Poisson's ratio in cubic materials
Expressions are given for the maximum and minimum values of Poisson's ratio ν for materials with cubic symmetry. Values less than −1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of o...
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| Veröffentlicht in: | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2006-11, Vol.462 (2075), p.3385-3405 |
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| container_title | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences |
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| creator | Norris, Andrew N |
| description | Expressions are given for the maximum and minimum values of Poisson's ratio ν for materials with cubic symmetry. Values less than −1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of occur in directions at which the Young modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than −1 and greater than +2. |
| doi_str_mv | 10.1098/rspa.2006.1726 |
| format | Article |
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Values less than −1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of occur in directions at which the Young modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than −1 and greater than +2.</description><identifier>ISSN: 1364-5021</identifier><identifier>EISSN: 1471-2946</identifier><identifier>DOI: 10.1098/rspa.2006.1726</identifier><language>eng</language><publisher>London: The Royal Society</publisher><subject>Anisotropy ; Cubic crystals ; Cubic Symmetry ; Elastic anisotropy ; Extrema ; Mathematical minima ; Moduli of elasticity ; Poisson ratio ; Poisson's Ratio ; Shear modulus ; Triangles ; Vertices ; Youngs modulus</subject><ispartof>Proceedings of the Royal Society. 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A, Mathematical, physical, and engineering sciences</title><addtitle>PROC R SOC A</addtitle><description>Expressions are given for the maximum and minimum values of Poisson's ratio ν for materials with cubic symmetry. Values less than −1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of occur in directions at which the Young modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than −1 and greater than +2.</description><subject>Anisotropy</subject><subject>Cubic crystals</subject><subject>Cubic Symmetry</subject><subject>Elastic anisotropy</subject><subject>Extrema</subject><subject>Mathematical minima</subject><subject>Moduli of elasticity</subject><subject>Poisson ratio</subject><subject>Poisson's Ratio</subject><subject>Shear modulus</subject><subject>Triangles</subject><subject>Vertices</subject><subject>Youngs modulus</subject><issn>1364-5021</issn><issn>1471-2946</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp9j0lPwzAQhSMEEqVw5YZUceGU4N3JDSg7lUBsV8uxHerSxpGdCvrvcRRUqQc4zYzefDPvJckhBBkERX7qQyMzBADLIEdsKxlAwmGKCsK2Y48ZSSlAcDfZC2EGAChozgfJ8ZOzIbj6JIy8bK0b2XqklqVVo4VsjbdyHvaTnSoWc_Bbh8nb9dXr-DadPN7cjc8nqSIEtyk3OVGMU11QZRjiZVkSqBnmGhjNYElwLqU0RvNcM2AqbSqqMcUVVVAWRuNhkvV3lXcheFOJxtuF9CsBgegSii6h6BKKLmEEcA94t4rGnLKmXYmZW_o6jn9TRz01C63z6x8IIFAAjqOe9roNrfle69J_CsYxp-I9J-Iyf74vHi6AeIn7qN-f2o_pl_VGbNiJQ-ODFISh-CPiGOc0Qmf_Qp1l5erW1O0mKarlfC4aXeEfRtWXsQ</recordid><startdate>20061108</startdate><enddate>20061108</enddate><creator>Norris, Andrew N</creator><general>The Royal Society</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20061108</creationdate><title>Poisson's ratio in cubic materials</title><author>Norris, Andrew N</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c443t-7e84c675d95ce627bbb41d637d0ed61b438aaaeed78d60efdef5d353f5c1a9ed3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Anisotropy</topic><topic>Cubic crystals</topic><topic>Cubic Symmetry</topic><topic>Elastic anisotropy</topic><topic>Extrema</topic><topic>Mathematical minima</topic><topic>Moduli of elasticity</topic><topic>Poisson ratio</topic><topic>Poisson's Ratio</topic><topic>Shear modulus</topic><topic>Triangles</topic><topic>Vertices</topic><topic>Youngs modulus</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Norris, Andrew N</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Norris, Andrew N</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Poisson's ratio in cubic materials</atitle><jtitle>Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences</jtitle><addtitle>PROC R SOC A</addtitle><date>2006-11-08</date><risdate>2006</risdate><volume>462</volume><issue>2075</issue><spage>3385</spage><epage>3405</epage><pages>3385-3405</pages><issn>1364-5021</issn><eissn>1471-2946</eissn><abstract>Expressions are given for the maximum and minimum values of Poisson's ratio ν for materials with cubic symmetry. Values less than −1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of occur in directions at which the Young modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than −1 and greater than +2.</abstract><cop>London</cop><pub>The Royal Society</pub><doi>10.1098/rspa.2006.1726</doi><tpages>21</tpages></addata></record> |
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| ispartof | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2006-11, Vol.462 (2075), p.3385-3405 |
| issn | 1364-5021 1471-2946 |
| language | eng |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; Alma/SFX Local Collection |
| subjects | Anisotropy Cubic crystals Cubic Symmetry Elastic anisotropy Extrema Mathematical minima Moduli of elasticity Poisson ratio Poisson's Ratio Shear modulus Triangles Vertices Youngs modulus |
| title | Poisson's ratio in cubic materials |
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