A fully non-linear 3-D constitutive relationship for the stress analysis of a pin-loaded composite laminate

Abstract

On the basis of the complementary energy function, a non-linear consistent constitutive relationship was established for orthotropic materials, e.g. laminated composite materials. The constitutive relationship is non-linear, both in normal and shear stress/strain relations. The non-linearity in normal stresses accounts for change in the compliance, hardening or softening, as well as change in the compliance in tension or compression. Of course, the change in the modulus in the reverse stress condition of normal stresses depends on the magnitude of the non-linear stress/strain relationship in that stress. In addition, the non-linear term will cause softening in one state of normal stress and hardening for the reverse state of that stress or vice-versa, depending on its sign. The constitutive model was applied to the data available for an AS4/3501-6 CFRP material. Then the off-axis stresses around the hole periphery of pin loaded composite plates of AS4/3501-6 for the linear and non-linear material models were compared. Generally, the non-linear relationship resulted in reducing σ xy and out-of-plane shear stresses, σ yz and σ xz . However, the normal out-of-plane stress σ zz was increased. The effect of a non-linear material model on in-plane normal stresses σ xx and σ yy is dependent on the layup.