{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/42393"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/42393","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Mathematical modeling of adhesive layer cracks utilizing integral equations","abstract":"Within recent years, Crack analysis in adhesive layers has become a topic of interest for many researchers. A common model which is used incorporates a 3-region elasticity problem consisting of only 2 materials, the adhesive layer bounded by 2 layers of a stiffer elastic substrate. Cracks have been experimentally observed to propagate in straight paths as well as wavy paths within the adhesive layer and even at its boundaries. A theoretical model based on work done by Fleck, Hutchinson, and Suo (1991) is used to study crack path selection. Complex stress potential functions are employed to develop a symbolic derivation. The method of distributed dislocations is utilized to represent the crack. A series of Chebyshev polynomials to approximate the unknown dislocations. The resulting integral equations are solved through the collocation method and the series coefficients are recovered. Several numerical packages, Mathcad 5.0+ and Mathematica 2.2.1, were used to study the computational aspects of the problem. The focus of the research was to develop efficient modular software packages to be run on a standard PC system. Several numerical techniques were utilized to reduce computational time and control the numerical accuracy of the problem. Some of these techniques included a \"numerical freeze\" algorithm, Fast Fourier Transform techniques, Gaussian inversion, Gaussian quadrature and Romberg quadrature. The numerically sensitive regions were identified. Finally, recommendations for future work and possible solutions to handle the numerically sensitive regions were presented.","abstract_html":"Within recent years, Crack analysis in adhesive layers has become a topic of interest for many researchers. A common model which is used incorporates a 3-region elasticity problem consisting of only 2 materials, the adhesive layer bounded by 2 layers of a stiffer elastic substrate. Cracks have been experimentally observed to propagate in straight paths as well as wavy paths within the adhesive layer and even at its boundaries. A theoretical model based on work done by Fleck, Hutchinson, and Suo (1991) is used to study crack path selection. Complex stress potential functions are employed to develop a symbolic derivation. The method of distributed dislocations is utilized to represent the crack. A series of Chebyshev polynomials to approximate the unknown dislocations. The resulting integral equations are solved through the collocation method and the series coefficients are recovered. Several numerical packages, Mathcad 5.0+ and Mathematica 2.2.1, were used to study the computational aspects of the problem. The focus of the research was to develop efficient modular software packages to be run on a standard PC system. Several numerical techniques were utilized to reduce computational time and control the numerical accuracy of the problem. Some of these techniques included a "numerical freeze" algorithm, Fast Fourier Transform techniques, Gaussian inversion, Gaussian quadrature and Romberg quadrature. The numerically sensitive regions were identified. Finally, recommendations for future work and possible solutions to handle the numerically sensitive regions were presented.","abstract_has_math":false,"creators":["Graffeo, Jeffrey K."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Giurgiutiu, Victor"],"committee_members":["Dillard, David A.","Reifsnider, Kenneth L."],"year":1995,"date_issued":"1995-08-05","date_published":"1995-08-05","updated_at":"2026-07-22T22:20:09Z","subjects":["crack analysis"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05022009-040448"],"render_values":[{"text":"etd-05022009-040448","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/42393","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Giurgiutiu, Victor"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Dillard, David A.","Reifsnider, Kenneth L."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Mechanics"]},{"key":"dc:creator","label":"Author","values":["Graffeo, Jeffrey K."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:35:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:35:13Z","2009-05-02"]},{"key":"dc:date.issued","label":"Date","values":["1995-08-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["crack analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05022009-040448"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/42393"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Within recent years, Crack analysis in adhesive layers has become a topic of interest for many researchers. A common model which is used incorporates a 3-region elasticity problem consisting of only 2 materials, the adhesive layer bounded by 2 layers of a stiffer elastic substrate. Cracks have been experimentally observed to propagate in straight paths as well as wavy paths within the adhesive layer and even at its boundaries. A theoretical model based on work done by Fleck, Hutchinson, and Suo (1991) is used to study crack path selection. Complex stress potential functions are employed to develop a symbolic derivation. The method of distributed dislocations is utilized to represent the crack. A series of Chebyshev polynomials to approximate the unknown dislocations. The resulting integral equations are solved through the collocation method and the series coefficients are recovered. Several numerical packages, Mathcad 5.0+ and Mathematica 2.2.1, were used to study the computational aspects of the problem. The focus of the research was to develop efficient modular software packages to be run on a standard PC system. Several numerical techniques were utilized to reduce computational time and control the numerical accuracy of the problem. Some of these techniques included a \"numerical freeze\" algorithm, Fast Fourier Transform techniques, Gaussian inversion, Gaussian quadrature and Romberg quadrature. The numerically sensitive regions were identified. Finally, recommendations for future work and possible solutions to handle the numerically sensitive regions were presented."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Mathematical modeling of adhesive layer cracks utilizing integral equations"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Giurgiutiu, Victor"],"dc:contributor.committeemember":["Dillard, David A.","Reifsnider, Kenneth L."],"dc:contributor.department":["Engineering Mechanics"],"dc:creator":["Graffeo, Jeffrey K."],"dc:date.accessioned":["2014-03-14T21:35:13Z"],"dc:date.available":["2014-03-14T21:35:13Z","2009-05-02"],"dc:date.issued":["1995-08-05"],"dc:description.abstract":["Within recent years, Crack analysis in adhesive layers has become a topic of interest for many researchers. A common model which is used incorporates a 3-region elasticity problem consisting of only 2 materials, the adhesive layer bounded by 2 layers of a stiffer elastic substrate. Cracks have been experimentally observed to propagate in straight paths as well as wavy paths within the adhesive layer and even at its boundaries. A theoretical model based on work done by Fleck, Hutchinson, and Suo (1991) is used to study crack path selection. Complex stress potential functions are employed to develop a symbolic derivation. The method of distributed dislocations is utilized to represent the crack. A series of Chebyshev polynomials to approximate the unknown dislocations. The resulting integral equations are solved through the collocation method and the series coefficients are recovered. Several numerical packages, Mathcad 5.0+ and Mathematica 2.2.1, were used to study the computational aspects of the problem. The focus of the research was to develop efficient modular software packages to be run on a standard PC system. Several numerical techniques were utilized to reduce computational time and control the numerical accuracy of the problem. Some of these techniques included a \"numerical freeze\" algorithm, Fast Fourier Transform techniques, Gaussian inversion, Gaussian quadrature and Romberg quadrature. The numerically sensitive regions were identified. 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