Analytic solution for the stress field in an orthotropic disc under diametral parabolic pressure
A full-field analytic solution for the stress field developed in a circular disc made of an orthotropic material is obtained assuming that the disc is under diametral compression. The solution is achieved with the aid of Lekhnitskii's complex potentials technique for rectilinear anisotropic mat...
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Veröffentlicht in: | International journal of rock mechanics and mining sciences (Oxford, England : 1997) England : 1997), 2020-10, Vol.134, p.104432, Article 104432 |
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container_title | International journal of rock mechanics and mining sciences (Oxford, England : 1997) |
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creator | Markides, Ch.F. Kourkoulis, S.K. |
description | A full-field analytic solution for the stress field developed in a circular disc made of an orthotropic material is obtained assuming that the disc is under diametral compression. The solution is achieved with the aid of Lekhnitskii's complex potentials technique for rectilinear anisotropic materials. The general formulae obtained for an orthotropic disc are particularized for a transversely isotropic one, since most rocks are described, in practice, as transversely isotropic materials. The innovation of the solution introduced, besides its applicability to both orthotropic and transverse isotropic materials, is the realistic simulation of the loading scheme at the disc's boundary. Indeed, the load applied is simulated by a parabolic distribution of radial stresses rather than by uniform pressure or diametral point forces. The solution is validated by considering special limiting cases both for the material and the loading scheme. The distribution of stresses along strategic loci is then considered, enlightening critical issues related to the severity of the stress field developed in the disc. Special attention is paid to the stress components at the disc's center, in an effort to assess the applicability of the Brazilian-disc test in determining the tensile fracture strength in case of materials for which the assumption of isotropy is not satisfactory. Before the development of the theoretical model proposed, a short chronological survey of the relative literature is presented, enlightening the path, full of thorns and difficulties that the pioneers of the relevant research have carved and travelled, in order to demonstrate the difficulties of the project and to pay tribute to their priceless contributions. |
doi_str_mv | 10.1016/j.ijrmms.2020.104432 |
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The solution is achieved with the aid of Lekhnitskii's complex potentials technique for rectilinear anisotropic materials. The general formulae obtained for an orthotropic disc are particularized for a transversely isotropic one, since most rocks are described, in practice, as transversely isotropic materials. The innovation of the solution introduced, besides its applicability to both orthotropic and transverse isotropic materials, is the realistic simulation of the loading scheme at the disc's boundary. Indeed, the load applied is simulated by a parabolic distribution of radial stresses rather than by uniform pressure or diametral point forces. The solution is validated by considering special limiting cases both for the material and the loading scheme. The distribution of stresses along strategic loci is then considered, enlightening critical issues related to the severity of the stress field developed in the disc. Special attention is paid to the stress components at the disc's center, in an effort to assess the applicability of the Brazilian-disc test in determining the tensile fracture strength in case of materials for which the assumption of isotropy is not satisfactory. Before the development of the theoretical model proposed, a short chronological survey of the relative literature is presented, enlightening the path, full of thorns and difficulties that the pioneers of the relevant research have carved and travelled, in order to demonstrate the difficulties of the project and to pay tribute to their priceless contributions.</description><identifier>ISSN: 1365-1609</identifier><identifier>EISSN: 1873-4545</identifier><identifier>DOI: 10.1016/j.ijrmms.2020.104432</identifier><language>eng</language><publisher>Berlin: Elsevier Ltd</publisher><subject>Brazilian-disc test ; Complex potentials ; Compression ; Exact solutions ; Fracture strength ; Isotropic material ; Isotropy ; Load distribution ; Mechanical properties ; Orthotropy ; Parabolic pressure ; Rocks ; Stress ; Stress concentration ; Stress distribution ; Transverse isotropy</subject><ispartof>International journal of rock mechanics and mining sciences (Oxford, England : 1997), 2020-10, Vol.134, p.104432, Article 104432</ispartof><rights>2020 Elsevier Ltd</rights><rights>Copyright Elsevier BV Oct 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a357t-6a90e23c7942678d60c04d6eaa170d8edc1411e9fa076db328fd7a5c953b1dda3</citedby><cites>FETCH-LOGICAL-a357t-6a90e23c7942678d60c04d6eaa170d8edc1411e9fa076db328fd7a5c953b1dda3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.ijrmms.2020.104432$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Markides, Ch.F.</creatorcontrib><creatorcontrib>Kourkoulis, S.K.</creatorcontrib><title>Analytic solution for the stress field in an orthotropic disc under diametral parabolic pressure</title><title>International journal of rock mechanics and mining sciences (Oxford, England : 1997)</title><description>A full-field analytic solution for the stress field developed in a circular disc made of an orthotropic material is obtained assuming that the disc is under diametral compression. The solution is achieved with the aid of Lekhnitskii's complex potentials technique for rectilinear anisotropic materials. The general formulae obtained for an orthotropic disc are particularized for a transversely isotropic one, since most rocks are described, in practice, as transversely isotropic materials. The innovation of the solution introduced, besides its applicability to both orthotropic and transverse isotropic materials, is the realistic simulation of the loading scheme at the disc's boundary. Indeed, the load applied is simulated by a parabolic distribution of radial stresses rather than by uniform pressure or diametral point forces. The solution is validated by considering special limiting cases both for the material and the loading scheme. The distribution of stresses along strategic loci is then considered, enlightening critical issues related to the severity of the stress field developed in the disc. Special attention is paid to the stress components at the disc's center, in an effort to assess the applicability of the Brazilian-disc test in determining the tensile fracture strength in case of materials for which the assumption of isotropy is not satisfactory. Before the development of the theoretical model proposed, a short chronological survey of the relative literature is presented, enlightening the path, full of thorns and difficulties that the pioneers of the relevant research have carved and travelled, in order to demonstrate the difficulties of the project and to pay tribute to their priceless contributions.</description><subject>Brazilian-disc test</subject><subject>Complex potentials</subject><subject>Compression</subject><subject>Exact solutions</subject><subject>Fracture strength</subject><subject>Isotropic material</subject><subject>Isotropy</subject><subject>Load distribution</subject><subject>Mechanical properties</subject><subject>Orthotropy</subject><subject>Parabolic pressure</subject><subject>Rocks</subject><subject>Stress</subject><subject>Stress concentration</subject><subject>Stress distribution</subject><subject>Transverse isotropy</subject><issn>1365-1609</issn><issn>1873-4545</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LxDAULKLguvoPPAQ8d02aNG0vwrL4BQte9ByzySub0jb1JRX892apZ09veG9meDNZdsvohlEm77uN63AYwqagxWklBC_OshWrK56LUpTnCXNZ5kzS5jK7CqGjlMpCVqvsczvq_ic6Q4Lv5-j8SFqPJB6BhIgQAmkd9Ja4keiReIxHH9FPiW9dMGQeLWCCeoCIuieTRn3wfTpPJ_GMcJ1dtLoPcPM319nH0-P77iXfvz2_7rb7XPOyirnUDYWCm6oR6a_aSmqosBK0ZhW1NVjDBGPQtJpW0h54Ube20qVpSn5g1mq-zu4W3wn91wwhqs7PmMIFVQhZy4aWhUwssbAM-hAQWjWhGzT-KEbVqUvVqaVLdepSLV0m2cMig5Tg2wGqYByMBqxDMFFZ7_43-AUp-4B2</recordid><startdate>202010</startdate><enddate>202010</enddate><creator>Markides, Ch.F.</creator><creator>Kourkoulis, S.K.</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7UA</scope><scope>8FD</scope><scope>C1K</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>202010</creationdate><title>Analytic solution for the stress field in an orthotropic disc under diametral parabolic pressure</title><author>Markides, Ch.F. ; Kourkoulis, S.K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a357t-6a90e23c7942678d60c04d6eaa170d8edc1411e9fa076db328fd7a5c953b1dda3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Brazilian-disc test</topic><topic>Complex potentials</topic><topic>Compression</topic><topic>Exact solutions</topic><topic>Fracture strength</topic><topic>Isotropic material</topic><topic>Isotropy</topic><topic>Load distribution</topic><topic>Mechanical properties</topic><topic>Orthotropy</topic><topic>Parabolic pressure</topic><topic>Rocks</topic><topic>Stress</topic><topic>Stress concentration</topic><topic>Stress distribution</topic><topic>Transverse isotropy</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Markides, Ch.F.</creatorcontrib><creatorcontrib>Kourkoulis, S.K.</creatorcontrib><collection>CrossRef</collection><collection>Water Resources Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>International journal of rock mechanics and mining sciences (Oxford, England : 1997)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Markides, Ch.F.</au><au>Kourkoulis, S.K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytic solution for the stress field in an orthotropic disc under diametral parabolic pressure</atitle><jtitle>International journal of rock mechanics and mining sciences (Oxford, England : 1997)</jtitle><date>2020-10</date><risdate>2020</risdate><volume>134</volume><spage>104432</spage><pages>104432-</pages><artnum>104432</artnum><issn>1365-1609</issn><eissn>1873-4545</eissn><abstract>A full-field analytic solution for the stress field developed in a circular disc made of an orthotropic material is obtained assuming that the disc is under diametral compression. The solution is achieved with the aid of Lekhnitskii's complex potentials technique for rectilinear anisotropic materials. The general formulae obtained for an orthotropic disc are particularized for a transversely isotropic one, since most rocks are described, in practice, as transversely isotropic materials. The innovation of the solution introduced, besides its applicability to both orthotropic and transverse isotropic materials, is the realistic simulation of the loading scheme at the disc's boundary. Indeed, the load applied is simulated by a parabolic distribution of radial stresses rather than by uniform pressure or diametral point forces. The solution is validated by considering special limiting cases both for the material and the loading scheme. The distribution of stresses along strategic loci is then considered, enlightening critical issues related to the severity of the stress field developed in the disc. Special attention is paid to the stress components at the disc's center, in an effort to assess the applicability of the Brazilian-disc test in determining the tensile fracture strength in case of materials for which the assumption of isotropy is not satisfactory. Before the development of the theoretical model proposed, a short chronological survey of the relative literature is presented, enlightening the path, full of thorns and difficulties that the pioneers of the relevant research have carved and travelled, in order to demonstrate the difficulties of the project and to pay tribute to their priceless contributions.</abstract><cop>Berlin</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.ijrmms.2020.104432</doi></addata></record> |
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subjects | Brazilian-disc test Complex potentials Compression Exact solutions Fracture strength Isotropic material Isotropy Load distribution Mechanical properties Orthotropy Parabolic pressure Rocks Stress Stress concentration Stress distribution Transverse isotropy |
title | Analytic solution for the stress field in an orthotropic disc under diametral parabolic pressure |
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