{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71684"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71684","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Kinematic Constraints in Nonlinear Elasticity (Incompressibility, Perturbation, Convergence)","abstract":"The constitutive equations for a material which approximately satisfies a kinematic constraint are investigated for the particular case of an elastic material.","abstract_html":"The constitutive equations for a material which approximately satisfies a kinematic constraint are investigated for the particular case of an elastic material.","abstract_has_math":false,"creators":["Reed, John Keith"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical and Applied Mechanics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T19:12:35Z","date_published":"2014-12-16T19:12:35Z","updated_at":"2026-07-22T22:26:05Z","subjects":["Applied Mechanics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8600292"],"render_values":[{"text":"(UMI)AAI8600292","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71684","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Reed, John Keith"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T19:12:35Z","10000-01-01","1985"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical and Applied Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71684","(UMI)AAI8600292"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The constitutive equations for a material which approximately satisfies a kinematic constraint are investigated for the particular case of an elastic material.","Kinematically constrained materials in elasticity describe materials in which certain deformations are ruled out a priori. Since a constrained material is an idealization, we give a definition of a material which is almost constrained. The definition is based on the constitutive equation for the stress, not on the strain energy. The definition is constructed so that any material satisfying the definition may deviate only slightly from the constraint. Also, the stress must give the constrained theory in the limit as the constraint is satisfied.","A perturbation scheme based on the definition is given, with the constrained material as the lowest order approximation. Uniqueness for the higher order linear equations is determined.","Convergence for an almost incompressible material which is hyperelastic to that of an incompressible material is shown. The hypotheses on the strain energy needed to show convergence are compared and contrasted to penalty methods.","Made available in DSpace on 2014-12-16T19:12:35Z (GMT). No. of bitstreams: 1 8600292.pdf: 3419985 bytes, checksum: 48749d107693c9200abcc3c545db94fb (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 71850 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","158 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."]},{"key":"dc:title","label":"Title","values":["Kinematic Constraints in Nonlinear Elasticity (Incompressibility, Perturbation, Convergence)"]}]}],"canonical_facts":{"dc:creator":["Reed, John Keith"],"dc:date":["2014-12-16T19:12:35Z","10000-01-01","1985"],"dc:description":["The constitutive equations for a material which approximately satisfies a kinematic constraint are investigated for the particular case of an elastic material.","Kinematically constrained materials in elasticity describe materials in which certain deformations are ruled out a priori. Since a constrained material is an idealization, we give a definition of a material which is almost constrained. The definition is based on the constitutive equation for the stress, not on the strain energy. The definition is constructed so that any material satisfying the definition may deviate only slightly from the constraint. Also, the stress must give the constrained theory in the limit as the constraint is satisfied.","A perturbation scheme based on the definition is given, with the constrained material as the lowest order approximation. Uniqueness for the higher order linear equations is determined.","Convergence for an almost incompressible material which is hyperelastic to that of an incompressible material is shown. The hypotheses on the strain energy needed to show convergence are compared and contrasted to penalty methods.","Made available in DSpace on 2014-12-16T19:12:35Z (GMT). No. of bitstreams: 1 8600292.pdf: 3419985 bytes, checksum: 48749d107693c9200abcc3c545db94fb (MD5) Previous issue date: 1985","Embargo set by: Seth Robbins for item 71850 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","158 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985."],"dc:identifier":["http://hdl.handle.net/2142/71684","(UMI)AAI8600292"],"dc:subject":["Applied Mechanics"],"dc:title":["Kinematic Constraints in Nonlinear Elasticity (Incompressibility, Perturbation, Convergence)"],"dc:type":["text"],"thesis:degree_discipline":["Theoretical and Applied Mechanics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:05Z"}