Numerical simulation for deformation of laminates combining the novel shell element with the decoupled two-scale viscoelastic analysis of FRP

Abstract

This study proposes a numerical simulation for the deformation of laminates incorporating a combination of the novel shell element, whose thickness is allowed to change in a macro-scale model, with a decoupled two-scale viscoelastic analysis of FRP. The dependence of resin properties on the degree of cure (DOC) is considered in the simulation. Because the shell element of interest is enriched with degrees of freedom (DOFs) to represent the transverse deformations, it is capable of evaluating and controlling the thickness change during curing process of laminates. Since the additional DOFs are introduced to each element independently, they are condensed out at the element level in assembling the global finite element (FE) equation. Besides the force, the displacement can also be imposed on the outermost DOFs to control the change in thickness. Thus, numerical simulations where the plate thickness is controlled according to the requirements for molded products can be realized without introducing solid-shell-type formulations. The macroscopic mechanical behavior of FRP can be represented by the orthotropic version of the model employed for resin whose DOC-dependent macroscopic viscoelastic properties (the macroscopic coefficient of thermal expansions (CTEs) and coefficient of cure shrinkages (CCSs)) are identified from the relaxation curves obtained by results of numerical material tests (NMTs) conducted on the periodic microstructure (unit cell). The usefulness of the proposed approach was clarified by the results of the numerical verifications.