Composite Visco Elastic Properties Of Multi-scale Prediction Algorithms And Numerical Simulation

Composite materials often exhibit viscoelastic behavior. The creep and relaxation of composite materials may lead the structures losing their function. The wide applications of composite structures make the research of the composite material's viscoelastic properties become an important task. Recently, this research has attracted many attentions. The effective relaxation moduli of composites are dependent on the microstructure and viscoelastic properties of components of composite materials. Thus, materials with specific viscoelastic properties can be obtained by designing the microstructure and selecting the components of composite materials. A key problem is to determine the relationship of the macroscopic viscoelastic properties with the microstructure of the materials. In this thesis, homogenization-based methods for predicting the viscoelastic property of multi-layered composite materials and unidirectional fiber reinforced composite materials are presented, and the relation curves of the moduli of materials with and inclusion volume fraction are given in the article. The contents and the results of this research include:1. The engineering background and the importance of composition material research are presented. A review of the research developments in composite mechanics is given. And then the brief description of the researches in micro- mechanics is presented. (See Chapter 1)2. The basic conception of the homogenization theory is given, and then by Laplace transforming, the formulae for predicting the viscoelastic relaxation moduli in Laplace transformed domain are obtained from the governing equation of the problem of composite materials. (See Chapter 2)3. A homogenization-based method for predicting the viscoelastic property of multi-layered composite material is presented. By Laplace transforming the governing equation of the viscoellastic problem of jointed rock, the dependent relation of the Laplace transformation of the effective relaxation modulus of jointed rock on the joint distribution was derived by applying the homogenization method in Laplace transformed domain. Then, the effective relaxation modulus was obtained from the inverse transformation. Numerical example was presented. On base of those, effective relaxation moduli could be curve-fitted by the function form of the three-parameter solid model. The simpler explicit formulae for the prediction of the viscoelasticity property are obtained. (See Chapter 3)4. A homogenization-based method for predicting the viscoelastic property of unidirectional fiber reinforced composite materials is presented. By Laplace transforming the governing equation of the problem of unidirectional fiber reinforced composite materials, the formulae for predicting the viscoelastic relaxation moduli in Laplace transformed domain are obtained. According to correspondence principle of viscoellastic mechanics and elastic, mechanics, the results of effective moduli for several s are obtained by using the finite element method of the homogenization. Then effective relaxation moduli should be curve-fitted, according to the viscoelastic relaxation modulus formulae of many viscoelastic materials. The viscoelastic relaxation moduli in time domain are obtained by the inverse Laplace transform of the curve-fitted formulae. The method takes advantage of rational curve-fitted formulae and avoids complicated numerical inverse Laplace transform. That makes the prediction of viscoelastic relaxation moduli easy. The numerical example was presented in the end of this paper. (See Chapter 4)The work of this thesis is supported by National Nature Science Foundation of China (No. 10072016), and by Special Founding for University Key Teachers of Education Ministry of China and the Open Research Fund of the State Key Lab of Structure strength and Vibration, Xi'an Jiaotong University.