Numerical characterization of effective mechanical properties of composite/porous materials using pFFT-accelerated BEM

Characterization of composite/porous materials, particularly those with randomly distributed inclusions/voids of arbitrary shapes and sizes is of great importance in various applications. Due to the complexity of geometries and the involved physical processes, to date, an accurate approach for mechanical characterization, particularly dynamic characterization, of composite/porous materials is yet to be developed. Despite the great effort that has been devoted on the development of theoretical models, almost all of the existing models employ various assumptions. The implications of these assumptions are difficult to quantify theoretically and hence the application scope of these theoretical models is limited and difficult to define. For experimental measurements, in addition to the associated high cost, noise is another obstacle, which hinders its application in dynamic characterization.;The objective of this thesis is to develop an efficient numerical method to characterize composite/porous materials with randomly distributed inclusions/voids of arbitrary shapes and sizes. Due to its advantages in mesh generation and the treatment of boundary conditions at infinity, the pre-corrected Fast Fourier Transform (pFFT) accelerated boundary element method (BEM) is developed. A numerical technique based on multiple scattering theory is also developed for composite/porous materials with inclusions/voids of simple shapes. For the conventional BEM, the computational cost is of Niter x O(N2). N iter is the number of iterations and N is the number of elements. In order to reduce the computational cost, two techniques are employed. One is the pre-corrected Fast Fourier Transform algorithm to reduce the computational cost of each iteration from O( N2) to O(NlogN). The other is the block diagonal preconditioning technique to accelerate convergence rate.;Using the developed pFFT accelerated BEM, the effective Young's, shear and bulk moduli and Poisson's ratio of 3D porous materials with uniformly randomly distributed pores are calculated as functions of porosities. The shape effects of pores on the Young's modulus and Poisson's ratio are also investigated using ellipsoidal ones. For dynamic characterization, a new approach to compute the effective dynamic properties namely phase velocity and attenuation coefficient of coherent waves in composite/porous materials is proposed. Based on this approach, the phase velocity and attenuation coefficient of coherent SH waves propagating in four types of unidirectional fiber-reinforced composite materials are calculated. The influence of frequencies and volume fractions on both phase velocity and attenuation coefficient is investigated. A macro model for the attenuation coefficient of coherent SH waves in porous materials with unidirectional elliptical cylindrical voids of different aspect ratios is constructed. This model relates the attenuation coefficient with two parameters: the mean scattering cross section and number density of voids. Numerical results show that this model works better for cases with a low porosity. For cases with circular cylindrical voids, this model works well up to a porosity level of 10%. Finally, validation of several representative theoretical models using numerical results has been conducted. Results show that some models perform obviously better than the others. However, at high volume fractions, the performance of all the models considered deteriorates. For such cases, numerical simulation is the only viable approach.;Keywords: composite material; porous material; boundary element method; acceleration algorithm; pre-conditioner; coherent wave; phase velocity; attenuation coefficient.