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Peridynamic modeling of quasibrittle structures

  • Sau N
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Abstract

Construction materials research and prediction of the performance of civil engineering structures mandate the use of the best possible computational modeling tools. Conventional continuum models such as linear elastic, discrete crack, and smeared crack models have limited applications to quasibrittle structures. With the advance of computer technology, a number of discrete models have been developed, where emergent behavior appears as a consequence of the integration of simple constitutive equations. Silting in 1998 proposed a general theoretical framework called the peridynamic model. The peridynamic theory is a continuum generalization of the equations of motion of molecular dynamics. This model was formulated in order to correct the shortcomings of continuum models. Silling's peridynamic equations do not assume spatial differentiability of the displacement field and permit discontinuities to arise as part of the solution. In addition, Silling's peridynamic approach is non-local and can be considered as a generalization of conventional theory of elasticity. However, only materials with a fixed value of the Poisson's ratio can be modeled with Silling's original peridynamic formulation. In the present work Silling's peridynamic model is improved with the formulation of the micropolar peridynamic model. The micropolar peridynamic model is a generalization of the peridynamic model originally proposed by Silling in 1998. In this thesis different constitutive damage models for quasibrittle materials are proposed. Two computer models are developed based on the micropolar peridynamic model. In the first program, conventional finite elements are used in regions of the problem where the displacement is expected to be continuous and the peridynamic model is used in regions where discontinuities develop. The second program implements an explicit model that uses the dynamic relaxation method to solve the governing micropolar peridynamic equations. In this latter program written in MatLab, to increase computational efficiency, matrix functions are used as much as possible, while loops and logical blocks are used as little as possible. A number of benchmark problems are analyzed with these computer models. Results obtained with these models match fairly well with those obtained with typical laboratory experiments.

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Sau, N. (2008). Peridynamic modeling of quasibrittle structures. ProQuest Dissertations and Theses. Retrieved from http://search.proquest.com/docview/304526247?accountid=45156

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