{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:29:30Z","timestamp":1759091370206,"version":"3.38.0"},"reference-count":42,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T00:00:00Z","timestamp":1603324800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["028473 POCI-01-0145-FEDER- 028473"],"award-info":[{"award-number":["028473 POCI-01-0145-FEDER- 028473"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science"],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:p> The development of lighter structures and materials has been one of the main research concerns of the transportation industry during the last decade, driven by the necessity to decrease fuel consumption and emissions. Therefore, the use of several different new lightweight materials, such as special metal alloys, reinforced polymers and new advanced composite materials has been explored, leading to optimized structures which combine these novel materials. To manufacture these multi-material structures, adhesive bonding is one of best joining techniques available, as fasteners add weight to the structure and require holes to be drilled and welding is not easily applicable to reinforced plastics, composites and some high strength metal alloys. However, adhesive bonding also presents some limitations that need to be considered, such as the appearance of singularities and the resultant stress concentration at the edges of the bond line, which result in a reduction of the joint strength. In order to mitigate this effect, several techniques have been proposed, being the use of functionally graded adherends one of them. Functionally graded adherends consist in an adherend where the mechanical properties gradually change throughout the material, usually in the thickness or length direction. The present work introduces the concept of a layered functionally graded adherend, varying the flexibility of each layer through the thickness direction. Different ratios of stiffness variation, combined with different adhesive properties, were numerically evaluated for single lap joints, comparing the stress distribution of the adhesive layer and the resultant joint strength, using cohesive zone modelling. Moreover, an optimization process of typical graded material properties, where different distribution laws that consider material weight and strength are considered, is presented. <\/jats:p>","DOI":"10.1177\/0954406220967695","type":"journal-article","created":{"date-parts":[[2020,10,23]],"date-time":"2020-10-23T06:42:50Z","timestamp":1603435370000},"page":"508-517","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["Numerical modelling of functionally graded adherends"],"prefix":"10.1177","volume":"235","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6135-3665","authenticated-orcid":false,"given":"MQ","family":"dos Reis","sequence":"first","affiliation":[{"name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (INEGI), Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1933-0865","authenticated-orcid":false,"given":"RJC","family":"Carbas","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (INEGI), Porto, Portugal"},{"name":"Departamento de Engenharia Mec\u00e2nica e Gest\u00e3o Industrial, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2750-8184","authenticated-orcid":false,"given":"EAS","family":"Marques","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (INEGI), Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3272-4591","authenticated-orcid":false,"given":"LFM","family":"da Silva","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial (INEGI), Porto, Portugal"},{"name":"Departamento de Engenharia Mec\u00e2nica e Gest\u00e3o Industrial, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2020,10,22]]},"reference":[{"key":"bibr1-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1243\/14644207JMDA219"},{"key":"bibr2-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijadhadh.2016.10.010"},{"key":"bibr3-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1177\/0954408920916112"},{"journal-title":"Compos Sci Technol","year":"2008","author":"Moura MFSF","key":"bibr4-0954406220967695"},{"key":"bibr5-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijadhadh.2017.02.004"},{"key":"bibr6-0954406220967695","first-page":"41","volume":"15","author":"Volkersen O.","year":"1938","journal-title":"Luftfahrtforschung"},{"key":"bibr7-0954406220967695","doi-asserted-by":"crossref","first-page":"A17","DOI":"10.1115\/1.4009336","volume":"66","author":"Goland MaR E.","year":"1944","journal-title":"J Appl Mech"},{"key":"bibr8-0954406220967695","unstructured":"Hart-Smith LJ. Adhessive bonded double lap joints. 1973. NASA CR-112235."},{"key":"bibr9-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1243\/0309324981513039"},{"key":"bibr10-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(1999)125:11(1298)"},{"key":"bibr11-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.commatsci.2009.11.023"},{"key":"bibr12-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijadhadh.2006.04.001"},{"key":"bibr13-0954406220967695","first-page":"99","volume":"3","author":"Raphael C.","year":"1966","journal-title":"Appl Polym Symp"},{"key":"bibr14-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1163\/156856106779024436"},{"key":"bibr15-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2015.01.005"},{"key":"bibr16-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1080\/00218464.2019.1646647"},{"key":"bibr17-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijadhadh.2017.02.008"},{"journal-title":"Proc","year":"2018","author":"Shang X","key":"bibr18-0954406220967695"},{"key":"bibr19-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijadhadh.2019.102475"},{"key":"bibr20-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1177\/0021998304039271"},{"key":"bibr21-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-85573-831-7.50105-X"},{"key":"bibr22-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2019.107363"},{"key":"bibr23-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5416(72)90059-6"},{"key":"bibr24-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1007\/BF00549902"},{"key":"bibr25-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/S1359-8368(96)00016-9"},{"key":"bibr26-0954406220967695","volume":"13","author":"M.Niino TH","year":"1987","journal-title":"J Jpn Soc Compos Mater"},{"key":"bibr27-0954406220967695","doi-asserted-by":"publisher","DOI":"10.2497\/jjspm.37.241"},{"key":"bibr28-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2004.09.004"},{"key":"bibr29-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.engstruct.2016.06.036"},{"key":"bibr30-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.engstruct.2018.05.076"},{"key":"bibr31-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1007\/s11668-014-9790-x"},{"key":"bibr32-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/S1359-835X(02)00050-7"},{"key":"bibr33-0954406220967695","doi-asserted-by":"crossref","unstructured":"Kumar S, de Alvaro MT (eds). Modeling and experimental evaluation of geometrically graded multi-material single-lap joints. In: 56th AIAA\/ASCE\/AHS\/ASC structures, structural dynamics, and materials conference, Kissimmee, Florida, 5-9 January 2015.","DOI":"10.2514\/6.2015-1885"},{"key":"bibr34-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1080\/13588265.2016.1165440"},{"key":"bibr35-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijadhadh.2019.02.003"},{"key":"bibr36-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2019.111492"},{"key":"bibr37-0954406220967695","doi-asserted-by":"crossref","unstructured":"da Silva LFM and Campilho RDSG. Advances in Numerical Modelling of Adhesive Joints. In: Advances in Numerical Modeling of Adhesive Joints. SpringerBriefs in Applied Sciences and Technology. Springer, Berlin, Heidelberg, 2012.","DOI":"10.1007\/978-3-642-23608-2"},{"key":"bibr38-0954406220967695","volume":"28","author":"Moura MFSF","year":"2008","journal-title":"Int J Adhes Adhes"},{"key":"bibr39-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1080\/01694243.2015.1121801"},{"key":"bibr40-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2017.11.045"},{"key":"bibr41-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1080\/00218460902881808"},{"key":"bibr42-0954406220967695","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2018.06.009"}],"container-title":["Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0954406220967695","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0954406220967695","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0954406220967695","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T21:08:12Z","timestamp":1740863292000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0954406220967695"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,22]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["10.1177\/0954406220967695"],"URL":"https:\/\/doi.org\/10.1177\/0954406220967695","relation":{},"ISSN":["0954-4062","2041-2983"],"issn-type":[{"type":"print","value":"0954-4062"},{"type":"electronic","value":"2041-2983"}],"subject":[],"published":{"date-parts":[[2020,10,22]]}}}