A nonlinear constitutive model of rigid polyurethane foam considering direction-dependence and tension–compression asymmetry

Abstract

Rigid polyurethane foam (RPUF) is characterized by direction-dependence and significant nonlinear performance. The direction-dependence shows the differences between foaming plane and foaming direction, while the nonlinear performance of RPUF not only shows the nonlinear relation between stress and strain, but also the tension–compression asymmetry. A new principal strain definition method of RPUF considering its foaming direction and foaming plane is hereby proposed for three-dimensional constitutive modeling. The constitutive model is established under the material principal strain coordinate system, along which the normal strains of two perpendicular directions in the foaming plane reach the maximum. The elastic moduli and Poisson's ratios vary with the sign and magnitude of the material principal strains. The nonlinear constitutive equation under the material principal strain coordinate system is derived in incremental form. The physical equation in the global coordinate system is obtained with coordinate transformation. With Digital Image Correlation (DIC) technique, compression and tensile tests along the foaming direction and perpendicular to the foaming direction were carried out to determine the constitutive model parameters. The proposed RPUF nonlinear constitutive model is applied to FEM analysis with the iterative algorithm of Explicit Sub-stepping Method.