Micromechanical models based on hypersingular integro-differential equations for analyzing weak interfaces between dissimilar orthotropic materials

Abstract

This thesis is concerned with the development and formulation of micromechanical models for estimating the e¤ective sti¤ness coe¢ cients of a microscopically damaged interface between dissimilar orthotropic materials under antiplane and inplane deformations. The e¤ective sti¤ness coe¢ cients are important parameters in the macro-level spring-like model for a weak interface. The microscopically damaged interface is modeled as containing a periodic array of micro-cracks. Three di¤erent micromechanical models are proposed for the micro-cracked interface. The …rst model is the so called three-phase model which highly simpli…es a period interval of the interface into three parts: (i) a representative microcrack, (ii) perfectly bonded parts and (iii) e¤ective regions with an unknown sti¤ness. The only details of the original micro-cracked interface captured in the three-phase models are the density of the micro-cracks and the average micro-crack length which is the length of the representative micro-crack. In the second model, all the micro-cracks are of the same length and are evenly distributed throughout the interface. Like the three-phase model, this model is a highly simpli…ed one having only the density and the average length of the micro-cracks as micro-details of the micro-cracked interface. As may be expected, the values of the e¤ective sti¤ness coe¢ cients calculated using the second model are close to the ones predicted by the three-phase model. i I would like to express my most sincere gratitude to my supervisor Professor Ang Whye Teong for the consistent guidance he had given me throughout my entire Ph.D. studies. I have bene…ted from his expertise in the boundary element method, general knowledge in mathematics and sharp attention to details in research matters. His advice and encouragement had helped me to overcome di¢ culties encountered during the research and writing of this thesis. I would also like to express my deep appreciation to my co-supervisor Professor Fan Hui. He had provided me with valuable suggestions and comments on the micromechanical aspects of this research project. I am impressed by his academic insights and serious attitude to research work. Special thanks are due to all my seniors for sharing their research experience with me and always being there when I requested their help. Lastly but not least, I am eternally grateful for the constant encouragement, care and support from my beloved parents and loving …ancé.