{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T02:08:25Z","timestamp":1791770905256,"version":"4.3.4"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,4,2]],"date-time":"2024-04-02T00:00:00Z","timestamp":1712016000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,4,2]],"date-time":"2024-04-02T00:00:00Z","timestamp":1712016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001773","name":"University of New South Wales","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001773","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a novel and effective strategy for modelling three-dimensional periodic representative volume elements (RVE) of particulate composites. The proposed method aims to generate an RVE that can represent the microstructure of particulate composites with hollow spherical inclusions for homogenization (e.g., deriving the full-field effective elastic properties). The RVE features periodic and randomised geometry suitable for the application of periodic boundary conditions in finite element analysis. A robust algorithm is introduced following the combined theories of Monte Carlo and collision driven molecular dynamics to pack spherical particles in random spatial positions within the RVE. This novel technique can achieve a high particle-matrix volume ratio of up to 50% while still maintaining geometric periodicity across the domain and random distribution of inclusions within the RVE. Another algorithm is established to apply periodic boundary conditions (PBC) to precisely generate full field elastic properties of such microstructures. Furthermore, a user-friendly automatic ABAQUS CAE plug-in tool \u2018<jats:bold>Gen_PRVE<\/jats:bold>\u2019 is developed to generate three-dimensional RVE of any spherical particulate composite or porous material. <jats:bold>Gen_PRVE<\/jats:bold> provides users with a great deal of flexibility to generate Representative Volume Elements (RVEs) with varying side dimensions, sphere sizes, and periodic mesh resolutions. In addition, this tool can be effectively utilized to conduct a rapid mesh convergence study, an RVE size sensitivity study, and investigate the impact of inclusion\/matrix volume fraction on the solution. Lastly, examples of these applications are presented.<\/jats:p>","DOI":"10.1007\/s00366-024-01954-8","type":"journal-article","created":{"date-parts":[[2024,4,2]],"date-time":"2024-04-02T10:01:53Z","timestamp":1712052113000},"page":"3087-3113","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Multiscale modelling of particulate composites with spherical inclusions"],"prefix":"10.1007","volume":"40","author":[{"given":"Abdalla","family":"Elbana","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4091-809X","authenticated-orcid":false,"given":"Amar","family":"Khennane","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul J.","family":"Hazell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,4,2]]},"reference":[{"issue":"83","key":"1954_CR1","doi-asserted-by":"publisher","first-page":"52632","DOI":"10.1039\/C7RA10358A","volume":"7","author":"RA Ramli","year":"2017","unstructured":"Ramli RA (2017) Hollow polymer particles: a review. RSC Adv 7(83):52632\u201352650","journal-title":"RSC Adv"},{"key":"1954_CR2","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1039\/C7RA10358A","volume":"174","author":"M \u017byrkowski","year":"2016","unstructured":"\u017byrkowski M et al (2016) Characterization of fly-ash cenospheres from coal-fired power plant unit. Fuel 174:49\u201353. https:\/\/doi.org\/10.1039\/C7RA10358A","journal-title":"Fuel"},{"issue":"21","key":"1954_CR3","doi-asserted-by":"publisher","first-page":"2360","DOI":"10.1016\/j.matlet.2010.07.063","volume":"64","author":"R Poveda","year":"2010","unstructured":"Poveda R, Gupta N, Porfiri M (2010) Poisson\u2019s ratio of hollow particle filled composites. Mater Lett 64(21):2360\u20132362. https:\/\/doi.org\/10.1016\/j.matlet.2010.07.063","journal-title":"Mater Lett"},{"issue":"46","key":"1954_CR4","doi-asserted-by":"publisher","first-page":"20880","DOI":"10.1021\/acs.iecr.9b02330","volume":"58","author":"W Wichaita","year":"2019","unstructured":"Wichaita W, Polpanich D, Tangboriboonrat P (2019) Review on synthesis of colloidal hollow particles and their applications. Ind Eng Chem Res 58(46):20880\u201320901. https:\/\/doi.org\/10.1021\/acs.iecr.9b02330","journal-title":"Ind Eng Chem Res"},{"issue":"3","key":"1954_CR5","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/s0001-8686(02)00034-9","volume":"99","author":"CJ McDonald","year":"2002","unstructured":"McDonald CJ, Devon MJ (2002) Hollow latex particles: synthesis and applications. Adv Colloid Interface Sci 99(3):181\u2013213. https:\/\/doi.org\/10.1016\/s0001-8686(02)00034-9","journal-title":"Adv Colloid Interface Sci"},{"issue":"8","key":"1954_CR6","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1002\/ceat.200406138","volume":"27","author":"J Bertling","year":"2004","unstructured":"Bertling J, Bl\u00f6mer J, K\u00fcmmel R (2004) Hollow microsperes. Chem Eng Technol 27(8):829\u2013837. https:\/\/doi.org\/10.1002\/ceat.200406138","journal-title":"Chem Eng Technol"},{"issue":"6","key":"1954_CR7","doi-asserted-by":"publisher","first-page":"3437","DOI":"10.1021\/ef700340k","volume":"21","author":"L-N Ngu","year":"2007","unstructured":"Ngu L-N, Wu H, Zhang D-K (2007) Characterization of Ash cenospheres in fly ash from Australian power stations. Energy Fuels 21(6):3437\u20133445. https:\/\/doi.org\/10.1021\/ef700340k","journal-title":"Energy Fuels"},{"issue":"1","key":"1954_CR8","doi-asserted-by":"publisher","first-page":"23","DOI":"10.3390\/environsciproc2021012023","volume":"12","author":"A Elbana","year":"2022","unstructured":"Elbana A et al (2022) Multi-scale modelling of particulate composite. Environ Sci Proc 12(1):23. https:\/\/doi.org\/10.3390\/environsciproc2021012023","journal-title":"Environ Sci Proc"},{"issue":"6","key":"1954_CR9","doi-asserted-by":"publisher","first-page":"774","DOI":"10.1038\/s41563-020-00913-0","volume":"20","author":"J Fish","year":"2021","unstructured":"Fish J, Wagner GJ, Keten S (2021) Mesoscopic and multiscale modelling in materials. Nat Mater 20(6):774\u2013786. https:\/\/doi.org\/10.1038\/s41563-020-00913-0","journal-title":"Nat Mater"},{"issue":"2021","key":"1954_CR10","doi-asserted-by":"publisher","first-page":"20130390","DOI":"10.1098\/rsta.2013.0390","volume":"372","author":"S Karabasov","year":"2021","unstructured":"Karabasov S et al (2021) Multiscale modelling: approaches and challenges. Philos Trans R Soc A Math Phys Eng Sci 372(2021):20130390. https:\/\/doi.org\/10.1098\/rsta.2013.0390","journal-title":"Philos Trans R Soc A Math Phys Eng Sci"},{"key":"1954_CR11","unstructured":"B\u00f6hm HJ (1998) A short introduction to basic aspects of continuum micromechanics. Cdl-fmd Report, vol 3. https:\/\/www.ilsb.tuwien.ac.at\/links\/downloads\/ilsbrep206.pdf"},{"issue":"5","key":"1954_CR12","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/0022-5096(63)90036-X","volume":"11","author":"R Hill","year":"1963","unstructured":"Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11(5):357\u2013372. https:\/\/doi.org\/10.1016\/0022-5096(63)90036-X","journal-title":"J Mech Phys Solids"},{"key":"1954_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-67125-3","volume-title":"Finite element applications","author":"M Okereke","year":"2018","unstructured":"Okereke M, Keates S (2018) Finite element applications. Springer, Cham. https:\/\/doi.org\/10.1007\/978-3-319-67125-3"},{"issue":"4","key":"1954_CR14","doi-asserted-by":"publisher","first-page":"471","DOI":"10.2140\/jomms.2017.12.471","volume":"12","author":"K Schneider","year":"2017","unstructured":"Schneider K, Klusemann B, Bargmann S (2017) Fully periodic RVEs for technological relevant composites: not worth the effort! J Mech Mater Struct 12(4):471\u2013484. https:\/\/doi.org\/10.2140\/jomms.2017.12.471","journal-title":"J Mech Mater Struct"},{"issue":"2","key":"1954_CR15","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.commatsci.2006.12.008","volume":"40","author":"SR Annapragada","year":"2007","unstructured":"Annapragada SR, Sun D, Garimella SV (2007) Prediction of effective thermo-mechanical properties of particulate composites. Comput Mater Sci 40(2):255\u2013266. https:\/\/doi.org\/10.1016\/j.commatsci.2006.12.008","journal-title":"Comput Mater Sci"},{"key":"1954_CR16","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.compscitech.2016.04.011","volume":"129","author":"W Xu","year":"2016","unstructured":"Xu W et al (2016) Analytical effective elastic properties of particulate composites with soft interfaces around anisotropic particles. Compos Sci Technol 129:10\u201318. https:\/\/doi.org\/10.1016\/j.compscitech.2016.04.011","journal-title":"Compos Sci Technol"},{"issue":"21","key":"1954_CR17","doi-asserted-by":"publisher","first-page":"6945","DOI":"10.1016\/j.ijsolstr.2007.03.019","volume":"44","author":"O Pierard","year":"2007","unstructured":"Pierard O et al (2007) Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions. Int J Solids Struct 44(21):6945\u20136962. https:\/\/doi.org\/10.1016\/j.ijsolstr.2007.03.019","journal-title":"Int J Solids Struct"},{"issue":"32\u201333","key":"1954_CR18","doi-asserted-by":"publisher","first-page":"5789","DOI":"10.1016\/S0020-7683(00)00370-X","volume":"38","author":"L Shen","year":"2001","unstructured":"Shen L, Yi S (2001) An effective inclusion model for effective moduli of heterogeneous materials with ellipsoidal inhomogeneities. Int J Solids Struct 38(32\u201333):5789\u20135805. https:\/\/doi.org\/10.1016\/S0020-7683(00)00370-X","journal-title":"Int J Solids Struct"},{"key":"1954_CR19","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.compstruct.2018.02.075","volume":"192","author":"A Bahmani","year":"2018","unstructured":"Bahmani A et al (2018) Three-dimensional microscopic assessment of randomly distributed representative volume elements for high fiber volume fraction unidirectional composites. Compos Struct 192:153\u2013164. https:\/\/doi.org\/10.1016\/j.compstruct.2018.02.075","journal-title":"Compos Struct"},{"issue":"9","key":"1954_CR20","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1016\/j.mechmat.2004.10.003","volume":"37","author":"P Raghavan","year":"2005","unstructured":"Raghavan P, Ghosh S (2005) A continuum damage mechanics model for unidirectional composites undergoing interfacial debonding. Mech Mater 37(9):955\u2013979. https:\/\/doi.org\/10.1016\/j.mechmat.2004.10.003","journal-title":"Mech Mater"},{"key":"1954_CR21","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1016\/j.compstruct.2017.08.010","volume":"180","author":"B Wintiba","year":"2017","unstructured":"Wintiba B et al (2017) An automated procedure for the generation and conformal discretization of 3D woven composites RVEs. Compos Struct 180:955\u2013971. https:\/\/doi.org\/10.1016\/j.compstruct.2017.08.010","journal-title":"Compos Struct"},{"key":"1954_CR22","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.compscitech.2019.03.023","volume":"176","author":"G Pierreux","year":"2019","unstructured":"Pierreux G, Van Hemelrijck D, Massart TJ (2019) Automated generation of 3D orthogonal woven composites RVEs including yarn cross-section variations. Compos Sci Technol 176:90\u2013102. https:\/\/doi.org\/10.1016\/j.compscitech.2019.03.023","journal-title":"Compos Sci Technol"},{"key":"1954_CR23","doi-asserted-by":"publisher","first-page":"112929","DOI":"10.1016\/j.cma.2020.112929","volume":"364","author":"X Han","year":"2020","unstructured":"Han X et al (2020) Efficient multiscale modeling for woven composites based on self-consistent clustering analysis. Comput Methods Appl Mech Eng 364:112929. https:\/\/doi.org\/10.1016\/j.cma.2020.112929","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"8","key":"1954_CR24","doi-asserted-by":"publisher","first-page":"1907","DOI":"10.1016\/S0020-7683(03)00024-6","volume":"40","author":"Z Xia","year":"2003","unstructured":"Xia Z, Zhang Y, Ellyin F (2003) A unified periodical boundary conditions for representative volume elements of composites and applications. Int J Solids Struct 40(8):1907\u20131921. https:\/\/doi.org\/10.1016\/S0020-7683(03)00024-6","journal-title":"Int J Solids Struct"},{"key":"1954_CR25","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1007\/s00366-018-0616-4","volume":"35","author":"SL Omairey","year":"2019","unstructured":"Omairey SL, Dunning PD, Sriramula S (2019) Development of an ABAQUS plugin tool for periodic RVE homogenisation. Eng Comput 35:567\u2013577. https:\/\/doi.org\/10.1007\/s00366-018-0616-4","journal-title":"Eng Comput"},{"issue":"2","key":"1954_CR26","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0022-5193(80)90358-6","volume":"87","author":"J Feder","year":"1980","unstructured":"Feder J (1980) Random sequential adsorption. J Theor Biol 87(2):237\u2013254. https:\/\/doi.org\/10.1016\/0022-5193(80)90358-6","journal-title":"J Theor Biol"},{"key":"1954_CR27","unstructured":"Stachurski ZH (2015) Fundamentals of amorphous solids: structure and properties. Wiley. ISBN: 978-3-527-33707-1"},{"issue":"11\u201312","key":"1954_CR28","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1016\/j.ijsolstr.2012.02.021","volume":"49","author":"E Ghossein","year":"2012","unstructured":"Ghossein E, L\u00e9vesque M (2012) A fully automated numerical tool for a comprehensive validation of homogenization models and its application to spherical particles reinforced composites. Int J Solids Struct 49(11\u201312):1387\u20131398. https:\/\/doi.org\/10.1016\/j.ijsolstr.2012.02.021","journal-title":"Int J Solids Struct"},{"key":"1954_CR29","doi-asserted-by":"publisher","first-page":"108714","DOI":"10.1016\/j.compscitech.2021.108714","volume":"207","author":"W Tian","year":"2021","unstructured":"Tian W et al (2021) An algorithm for generation of RVEs of composites with high particle volume fractions. Compos Sci Technol 207:108714. https:\/\/doi.org\/10.1016\/j.compscitech.2021.108714","journal-title":"Compos Sci Technol"},{"issue":"10","key":"1954_CR30","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.3390\/ma10101201","volume":"10","author":"YJ Cho","year":"2017","unstructured":"Cho YJ, Lee W, Park YH (2017) Finite element modeling of tensile deformation behaviors of iron syntactic foam with hollow glass microspheres. Materials 10(10):1201. https:\/\/doi.org\/10.3390\/ma10101201","journal-title":"Materials"},{"key":"1954_CR31","doi-asserted-by":"publisher","DOI":"10.1002\/app.44188","author":"W Yu","year":"2016","unstructured":"Yu W, Qian M, Li H (2016) Elastic and plastic properties of epoxy resin syntactic foams filled with hollow glass microspheres and glass fibers. J Appl Polym Sci. https:\/\/doi.org\/10.1002\/app.44188","journal-title":"J Appl Polym Sci"},{"key":"1954_CR32","doi-asserted-by":"publisher","first-page":"107701","DOI":"10.1016\/j.compositesb.2019.107701","volume":"183","author":"D Carolan","year":"2020","unstructured":"Carolan D et al (2020) Micromechanical modelling of syntactic foam. Compos B Eng 183:107701. https:\/\/doi.org\/10.1016\/j.compositesb.2019.107701","journal-title":"Compos B Eng"},{"key":"1954_CR33","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.compstruct.2015.11.039","volume":"138","author":"G Catalanotti","year":"2016","unstructured":"Catalanotti G (2016) On the generation of RVE-based models of composites reinforced with long fibres or spherical particles. Compos Struct 138:84\u201395. https:\/\/doi.org\/10.1016\/j.compstruct.2015.11.039","journal-title":"Compos Struct"},{"key":"1954_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/s12008-022-01080-z","author":"SK Sahu","year":"2022","unstructured":"Sahu SK, Rama Sreekanth PS (2022) Multiscale RVE modeling for assessing effective elastic modulus of HDPE based polymer matrix nanocomposite reinforced with nanodiamond. Int J Interact Des Manuf (IJIDeM). https:\/\/doi.org\/10.1007\/s12008-022-01080-z","journal-title":"Int J Interact Des Manuf (IJIDeM)"},{"issue":"16","key":"1954_CR35","doi-asserted-by":"publisher","first-page":"5602","DOI":"10.3390\/ma15165602","volume":"15","author":"J-H Yun","year":"2022","unstructured":"Yun J-H, Jeon Y-J, Kang M-S (2022) Analysis of elastic properties of polypropylene composite materials with ultra-high molecular weight polyethylene spherical reinforcement. Materials 15(16):5602. https:\/\/doi.org\/10.3390\/ma15165602","journal-title":"Materials"},{"issue":"1","key":"1954_CR36","doi-asserted-by":"publisher","first-page":"11076","DOI":"10.1038\/s41598-022-14685-x","volume":"12","author":"MM Shahzamanian","year":"2022","unstructured":"Shahzamanian MM et al (2022) Thermo-mechanical properties prediction of Ni-reinforced Al2O3 composites using micro-mechanics based representative volume elements. Sci Rep 12(1):11076. https:\/\/doi.org\/10.1038\/s41598-022-14685-x","journal-title":"Sci Rep"},{"key":"1954_CR37","doi-asserted-by":"publisher","first-page":"108247","DOI":"10.1016\/j.compositesb.2020.108247","volume":"202","author":"E Wang","year":"2020","unstructured":"Wang E et al (2020) Characterization of initial and subsequent yield behaviors of closed-cell aluminum foams under multiaxial loadings. Compos B Eng 202:108247. https:\/\/doi.org\/10.1016\/j.compositesb.2020.108247","journal-title":"Compos B Eng"},{"issue":"5","key":"1954_CR38","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1134\/S1029959921050131","volume":"24","author":"MA Tashkinov","year":"2021","unstructured":"Tashkinov MA, Shalimov AS (2021) Modeling of the effect of microscale morphological parameters on the deformation behavior of porous materials with a metal matrix. Phys Mesomech 24(5):618\u2013624. https:\/\/doi.org\/10.1134\/S1029959921050131","journal-title":"Phys Mesomech"},{"key":"1954_CR39","doi-asserted-by":"publisher","first-page":"106164","DOI":"10.1016\/j.ijmecsci.2020.106164","volume":"193","author":"Y He","year":"2021","unstructured":"He Y et al (2021) Construction of 3-D realistic representative volume element failure prediction model of high density rigid polyurethane foam treated under complex thermal-vibration conditions. Int J Mech Sci 193:106164. https:\/\/doi.org\/10.1016\/j.ijmecsci.2020.106164","journal-title":"Int J Mech Sci"},{"issue":"23","key":"1954_CR40","doi-asserted-by":"publisher","first-page":"7881","DOI":"10.1021\/acs.iecr.1c04484","volume":"61","author":"A Heydari","year":"2022","unstructured":"Heydari A et al (2022) Real 3D structure-based finite element simulation of elastomer foams: effect of the foaming agent content. Ind Eng Chem Res 61(23):7881\u20137890. https:\/\/doi.org\/10.1021\/acs.iecr.1c04484","journal-title":"Ind Eng Chem Res"},{"key":"1954_CR41","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1007\/BF01048304","volume":"64","author":"BD Lubachevsky","year":"1991","unstructured":"Lubachevsky BD, Stillinger FH, Pinson EN (1991) Disks vs. spheres: contrasting properties of random packings. J Stat Phys 64:501\u2013524. https:\/\/doi.org\/10.1007\/BF01048304","journal-title":"J Stat Phys"},{"issue":"6","key":"1954_CR42","doi-asserted-by":"publisher","first-page":"061302","DOI":"10.1103\/PhysRevE.82.061302","volume":"82","author":"S Torquato","year":"2010","unstructured":"Torquato S, Jiao Y (2010) Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming. Phys Rev E 82(6):061302. https:\/\/doi.org\/10.1103\/PhysRevE.82.061302","journal-title":"Phys Rev E"},{"issue":"10","key":"1954_CR43","doi-asserted-by":"publisher","first-page":"2107","DOI":"10.1016\/S0022-5096(02)00021-2","volume":"50","author":"J Segurado","year":"2002","unstructured":"Segurado J, Llorca J (2002) A numerical approximation to the elastic properties of sphere-reinforced composites. J Mech Phys Solids 50(10):2107\u20132121. https:\/\/doi.org\/10.1016\/S0022-5096(02)00021-2","journal-title":"J Mech Phys Solids"},{"issue":"16","key":"1954_CR44","doi-asserted-by":"publisher","first-page":"2518","DOI":"10.1016\/j.engfracmech.2006.12.021","volume":"74","author":"I Gitman","year":"2007","unstructured":"Gitman I, Askes H, Sluys L (2007) Representative volume: existence and size determination. Eng Fract Mech 74(16):2518\u20132534. https:\/\/doi.org\/10.1016\/j.engfracmech.2006.12.021","journal-title":"Eng Fract Mech"},{"issue":"1","key":"1954_CR45","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s007910050004","volume":"1","author":"J Sch\u00f6berl","year":"1997","unstructured":"Sch\u00f6berl J (1997) NETGEN An advancing front 2D\/3D-mesh generator based on abstract rules. Comput Vis Sci 1(1):41\u201352. https:\/\/doi.org\/10.1007\/s007910050004","journal-title":"Comput Vis Sci"},{"key":"1954_CR46","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.advengsoft.2016.06.001","volume":"99","author":"K Schneider","year":"2016","unstructured":"Schneider K, Klusemann B, Bargmann S (2016) Automatic three-dimensional geometry and mesh generation of periodic representative volume elements for matrix-inclusion composites. Adv Eng Softw 99:177\u2013188. https:\/\/doi.org\/10.1016\/j.advengsoft.2016.06.001","journal-title":"Adv Eng Softw"},{"issue":"11","key":"1954_CR47","doi-asserted-by":"publisher","first-page":"2557","DOI":"10.1016\/S0022-5096(01)00068-0","volume":"49","author":"Q-C He","year":"2001","unstructured":"He Q-C (2001) Effects of size and boundary conditions on the yield strength of heterogeneous materials. J Mech Phys Solids 49(11):2557\u20132575. https:\/\/doi.org\/10.1016\/S0022-5096(01)00068-0","journal-title":"J Mech Phys Solids"},{"issue":"12","key":"1954_CR48","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1016\/S0167-6636(99)00038-1","volume":"31","author":"C Huet","year":"1999","unstructured":"Huet C (1999) Coupled size and boundary-condition effects in viscoelastic heterogeneous and composite bodies. Mech Mater 31(12):787\u2013829. https:\/\/doi.org\/10.1016\/S0167-6636(99)00038-1","journal-title":"Mech Mater"},{"issue":"9","key":"1954_CR49","doi-asserted-by":"publisher","first-page":"2092","DOI":"10.1016\/j.compscitech.2008.03.013","volume":"68","author":"A Melro","year":"2008","unstructured":"Melro A, Camanho P, Pinho S (2008) Generation of random distribution of fibres in long-fibre reinforced composites. Compos Sci Technol 68(9):2092\u20132102. https:\/\/doi.org\/10.1016\/j.compscitech.2008.03.013","journal-title":"Compos Sci Technol"},{"key":"1954_CR50","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.commatsci.2012.12.036","volume":"70","author":"M Okereke","year":"2013","unstructured":"Okereke M, Akpoyomare A (2013) A virtual framework for prediction of full-field elastic response of unidirectional composites. Comput Mater Sci 70:82\u201399. https:\/\/doi.org\/10.1016\/j.commatsci.2012.12.036","journal-title":"Comput Mater Sci"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-024-01954-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-024-01954-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-024-01954-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T14:56:39Z","timestamp":1729004199000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-024-01954-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,2]]},"references-count":50,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["1954"],"URL":"https:\/\/doi.org\/10.1007\/s00366-024-01954-8","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,2]]},"assertion":[{"value":"25 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}