{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/20893"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/20893","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the stress in an internally constrained elastic material","abstract":"The admissible deformation gradients at an internally constrained elastic material point form a closed submanifold in the space of invertible tensors. This submanifold, the constraint manifold, is described locally in terms of a manifold structure on the invertible tensors. Constraint functions arise naturally from the submanifold properties of the constraint manifold.","abstract_html":"The admissible deformation gradients at an internally constrained elastic material point form a closed submanifold in the space of invertible tensors. This submanifold, the constraint manifold, is described locally in terms of a manifold structure on the invertible tensors. Constraint functions arise naturally from the submanifold properties of the constraint manifold.","abstract_has_math":false,"creators":["Marlow, Randall Scot"],"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":["Carlson, Donald E."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:52:19Z","date_published":"2011-05-07T12:52:19Z","updated_at":"2026-07-22T22:25:16Z","subjects":["Applied Mechanics","Mathematics"],"languages":["eng"],"rights":["Copyright 1989 Marlow, Randall Scot"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8924892","(UMI)AAI8924892"],"render_values":[{"text":"AAI8924892","href":null,"code":true},{"text":"(UMI)AAI8924892","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/20893","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Carlson, Donald E."]},{"key":"dc:creator","label":"Author","values":["Marlow, Randall Scot"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:52:19Z","10000-01-01","1989"]},{"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","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Marlow, Randall Scot"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8924892","(UMI)AAI8924892","http://hdl.handle.net/2142/20893"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The admissible deformation gradients at an internally constrained elastic material point form a closed submanifold in the space of invertible tensors. This submanifold, the constraint manifold, is described locally in terms of a manifold structure on the invertible tensors. Constraint functions arise naturally from the submanifold properties of the constraint manifold.","The stress in the constrained material is determined by the deformation gradient only to within an additive reaction stress. A representation for the reaction stress involving the gradients of the constraint functions is derived. The determinate stress is assumed to be given by a function defined on the constraint manifold and having normalized values.","Symmetry of internally constrained elastic materials is investigated, as well as the principle of material indifference. These basic concepts are discussed in relation to the stress spaces.","\"A theory of constrained elastic materials for \"\"small\"\" displacement gradients is derived directly from the general theory. Since an explicit relation for the reaction stress exists, the derivation is straight-forward. The results are significantly different from what has been done previously. To illustrate the differences, the torsion of an inextensible cylinder is discussed.\"","Made available in DSpace on 2011-05-07T12:52:19Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924892.pdf: 1306210 bytes, checksum: fac263062f8f8a6210bc75fcfd1cbc14 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:47:00Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:21:10-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["On the stress in an internally constrained elastic material"]}]}],"canonical_facts":{"dc:contributor":["Carlson, Donald E."],"dc:creator":["Marlow, Randall Scot"],"dc:date":["2011-05-07T12:52:19Z","10000-01-01","1989"],"dc:description":["The admissible deformation gradients at an internally constrained elastic material point form a closed submanifold in the space of invertible tensors. This submanifold, the constraint manifold, is described locally in terms of a manifold structure on the invertible tensors. Constraint functions arise naturally from the submanifold properties of the constraint manifold.","The stress in the constrained material is determined by the deformation gradient only to within an additive reaction stress. A representation for the reaction stress involving the gradients of the constraint functions is derived. The determinate stress is assumed to be given by a function defined on the constraint manifold and having normalized values.","Symmetry of internally constrained elastic materials is investigated, as well as the principle of material indifference. These basic concepts are discussed in relation to the stress spaces.","\"A theory of constrained elastic materials for \"\"small\"\" displacement gradients is derived directly from the general theory. Since an explicit relation for the reaction stress exists, the derivation is straight-forward. The results are significantly different from what has been done previously. To illustrate the differences, the torsion of an inextensible cylinder is discussed.\"","Made available in DSpace on 2011-05-07T12:52:19Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924892.pdf: 1306210 bytes, checksum: fac263062f8f8a6210bc75fcfd1cbc14 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:47:00Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:21:10-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI8924892","(UMI)AAI8924892","http://hdl.handle.net/2142/20893"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Marlow, Randall Scot"],"dc:subject":["Applied Mechanics","Mathematics"],"dc:title":["On the stress in an internally constrained elastic material"],"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":"2026-07-22T22:25:16Z"}