{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/48121"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/48121","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Finite Element Simulations of Two Dimensional Peridynamic Models","abstract":"This thesis explores the science of solid mechanics via the theory of peridynamics. Peridynamics has several key advantages over the classical theory of elasticity. The most notable of which is the ease with which fractures in the the material are handled. The goal here is to study the two theories and how they relate for problems in which the classical method is known to work well. While it is known that state-based peridynamic models agree with classical elasticity as the horizon radius vanishes, similar results for bond-based models have yet to be developed. In this study, we use numerical simulations to investigate the behavior of bond-based peridynamic models under this limit for a number of cases where analytic solutions of the classical elasticity problem are known. To carry out this study, the integral-based peridynamic model is solved using the finite element method in two dimensions and compared against solutions using the classical approach.","abstract_html":"This thesis explores the science of solid mechanics via the theory of peridynamics. Peridynamics has several key advantages over the classical theory of elasticity. The most notable of which is the ease with which fractures in the the material are handled. The goal here is to study the two theories and how they relate for problems in which the classical method is known to work well. While it is known that state-based peridynamic models agree with classical elasticity as the horizon radius vanishes, similar results for bond-based models have yet to be developed. In this study, we use numerical simulations to investigate the behavior of bond-based peridynamic models under this limit for a number of cases where analytic solutions of the classical elasticity problem are known. To carry out this study, the integral-based peridynamic model is solved using the finite element method in two dimensions and compared against solutions using the classical approach.","abstract_has_math":false,"creators":["Glaws, Andrew Taylor"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Borggaard, Jeffrey T."],"committee_members":["Zietsman, Lizette","Lin, Tao"],"year":2014,"date_issued":"2014-05-27","date_published":"2014-05-27","updated_at":"2026-07-22T22:19:41Z","subjects":["Peridynamics","Elasticity","Solid Mechanics"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:3178"],"render_values":[{"text":"vt_gsexam:3178","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/48121","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Borggaard, Jeffrey T."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Zietsman, Lizette","Lin, Tao"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Glaws, Andrew Taylor"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-05-28T08:00:14Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-05-28T08:00:14Z"]},{"key":"dc:date.issued","label":"Date","values":["2014-05-27"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Peridynamics","Elasticity","Solid Mechanics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"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":["vt_gsexam:3178"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/48121"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis explores the science of solid mechanics via the theory of peridynamics. Peridynamics has several key advantages over the classical theory of elasticity. The most notable of which is the ease with which fractures in the the material are handled. The goal here is to study the two theories and how they relate for problems in which the classical method is known to work well. While it is known that state-based peridynamic models agree with classical elasticity as the horizon radius vanishes, similar results for bond-based models have yet to be developed. In this study, we use numerical simulations to investigate the behavior of bond-based peridynamic models under this limit for a number of cases where analytic solutions of the classical elasticity problem are known. To carry out this study, the integral-based peridynamic model is solved using the finite element method in two dimensions and compared against solutions using the classical approach."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Finite Element Simulations of Two Dimensional Peridynamic Models"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Borggaard, Jeffrey T."],"dc:contributor.committeemember":["Zietsman, Lizette","Lin, Tao"],"dc:contributor.department":["Mathematics"],"dc:creator":["Glaws, Andrew Taylor"],"dc:date.accessioned":["2014-05-28T08:00:14Z"],"dc:date.available":["2014-05-28T08:00:14Z"],"dc:date.issued":["2014-05-27"],"dc:description.abstract":["This thesis explores the science of solid mechanics via the theory of peridynamics. Peridynamics has several key advantages over the classical theory of elasticity. The most notable of which is the ease with which fractures in the the material are handled. The goal here is to study the two theories and how they relate for problems in which the classical method is known to work well. While it is known that state-based peridynamic models agree with classical elasticity as the horizon radius vanishes, similar results for bond-based models have yet to be developed. In this study, we use numerical simulations to investigate the behavior of bond-based peridynamic models under this limit for a number of cases where analytic solutions of the classical elasticity problem are known. 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