Composite Elastic Mechanical Properties Of Numerical Prediction

Composite materials have attracted dramatic attention in the last few decades for their outstanding properties and the main focus of this thesis concerns the predictions of their macroscopically elastic moduli. To predict the effective moduli of composite materials, a direct modeling strategy based on the finite element method is investigated and the well-known Hashin-Shtrikman bounds and the general self-consistent method are reintroduced for the validation and comparison purposes. Considering the extensive and relatively ripe study on the traditional inclusion-matrix composite materials, this thesis addresses the non-particulate composites, in which the matrix and particulate (or fiber) phases can not be distinguished clearly. The specific works finished are listed as below:1. The classical bounds and analytical models on the elastic moduli of composite materials are reviewed and analyzed. The well-known Hashin-Shtrikman bounds and Voigt-Reuss bounds are compared under the different scenarios of the elastic property contrast of constituent phases. The connections between the Hashin-Shtrikman bounds and the analytical models (the general consistent method, the Mori-Tanaka method and the Halpin-Tsai method) are investigated numerically by applying to bi-continuous composite materials.2. The direct modeling strategy based on the finite element method is proposed. Simply stated, the model is constructed from equal-size domains, which are then assigned with material labels to distinguish constituent phases and further divided into several finite elements to mimic the microstructure of the composite materials. Based on such method, the two-dimension and three-dimension sample models have been constructed.3. The direct modeling strategy is applied to build up bi-continuous composite materials and the successive finite element analysis (FEA) gives out the predictions of the effective elastic moduli of the constructed samples under the planar and three-dimensional settings. The validity of the prediction is endorsed by the agreement of the FEA results to the corresponding Hashin-Shtrikman bounds. The comparison of the predictions from the direct modeling strategy and the general consistent method shows that classical analytical models for inclusion-matrix composites can not be simply extended to non-inclusion composites.4. The effects of the two parameters introduced by the modeling process, the size of the initial domains and their further refinement (element density) on the predictions of the effective elastic moduli are discussed to provide indications for selecting the parameters properly to reduce the computation time while the accuracy issue is not affected. With the proper selection of the two modeling parameters, the effect of the constituent phase's volume fraction on the elastic property of the composites is investigated.In short, the direct modeling strategy based the finite element method proposed in this dissertation can provide valuable information on the elastic properties of non-particulate composites with random constituent phase distribution when only the phase properties and volume fractions of each constituent phase are available.