A multi-scale constitutive formulation for the nonlinear viscoelastic analysis of laminated composite materials and structures

This paper presents an integrated micromechanical and structural framework for the nonlinear viscoelastic analysis of laminated composite materials and structures. Each unidirectional lamina is idealized using the Aboudi four-cell micromodel with incremental formulation in terms of the average strain and stress in the subcells. The fiber medium is considered as transversely isotropic and linear elastic. The Schapery nonlinear viscoelastic model is used to describe the isotropic viscoelastic behavior of the matrix subcells. A previously developed recursive-iterative method is employed for the numerical integration of the Schapery model. The subcells' constitutive models are nested through a numerical stress-update algorithm. The latter is based on a predictor-corrector scheme that satisfies the fiber and matrix viscoelastic constitutive relations along with the micromechanical equations in the form of traction continuity and strain compatibility between the subcells. The effect of physical aging on creep is also examined. Several experimental creep tests on off-axis specimen, available in the literature, are used to validate the formulation. The proposed material and structural framework is general and can easily incorporate temperature, moisture, and physical aging effects. The micromechanical model is numerically implemented within a shell-based nonlinear finite element (FE) by imposing a plane stress constraint on its 3D formulation. Examples for nonlinear viscoelastic structural analyses are demonstrated for a laminated panel and a composite ring.