A constitutive model for fiber reinforced polymer plies – Implicit anisotropic evolution of damage and plasticity based on effective strengths

Abstract

The present paper proposes a constitutive model for the prediction of damage and plasticity in continuous fiber reinforced polymer plies. The model combines an explicit damage model for fiber rupture, an implicit damage model for matrix cracking, and a plasticity model for unrecoverable strains. The stiffness degradation of the matrix damage is formulated by recourse to a micromechanics method. Its damage evolution is computed implicitly based on an effective strength-based damage condition and a damage flow rule. Loading-threshold functions are introduced to formulate the dependence of the damage condition on the damage variables. They are calibrated according to experiments for uniaxial transverse (in-plane) tension, uniaxial transverse (in-plane) compression, and in-plane shear. To simplify the numerical time integration of the evolution equations, the damage condition, and the loading-threshold functions are formulated in terms of effective stresses, as defined in CDM. The evolution of the plastic state variables is formulated by maximizing the effective plastic dissipation to be independent of the damage variables. The predictions of the model are shown for an open hole tension test of a [±45]sym and a [0/90]sym-laminate.

Keywords

• Composite laminates
• Anisotropic constitutive model
• Continuum damage mechanics
• Plasticity
• Implicit constitutive integration
• Finite Element Analysis