{"id":{"repo_id":"trento","oai_identifier":"oai:iris.unitn.it:11572/367875"},"canonical_url":"https://search.dev.ndltd.org/etd/trento/oai:iris.unitn.it:11572/367875","repository":{"repo_id":"trento","name":"Università degli Studi di Trento","base_url":"https://iris.unitn.it/oai/request"},"display":{"title":"Homogenization of heterogeneous Cauchy-elastic materials leads to Mindlin second-gradient elasticity","abstract":"Through a second-order homogenization procedure, the explicit relation is obtained between the non-local parameters of a second gradient elastic ma- terial and the microstructure of a composite material. This result is instru- mental for the definition of higher-order models, to be used for the analysis of mechanics at micro- and nano-scale, where size-effects become important. The obtained relation is valid for both plane and three-dimensional prob- lems and generalizes earlier findings by Bigoni and Drugan (Analytical deriva- tion of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech., 2007, 74, 741753) from several points of view: i) the result holds for anisotropic phases with spherical or circular ellipsoid of inertia; ii) the displacement boundary conditions considered in the homogenization procedure is independent of the characteristics of the material; iii) a perfect energy match is found between heterogeneous and equivalent materials (instead of an optimal bound). From the obtained solution it follows that the equivalent second-gradient Mindlin elastic solid: a) is positive definite only when the discrepancy tensor is negative defined; b) the non-local material symmetries are the same of the discrepancy tensor; c) the non-local effective behaviour is affected by the shape of the RVE, which does not influence the first-order homogenized response. Finally, explicit derivations of non-local parameters from heterogeneous Cauchy elastic composites are obtained in particular cases.","abstract_html":"Through a second-order homogenization procedure, the explicit relation is obtained between the non-local parameters of a second gradient elastic ma- terial and the microstructure of a composite material. This result is instru- mental for the definition of higher-order models, to be used for the analysis of mechanics at micro- and nano-scale, where size-effects become important. The obtained relation is valid for both plane and three-dimensional prob- lems and generalizes earlier findings by Bigoni and Drugan (Analytical deriva- tion of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech., 2007, 74, 741753) from several points of view: i) the result holds for anisotropic phases with spherical or circular ellipsoid of inertia; ii) the displacement boundary conditions considered in the homogenization procedure is independent of the characteristics of the material; iii) a perfect energy match is found between heterogeneous and equivalent materials (instead of an optimal bound). From the obtained solution it follows that the equivalent second-gradient Mindlin elastic solid: a) is positive definite only when the discrepancy tensor is negative defined; b) the non-local material symmetries are the same of the discrepancy tensor; c) the non-local effective behaviour is affected by the shape of the RVE, which does not influence the first-order homogenized response. Finally, explicit derivations of non-local parameters from heterogeneous Cauchy elastic composites are obtained in particular cases.","abstract_has_math":false,"creators":["Bacca, Mattia"],"institution":"Università degli studi di Trento","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Bigoni, Davide"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-24T05:04:24Z","subjects":["Settore ICAR/08 - Scienza delle Costruzioni"],"languages":["eng"],"rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["http://dx.doi.org/10.15168/11572_367875","10.15168/11572_367875"],"render_values":[{"text":"http://dx.doi.org/10.15168/11572_367875","href":"http://dx.doi.org/10.15168/11572_367875","code":true},{"text":"10.15168/11572_367875","href":"https://doi.org/10.15168/11572_367875","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/11572/367875","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bacca, Mattia","Bigoni, Davide"]},{"key":"dc:creator","label":"Author","values":["Bacca, Mattia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013"]},{"key":"dc:publisher","label":"Institution","values":["Università degli studi di Trento","place:TRENTO"]},{"key":"dc:relation","label":"Dc Relation","values":["firstpage:1","lastpage:84","numberofpages:84"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Settore ICAR/08 - Scienza delle Costruzioni"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/11572/367875","http://dx.doi.org/10.15168/11572_367875","10.15168/11572_367875"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Through a second-order homogenization procedure, the explicit relation is obtained between the non-local parameters of a second gradient elastic ma- terial and the microstructure of a composite material. This result is instru- mental for the definition of higher-order models, to be used for the analysis of mechanics at micro- and nano-scale, where size-effects become important. The obtained relation is valid for both plane and three-dimensional prob- lems and generalizes earlier findings by Bigoni and Drugan (Analytical deriva- tion of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech., 2007, 74, 741753) from several points of view: i) the result holds for anisotropic phases with spherical or circular ellipsoid of inertia; ii) the displacement boundary conditions considered in the homogenization procedure is independent of the characteristics of the material; iii) a perfect energy match is found between heterogeneous and equivalent materials (instead of an optimal bound). From the obtained solution it follows that the equivalent second-gradient Mindlin elastic solid: a) is positive definite only when the discrepancy tensor is negative defined; b) the non-local material symmetries are the same of the discrepancy tensor; c) the non-local effective behaviour is affected by the shape of the RVE, which does not influence the first-order homogenized response. Finally, explicit derivations of non-local parameters from heterogeneous Cauchy elastic composites are obtained in particular cases."]},{"key":"dc:title","label":"Title","values":["Homogenization of heterogeneous Cauchy-elastic materials leads to Mindlin second-gradient elasticity"]}]}],"canonical_facts":{"dc:contributor":["Bacca, Mattia","Bigoni, Davide"],"dc:creator":["Bacca, Mattia"],"dc:date":["2013"],"dc:description":["Through a second-order homogenization procedure, the explicit relation is obtained between the non-local parameters of a second gradient elastic ma- terial and the microstructure of a composite material. This result is instru- mental for the definition of higher-order models, to be used for the analysis of mechanics at micro- and nano-scale, where size-effects become important. The obtained relation is valid for both plane and three-dimensional prob- lems and generalizes earlier findings by Bigoni and Drugan (Analytical deriva- tion of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech., 2007, 74, 741753) from several points of view: i) the result holds for anisotropic phases with spherical or circular ellipsoid of inertia; ii) the displacement boundary conditions considered in the homogenization procedure is independent of the characteristics of the material; iii) a perfect energy match is found between heterogeneous and equivalent materials (instead of an optimal bound). From the obtained solution it follows that the equivalent second-gradient Mindlin elastic solid: a) is positive definite only when the discrepancy tensor is negative defined; b) the non-local material symmetries are the same of the discrepancy tensor; c) the non-local effective behaviour is affected by the shape of the RVE, which does not influence the first-order homogenized response. Finally, explicit derivations of non-local parameters from heterogeneous Cauchy elastic composites are obtained in particular cases."],"dc:identifier":["https://hdl.handle.net/11572/367875","http://dx.doi.org/10.15168/11572_367875","10.15168/11572_367875"],"dc:language":["eng"],"dc:publisher":["Università degli studi di Trento","place:TRENTO"],"dc:relation":["firstpage:1","lastpage:84","numberofpages:84"],"dc:rights":["info:eu-repo/semantics/openAccess","license:Tutti i diritti riservati (All rights reserved)"],"dc:subject":["Settore ICAR/08 - Scienza delle Costruzioni"],"dc:title":["Homogenization of heterogeneous Cauchy-elastic materials leads to Mindlin second-gradient elasticity"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T05:04:24Z"}