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AuthorQuing Yu
TitleComputational Homogenization for the Advanced Materials and Structures with Multiple Spatial and Temporal Scales
Year2001
SchoolSCOREC - RPI
Abstract This thesis is aimed at exploring a class of multiscale physical processes using asymptotic homogenization method. The emphasis is given to establishing (i) the homogenized descriptions for obtaining the global response fields, and (ii) the global-local interscale relations among the response fields at various scales. The multiple length scales are defined in either space or time domain. The interactions between multiple spatial and temporal scales are also studied for the multi-physical behavior of composite materials. Four major topics are covered in this research: * Damage evolution in brittle composites A nonlocal damage theory for obtaining numerical approximation to a boundary value problem describing damage phenomena in brittle composites is developed. The damage evolution is defined on the smallest scale of interest and described within the context of Continuum Damage Mechanics. Nonlocal damage theory is developed by introducing the concept of nonlocal phase fields. The mathematical homogenization method based on the asymptotic expansion is generalized to account for damage effects in heterogeneous media. A two-scale nonlocal damage mechanics model is developed first and then extended to the case of three scales for the composites with heterogeneous microphases. * Fatigue in brittle composites By extending the damage cumulative law defined for the monotonic loading to the case of cyclic loading, the homogenization framework of the two-scale nonlocal damage theory is applied to the fatigue damage in brittle composites. A novel accelerating technique to alleviate the computational inefficiency due to the coupling between damage evolution and the mechanical response is developed for the integration of the fatigue damage cumulative law. * Multiple temporal scale analysis for the rate-dependent solids under locally periodic loading For the rate-dependent solids under locally periodic loading, the multiple temporal scales are determined by the material intrinsic time, such as creep time, and the frequency of the external loading. The temporal homogenization is developed for two rate-dependent material models, including the Maxwell viscoelastic model and the power-law viscoplastic model, as illustrative examples. * Interactions among multiple spatial-temporal scales and multiple physical processes The coupling of multiple physical processes may introduce additional temporal scale separations which interact with the existing multiple length scales in space and time on a single physical process. A general setting of the space-time asymptotic homogenization process is developed and then applied to the coupled thermo-viscoelastic composites with microscopically periodic mechanical and thermal properties. The validity limits of the proposed spatial-temporal homogenized solution are established.