HOMOGENIZATION OF THE DYNAMICAL BEHAVIOUR OF HETEROGENEOUS MATERIALS

Abstract

In the stress analyses of structures, density, elastic modulus and Poisson’s ratio are the material parameters used to characterize the linear elastic behaviour of heterogeneous materials such as composites, porous media and polycrystalline materials. However, these three parameters are insufficient to describe the dynamic behaviour of heterogeneous materials when the dominant elastic stress wavelength is smaller or in the same order of the characteristic length of the meso-scale structure of the heterogeneous material, which may cause the macroscopic attenuation and dispersion effects during the wave propagation. The attenuation of the high frequency stress wave propagation in heterogeneous materials is a frequently observed phenomenon in various engineering and material problems. For example, seismic intensity, which measures the severity of the earthquake-induced ground shock at a given location, decreases with the increase of distance to the epicentre; porous media like cellular material and foam are widely used in sound absorption to attenuate the noise; The meso-scale polycrystalline structures in metal and ceramic materials significantly contribute to the decline of the received signal in industrial ultrasonic detection. In order to perform efficient analysis at the structural level, it is necessary to develop homogenised model for heterogeneous isotropic material whose meso-scale characteristics can be represented by ‘smeared’ macroscopic parameters. A ‘pseudo-damping’ method is proposed in this study to describe the wave attenuation phenomena caused by the meso-scale structure in a homogenized material model. To characterize the pseudo-damping parameter, the attenuation effect caused by the multiple scattering of incident waves must be quantified by analytical, numerical or experimental method. In the past decades, significant progresses on analytical predicting of attenuation effect in the elastic wave propagation process have been made, such as global matrix method for multi-layered media, multiple scattering theory for composite material and unified theory for polycrystalline materials. But there are still limitations on their numerical verifications, lack of practical dynamic homogenization models and lack of their engineering applications for the descriptions of the macroscopic attenuation effects caused by the wave scattering at meso-scale scatterers or inclusions. This thesis starts the research from predicting the attenuation effect in the steady-state SH dynamic behaviour of a one-dimensional two-phase multi-layer media, in which a new analytical method based on global matrix method is developed. This new analytical model is verified using a finite element model sandwiched by non-reflective boundaries. Two Monte Carlo studies are conducted to investigate the influence of randomness of segment length on the wave propagation behaviour and band structure. An elastic model with pseudo-damping is proposed to describe the statically homogenized wave behaviour in the multi-layer medium. Then, the research is extended to two-dimensional porous media. An averaging technique based on the combination of the eigenfunction expansion method and the collaboration method is developed to investigate the multiple scattering effect of the SH wave (a shear wave where the particle motion is out of the plane containing the particles before excitation) propagation in a porous medium. The semi-analytical averaging technique is proposed based on the statistical volume element (SVE) and Monto Carlo methods to characterize the macroscopic attenuation phenomena of the stress wave propagation in a porous solid caused by the multiple scattering effects, which is verified by finite element analysis. An elastic model with pseudo-damping is developed to describe the macroscopic attenuation effects of SH waves in porous media. Finally, this research is extended to two-dimensional polycrystalline materials. A new 2D finite element mo

Date of Award	31 Dec 2021
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Zhenmin Zou (Supervisor) & Qing Li (Supervisor)