{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1093"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1093","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"Elasticity in Microstructure Sensitive Design Through the use of Hill Bounds","abstract":"In engineering, materials are often assumed to be homogeneous and isotropic; in actuality, material properties do change with sample direction and location. This variation is due to the anisotropy of the individual grains and their spatial distribution in the material. Currently there is a lack of communication between the design engineer, material scientist, and processor for solving multi-objective/constrained designs. If communication existed between these groups then materials could be designed for applications, instead of the reverse. Microstructure sensitive design introduces a common language, a spectral representation, where both design properties and microstructures are expressed. <p>Using Hill bounds, effective elastic properties are expressed within the spectral representation. For the elastic properties, two FCC materials, copper and nickel, were chosen for computation and to demonstrate how symmetry enters into the methodology. This spectral representation renders properties as hyper-surfaces that translate through a multi-dimensional Fourier space depending on the property value of the hyper-surface. Property closures are generated by condensing the information contained within the multi-dimensional Fourier space into a 2-D representation. This compaction of information is beneficial for a quick determination of property limits for a particular alloy system. The design engineer can now dictate the critical design properties and receive sets of microstructures that satisfy the design objectives.","abstract_html":"In engineering, materials are often assumed to be homogeneous and isotropic; in actuality, material properties do change with sample direction and location. This variation is due to the anisotropy of the individual grains and their spatial distribution in the material. Currently there is a lack of communication between the design engineer, material scientist, and processor for solving multi-objective/constrained designs. If communication existed between these groups then materials could be designed for applications, instead of the reverse. Microstructure sensitive design introduces a common language, a spectral representation, where both design properties and microstructures are expressed. <p>Using Hill bounds, effective elastic properties are expressed within the spectral representation. For the elastic properties, two FCC materials, copper and nickel, were chosen for computation and to demonstrate how symmetry enters into the methodology. This spectral representation renders properties as hyper-surfaces that translate through a multi-dimensional Fourier space depending on the property value of the hyper-surface. Property closures are generated by condensing the information contained within the multi-dimensional Fourier space into a 2-D representation. This compaction of information is beneficial for a quick determination of property limits for a particular alloy system. The design engineer can now dictate the critical design properties and receive sets of microstructures that satisfy the design objectives.","abstract_has_math":false,"creators":["Henrie, Benjamin L."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:27:16Z","subjects":["microstructure sensitive design","elastic properties","Hill bounds","design properties","microstructures","hyper-surfaces","fourier space","Mechanical Engineering"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/94","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Henrie, Benjamin L."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2002-05-31T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["microstructure sensitive design","elastic properties","Hill bounds","design properties","microstructures","hyper-surfaces","fourier space","Mechanical Engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/94","https://scholarsarchive.byu.edu/context/etd/article/1093/viewcontent/ETD_CISOPTR_6.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ira A. Fulton College of Engineering and Technology; Mechanical Engineering"]},{"key":"dc:description.abstract","label":"Abstract","values":["In engineering, materials are often assumed to be homogeneous and isotropic; in actuality, material properties do change with sample direction and location. This variation is due to the anisotropy of the individual grains and their spatial distribution in the material. Currently there is a lack of communication between the design engineer, material scientist, and processor for solving multi-objective/constrained designs. If communication existed between these groups then materials could be designed for applications, instead of the reverse. Microstructure sensitive design introduces a common language, a spectral representation, where both design properties and microstructures are expressed. <p>Using Hill bounds, effective elastic properties are expressed within the spectral representation. For the elastic properties, two FCC materials, copper and nickel, were chosen for computation and to demonstrate how symmetry enters into the methodology. This spectral representation renders properties as hyper-surfaces that translate through a multi-dimensional Fourier space depending on the property value of the hyper-surface. Property closures are generated by condensing the information contained within the multi-dimensional Fourier space into a 2-D representation. This compaction of information is beneficial for a quick determination of property limits for a particular alloy system. The design engineer can now dictate the critical design properties and receive sets of microstructures that satisfy the design objectives."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["Elasticity in Microstructure Sensitive Design Through the use of Hill Bounds"]}]}],"canonical_facts":{"dc:creator":["Henrie, Benjamin L."],"dc:date":["2002-05-31T07:00:00Z"],"dc:description":["Ira A. Fulton College of Engineering and Technology; Mechanical Engineering"],"dc:description.abstract":["In engineering, materials are often assumed to be homogeneous and isotropic; in actuality, material properties do change with sample direction and location. This variation is due to the anisotropy of the individual grains and their spatial distribution in the material. Currently there is a lack of communication between the design engineer, material scientist, and processor for solving multi-objective/constrained designs. If communication existed between these groups then materials could be designed for applications, instead of the reverse. Microstructure sensitive design introduces a common language, a spectral representation, where both design properties and microstructures are expressed. <p>Using Hill bounds, effective elastic properties are expressed within the spectral representation. For the elastic properties, two FCC materials, copper and nickel, were chosen for computation and to demonstrate how symmetry enters into the methodology. This spectral representation renders properties as hyper-surfaces that translate through a multi-dimensional Fourier space depending on the property value of the hyper-surface. Property closures are generated by condensing the information contained within the multi-dimensional Fourier space into a 2-D representation. This compaction of information is beneficial for a quick determination of property limits for a particular alloy system. The design engineer can now dictate the critical design properties and receive sets of microstructures that satisfy the design objectives."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/94","https://scholarsarchive.byu.edu/context/etd/article/1093/viewcontent/ETD_CISOPTR_6.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["microstructure sensitive design","elastic properties","Hill bounds","design properties","microstructures","hyper-surfaces","fourier space","Mechanical Engineering"],"dc:title":["Elasticity in Microstructure Sensitive Design Through the use of Hill Bounds"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:27:16Z"}