Abstract

A multiscale model based on finite element (FE) and the Parametric High-Fidelity-GeneralizedMethod-of-Cells (PHFGMC) micromechanical model was formulated and implemented to solve the compression problem in unidirectional IM7/977-3 carbon epoxy composite. The nonlinear PHFGMC governing equations were obtained from a two-layered (local-global) virtual work principle and solved using a incremental-iterative formulation. In addition, the semi-analytical modified Lo and Chim failure criterion (based on the buckling of Timoshenko's beam) for unidirectional fiber-reinforced composite materials under compression [1] was adopted and combined with the FE-PHFGMC multiscale model. In this study, the criterion was employed for the general case of a multi-axial loading state accompanied with a nonlinear polymeric matrix behavior, where the local and thus effective properties of the composite change continuously throughout the loading path. Therefore the predicted lamina strength was incrementally reevaluated. In the present model, the use of the nonlinear constitutive model RambergOsgood was used for the matrix media and a linear-elastic transversely-isotropic law for the fiber, as common for carbon fibrous composites. This extends the existing criterion to account for the material microstructure with a refined parametric discretization, as well as the effect of a nonlinear constitutive law. The advantage of the proposed model is to predict the compressive damage (kink band formation and its width) and the compressive strength (within 11% of experimental data).

Abstract

Biot's theory of coupled mechanical-transport behavior of porous materials is applied in the framework of discrete mesoscale modeling. The contribution presents asymptotic expansion homogenization of the discrete poromechanical model. The macroscale becomes homogeneous and continuous and contains all the coupling effects. In contrast, the microscale is discrete and completely decoupled, separate representative volume elements (RVEs) appear for mechanical and mass transport problems. Linear elastic material behavior is assumed, therefore response of the RVEs can be pre-computed in advance and used repetitively at integration points of the macroscopic model.