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The profound implication of the SIR model is viewed as the propagation and dynamic evolutionary process of the different internal components and the characteristics in a complex system subject to external effect. The uniaxial stress-strain curve of engineering material represents the basic constitutive relation, which also represents the damage propagation in the units of the damaged member. Hence, a novel dynamic stress-strain model is established based on the SIR model. The analytical solution and the approximate solution for the proposed model are represented according to the homotopy analysis method (HAM), and the relationship of the solution and the size effect and the strain rate is discussed. In addition, an experiment on the size effect of confined concrete is carried out and the solution of SIR model is suitable for simulation. The results show that the mechanical mechanism of the parameters of the uniaxial stress-strain model proposed in this paper reflects the actual characteristics of the materials. The solution of the SIR model can fully and accurately show the change of the mechanical performance and the influence of the size effect and the strain rate.<\/jats:p>","DOI":"10.1155\/2014\/624863","type":"journal-article","created":{"date-parts":[[2014,6,22]],"date-time":"2014-06-22T17:03:06Z","timestamp":1403456586000},"page":"1-13","source":"Crossref","is-referenced-by-count":5,"title":["Constitutive Relation of Engineering Material Based on SIR Model and HAM"],"prefix":"10.1155","volume":"2014","author":[{"given":"Haoxiang","family":"He","sequence":"first","affiliation":[{"name":"Beijing Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enzhen","family":"Han","sequence":"additional","affiliation":[{"name":"Beijing Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maolin","family":"Cong","sequence":"additional","affiliation":[{"name":"Beijing Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"19","year":"2008"},{"key":"7","year":"2007"},{"issue":"5-6","key":"13","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/0013-7944(86)90035-4","volume":"25","year":"1986","journal-title":"Engineering Fracture Mechanics"},{"issue":"3-4","key":"6","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0045-7825(99)00223-6","volume":"183","year":"2000","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1927.0118"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144500371907"},{"issue":"5","key":"24","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S0045-7949(98)00177-1","volume":"70","year":"1999","journal-title":"Computers and Structures"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.finel.2005.11.008"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(76)90174-8"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8289-6"},{"key":"8","first-page":"vi+260","year":"1968"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1002\/9783527617609"},{"key":"14","first-page":"xii+322","year":"2003"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.icheatmasstransfer.2008.08.008"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2007.12.011"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.5829\/idosi.wasj.2012.20.11.1707"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9590.2007.00387.x"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.07.065"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.08.007"},{"key":"23","year":"1970"},{"key":"5","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1115\/1.3101672","volume":"50","year":"1997","journal-title":"ASME Applied Mechanics Reviews"},{"key":"4","year":"1998"},{"issue":"6","key":"17","first-page":"735","volume":"95","year":"1998","journal-title":"ACI Materials Journal"},{"key":"9","year":"1993"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijimpeng.2004.02.005"},{"issue":"1","key":"16","first-page":"14","volume":"11","year":"2008","journal-title":"Journal of Building Materials"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/624863.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/624863.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/624863.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T11:22:18Z","timestamp":1498130538000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/624863\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":26,"alternative-id":["624863","624863"],"URL":"https:\/\/doi.org\/10.1155\/2014\/624863","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}