Integrated micromechanical-structural framework for the nonlinear viscoelastic behavior of laminated and pultruded composite materials and structures

This study introduces a new three-dimensional (3D) multi-scale constitutive framework for the nonlinear viscoelastic analysis of laminated and pultruded composites. Two previously developed nonlinear micromechanical models for unidirectional and in-plane random composite layers are modified to include time-dependent and nonlinear behavior. A new recursive-iterative numerical integration method is introduced for the Schapery nonlinear viscoelastic model and is used to model the isotropic matrix subcells in the two micromodels. In addition, a sublaminate model is used to provide for a through-thickness 3D nonlinear equivalent continuum of a layered medium. The fiber medium is considered as transversely isotropic and linear elastic. Incremental micromechanical formulations of the above three micromodels are geared towards the time integration scheme in the matrix phase. New iterative numerical algorithms with predictor-corrector type steps are derived and implemented for each micromodel to satisfy both the constitutive and homogenization equations. Experimental creep tests are performed for off-axis pultruded specimens in order to calibrate and examine the predictions of the constitutive framework for the multi-axial nonlinear viscoelastic response. Experimental creep data, available in the literature, is also used to validate the micromodel formulation for laminated composite materials. Nonlinear viscoelastic effects at the matrix level, such as aging, temperature, and moisture effects can be easily incorporated in the constitutive framework. The multi-scale constitutive framework is implemented in a displacement-based finite element (FE) code for the analysis of laminated and pultruded structures. Several examples are presented to demonstrate the coupled multi-scale material and structural analysis.