elements, subjected to complex loading and boundary conditions such as simulations of in-plane flexure and picture-frame pure shear tests. In this research, a commercial HRP-fiberglass/phenolic hexagonal cell honeycomb core was employed to generate benchmark data required to support and validate numerical models. Good agreement was observed between the model predictions and test data.