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Adam C. Powell, IV. Lok, Yi Cheung Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. Massachusetts Institute of Technology. Department of Materials Science and Engineering 2007-02-21T13:07:14Z 2007-02-21T13:07:14Z 2006 2006 http://hdl.handle.net/1721.1/36212 76906378 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2006. Includes bibliographical references (p. 112-113). The Boundary Element Method is used to study the interaction of second phase objects in a material. In particular, this study examines the relationship between stress parameters, such as stress concentration and normal traction, and geometrical parameters such as separation distance and orientation. The use of BEM enables easy manipulation of internal objects and rapid re-calculation in a series of simulations. Additional library functions are added to Julian, a general BEM solver, to expand its functionality to include elasticity calculation, inclusion modeling, and shape optimization with parallel processing. With a few thousand nodes, it is found that computation time scales as O(V), where N is the resolution of the mesh in each direction. An accuracy of over 99% is achieved in many benchmarks. A spherical cavity next to an inclusion is found to have higher stress concentration when aligned parallel to the loading direction. Stress analysis on a pair of neighboring cavities shows relatively small (less than 10%) increase in stress concentration beyond a separation of 0.5 diameter. (cont.) While highest stress is observed when two cavities are aligned perpendicular to loading direction at very close separation, the highest stress configuration deviates from that alignment to almost +/- 30 degrees as separation increases. The radius of interaction is found to be determined by the larger of two second phase objects and is larger for a cavity surrounded by eight cavities in three dimensions. Our result suggests that a 15% weight saving is possible in a closed-cell foam for less than 10% increase in stress concentration due to the presence of immediate neighbors. by Yi Cheung Lok. Ph.D. 113 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Materials Science and Engineering. Boundary element modeling of elasticity in materials in terms of distribution of second phase structures Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="de367dca-3d9f-4a8d-b36b-493625dd15bf"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Boundary element modeling of elasticity in materials in terms of distribution of second phase structures</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2006</PublicationDate> <Authors> <Author> <DisplayName>Lok, Yi Cheung</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Materials Science and Engineering.</Keyword> <Abstract>The Boundary Element Method is used to study the interaction of second phase objects in a material. In particular, this study examines the relationship between stress parameters, such as stress concentration and normal traction, and geometrical parameters such as separation distance and orientation. The use of BEM enables easy manipulation of internal objects and rapid re-calculation in a series of simulations. Additional library functions are added to Julian, a general BEM solver, to expand its functionality to include elasticity calculation, inclusion modeling, and shape optimization with parallel processing. With a few thousand nodes, it is found that computation time scales as O(V), where N is the resolution of the mesh in each direction. An accuracy of over 99% is achieved in many benchmarks. A spherical cavity next to an inclusion is found to have higher stress concentration when aligned parallel to the loading direction. Stress analysis on a pair of neighboring cavities shows relatively small (less than 10%) increase in stress concentration beyond a separation of 0.5 diameter.</Abstract> <Abstract>(cont.) While highest stress is observed when two cavities are aligned perpendicular to loading direction at very close separation, the highest stress configuration deviates from that alignment to almost +/- 30 degrees as separation increases. The radius of interaction is found to be determined by the larger of two second phase objects and is larger for a cavity surrounded by eight cavities in three dimensions. Our result suggests that a 15% weight saving is possible in a closed-cell foam for less than 10% increase in stress concentration due to the presence of immediate neighbors.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>