{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T17:55:09Z","timestamp":1760550909763},"reference-count":107,"publisher":"Elsevier","isbn-type":[{"value":"9780128163900","type":"print"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1016\/b978-0-12-816390-0.00010-8","type":"book-chapter","created":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T17:24:11Z","timestamp":1565976251000},"page":"201-213","source":"Crossref","is-referenced-by-count":2,"title":["Determination of the Anisotropic Mechanical Properties of Bone Tissue Using a Homogenization Technique Combined With Meshless Methods"],"prefix":"10.1016","author":[{"given":"Marco","family":"Marques","sequence":"first","affiliation":[]},{"given":"Jorge","family":"Belinha","sequence":"additional","affiliation":[]},{"given":"Ant\u00f3nio F.","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Renato M.","family":"Natal Jorge","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0010","first-page":"328","article-title":"Meshless Methods in Biomechanics: Bone Tissue Remodelling Analysis","volume":"vol. 2","author":"Belinha","year":"2014"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0015","series-title":"Seeley's Anatomy & Physiology","first-page":"8","volume":"vol. 2","author":"VanPutte","year":"2003"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0020","series-title":"Mechanics of Cellular Bone Remodeling","author":"Qin","year":"2012"},{"issue":"1 suppl","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0025","doi-asserted-by":"crossref","first-page":"5S","DOI":"10.1016\/8756-3282(95)00373-8","article-title":"Mechanical factors in bone growth and development","volume":"18","author":"Carter","year":"1996","journal-title":"Bone"},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0030","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0142-9612(92)90001-5","article-title":"Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures","volume":"13","author":"Mow","year":"1992","journal-title":"Biomaterials"},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0035","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/jbmr.320","article-title":"The amazing osteocyte","volume":"26","author":"Bonewald","year":"2011","journal-title":"J. Bone Miner. Res."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0040","first-page":"387","article-title":"Bone biology. II: formation, form, modeling, remodeling, and regulation of cell function","volume":"45","author":"Buckwalter","year":"1996","journal-title":"Instr. Course Lect."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0045","series-title":"Skeletal Tissue Mechanics","author":"Martin","year":"2015"},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0050","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1038\/nrrheum.2009.239","article-title":"Mechanical signals as anabolic agents in bone","volume":"6","author":"Ozcivici","year":"2010","journal-title":"Nat. Rev. Rheumatol."},{"issue":"9","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0055","doi-asserted-by":"crossref","first-page":"5866","DOI":"10.1074\/jbc.M705092200","article-title":"Mechanical stimulation of bone in vivo reduces osteocyte expression of SOST\/sclerostin","volume":"283","author":"Robling","year":"2008","journal-title":"J. Biol. Chem."},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0060","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.cytogfr.2004.06.004","article-title":"The molecular triad OPG\/RANK\/RANKL: involvement in the orchestration of pathophysiological bone remodeling","volume":"15","author":"Theoleyre","year":"2004","journal-title":"Cytokine Growth Factor Rev."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0065","first-page":"12-1","article-title":"Composite models of bone properties","author":"Lucchinetti","year":"2001"},{"issue":"3\u20134","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0070","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.mser.2012.04.001","article-title":"Elastic modeling of bone at nanostructural level","volume":"73","author":"Hamed","year":"2012","journal-title":"Mater. Sci. Eng. R Rep."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0075","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.cmpb.2016.07.005","article-title":"A multiscale modelling of bone ultrastructure elastic proprieties using finite elements simulation and neural network method","volume":"134","author":"Barkaoui","year":"2016","journal-title":"Comput. Methods Prog. Biomed."},{"issue":"1\u20132","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0080","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s00707-010-0326-5","article-title":"Multiscale modeling of elastic properties of cortical bone","volume":"213","author":"Hamed","year":"2010","journal-title":"Acta Mech."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0085","first-page":"281","article-title":"Micromechanics of bone modeled as a composite material","author":"Jasiuk","year":"2018"},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0090","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1063\/1.3156332","article-title":"Plasticity and toughness in bone","volume":"62","author":"Ritchie","year":"2009","journal-title":"Phys. Today"},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0095","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/8756-3282(95)00076-P","article-title":"The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix","volume":"16","author":"Landis","year":"1995","journal-title":"Bone"},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0100","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1096\/fasebj.6.3.1740237","article-title":"Bone structure: from angstroms to microns","volume":"6","author":"Weiner","year":"1992","journal-title":"FASEB J."},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0105","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1007\/BF00523401","article-title":"Eine neue theorie \u00fcber den Einflu\u03b2 mechanischer reize auf die differenzierung der st\u00fctzgewebe","volume":"121","author":"Pauwels","year":"1960","journal-title":"Z. Anat. Entwicklungsgesch."},{"issue":"5\u20136","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0110","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0895-7177(99)00145-4","article-title":"A simplified model of wound healing (with particular reference to the critical size defect)","volume":"30","author":"Adam","year":"1999","journal-title":"Math. Comput. Model."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0115","series-title":"Gesammelte Abhandlungen zur funktionellen Anatomie des\u2014Friedrich Pauwels\u2014Springer","first-page":"543","author":"Pauwels","year":"1965"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0120","series-title":"The Laws of Bone Structure","author":"Frost","year":"1964"},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0125","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/BF00040896","article-title":"Bone remodeling II: small strain adaptive elasticity","volume":"6","author":"Hegedus","year":"1976","journal-title":"J. Elast."},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0130","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF00130467","article-title":"Bone remodeling III: uniqueness and stability in adaptive elasticity theory","volume":"8","author":"Cowin","year":"1978","journal-title":"J. Elast."},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0135","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1115\/1.2895436","article-title":"An evolutionary Wolff's law for trabecular architecture","volume":"114","author":"Cowin","year":"1992","journal-title":"J. Biomech. Eng."},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0140","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0021-9290(89)90091-2","article-title":"Relationships between loading history and femoral cancellous bone architecture","volume":"22","author":"Carter","year":"1989","journal-title":"J. Biomech."},{"issue":"11\u201312","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0145","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1016\/0021-9290(87)90027-3","article-title":"Mechanical loading history and skeletal biology","volume":"20","author":"Carter","year":"1987","journal-title":"J. Biomech."},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0150","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1002\/jor.1100040307","article-title":"A unifying principle relating stress to trabecular bone morphology","volume":"4","author":"Fyhrie","year":"1986","journal-title":"J. Orthop. Res."},{"issue":"10","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0155","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1016\/0021-9290(88)90015-2","article-title":"Influence of physical activity on the regulation of bone density","volume":"21","author":"Whalen","year":"1988","journal-title":"J. Biomech."},{"issue":"11\u201312","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0160","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1016\/0021-9290(87)90030-3","article-title":"Adaptive bone-remodeling theory applied to prosthetic-design analysis","volume":"20","author":"Huiskes","year":"1987","journal-title":"J. Biomech."},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0165","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF02737117","article-title":"Computational simulation of internal bone remodeling","volume":"4","author":"Pettermann","year":"1997","journal-title":"Arch. Comput. Methods Eng."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0170","first-page":"181","article-title":"Numerical Algorithm for the Simulation of Bone Remodeling","volume":"vol. 17","author":"Reiter","year":"1990"},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0175","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/S0021-9290(96)00140-6","article-title":"Biophysical stimuli on cells during tissue differentiation at implant interfaces","volume":"30","author":"Prendergast","year":"1997","journal-title":"J. Biomech."},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0180","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF02347690","article-title":"Biomechanical model to simulate tissue differentiation and bone regeneration: application to fracture healing","volume":"40","author":"Lacroix","year":"2002","journal-title":"Med. Biol. Eng. Comput."},{"issue":"9","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0185","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1016\/S0021-9290(02)00086-6","article-title":"A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading","volume":"35","author":"Lacroix","year":"2002","journal-title":"J. Biomech."},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0190","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1016\/j.jbiomech.2006.05.007","article-title":"Bone remodelling algorithms incorporating both strain and microdamage stimuli","volume":"40","author":"McNamara","year":"2007","journal-title":"J. Biomech."},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0195","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0021-9290(01)00178-6","article-title":"Anisotropic bone remodelling model based on a continuum damage-repair theory","volume":"35","author":"Doblar\u00e9","year":"2002","journal-title":"J. Biomech."},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0200","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.clinbiomech.2010.01.006","article-title":"Mechanobiological regulation of the remodelling cycle in trabecular bone and possible biomechanical pathways for osteoporosis","volume":"25","author":"Mulvihill","year":"2010","journal-title":"Clin. Biomech."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0205","first-page":"1","article-title":"A meshless microscale bone tissue trabecular remodelling analysis considering a new anisotropic bone tissue material law","volume":"5842","author":"Belinha","year":"2012","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"issue":"8","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0210","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1016\/0021-9290(87)90058-3","article-title":"Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy","volume":"20","author":"Carter","year":"1987","journal-title":"J. Biomech."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0215","first-page":"303","article-title":"The mechanologic bone tissue remodeling analysis","author":"Peyroteo","year":"2018"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0220","article-title":"Mechanical bone remodelling: comparative study of distinct numerical approaches","author":"Peyroteo","year":"2018","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0225","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1006\/jtbi.2001.2372","article-title":"A mathematical framework to study the effects of growth factor influences on fracture healing","volume":"212","author":"Bail\u00f3n-Plaza","year":"2001","journal-title":"J. Theor. Biol."},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0230","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/S8756-3282(03)00157-1","article-title":"Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling","volume":"33","author":"Komarova","year":"2003","journal-title":"Bone"},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0235","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.jtbi.2004.03.023","article-title":"Modeling the interactions between osteoblast and osteoclast activities in bone remodeling","volume":"229","author":"Lemaire","year":"2004","journal-title":"J. Theor. Biol."},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0240","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.bone.2008.03.025","article-title":"Model structure and control of bone remodeling: a theoretical study","volume":"43","author":"Pivonka","year":"2008","journal-title":"Bone"},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0245","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1359\/jbmr.081229","article-title":"Mathematical modeling of spatio-temporal dynamics of a single bone multicellular unit","volume":"24","author":"Ryser","year":"2009","journal-title":"J. Bone Miner. Res."},{"issue":"12","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0250","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1023\/A:1018520914512","article-title":"A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation","volume":"8","author":"Huiskes","year":"1997","journal-title":"J. Mater. Sci. Mater. Med."},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0255","doi-asserted-by":"crossref","first-page":"e0124529","DOI":"10.1371\/journal.pone.0124529","article-title":"Role of mechanical cues in cell differentiation and proliferation: a 3D numerical model","volume":"10","author":"Mousavi","year":"2015","journal-title":"PLoS ONE"},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0260","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s10237-015-0705-x","article-title":"A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse","volume":"15","author":"Lerebours","year":"2016","journal-title":"Biomech. Model. Mechanobiol."},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0265","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1115\/1.3138503","article-title":"A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling","volume":"106","author":"Hart","year":"1984","journal-title":"J. Biomech. Eng."},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0270","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1002\/jor.1100080506","article-title":"An approach for time-dependent bone modeling and remodeling-theoretical development","volume":"8","author":"Beaupr\u00e9","year":"1990","journal-title":"J. Orthop. Res."},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0275","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1016\/S0021-9290(96)00189-3","article-title":"Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations","volume":"30","author":"Jacobs","year":"1997","journal-title":"J. Biomech."},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0280","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/S0045-7949(98)00312-5","article-title":"Topology optimization of three-dimensional linear elastic structures with a constraint on \u201cperimeter\u201d","volume":"73","author":"Fernandes","year":"1999","journal-title":"Comput. Struct."},{"issue":"9","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0285","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1016\/S0021-9290(01)00069-0","article-title":"Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement","volume":"34","author":"Doblar\u00e9","year":"2001","journal-title":"J. Biomech."},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0290","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s10237-014-0584-6","article-title":"A novel approach to estimate trabecular bone anisotropy from stress tensors","volume":"14","author":"Hazrati Marangalou","year":"2015","journal-title":"Biomech. Model. Mechanobiol."},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0295","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1007\/s10237-015-0726-5","article-title":"Prediction of apparent trabecular bone stiffness through fourth-order fabric tensors","volume":"15","author":"Moreno","year":"2016","journal-title":"Biomech. Model. Mechanobiol."},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0300","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/S8756-3282(99)00190-8","article-title":"Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture","volume":"25","author":"Kabel","year":"1999","journal-title":"Bone"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0305","series-title":"Tissue Mechanics","isbn-type":"print","author":"Cowin","year":"2007","ISBN":"http:\/\/id.crossref.org\/isbn\/0387368256"},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0310","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0021-9290(88)90008-5","article-title":"On the dependence of the elasticity and strength of cancellous bone on apparent density","volume":"21","author":"Rice","year":"1988","journal-title":"J. Biomech."},{"issue":"10","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0315","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1016\/S0021-9290(03)00128-3","article-title":"A review of morphology-elasticity relationships in human trabecular bone: theories and experiments","volume":"36","author":"Zysset","year":"2003","journal-title":"J. Biomech."},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0320","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/0021-9290(83)90072-6","article-title":"A survey of finite element analysis in orthopedic biomechanics: the first decade","volume":"16","author":"Huiskes","year":"1983","journal-title":"J. Biomech."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0325","series-title":"The Finite Element Method","author":"Zienkiewicz","year":"1994"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0330","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1093\/mnras\/181.3.375","article-title":"Smooth particle hydrodynamics: theory and application to non-spherical stars","volume":"181","author":"Gingold","year":"1977","journal-title":"Mon. Notices R. Astron. Soc."},{"issue":"13\u201316","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0335","doi-asserted-by":"crossref","first-page":"2009","DOI":"10.1016\/j.cma.2006.11.002","article-title":"Analysis of 3D solids using the natural neighbour radial point interpolation method","volume":"196","author":"Dinis","year":"2007","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"12","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0340","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1002\/nme.4427","article-title":"The natural radial element method","volume":"93","author":"Belinha","year":"2013","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0345","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1108\/02644400610671126","article-title":"Elasto-plastic analysis of plates by the element free Galerkin method","volume":"23","author":"Belinha","year":"2006","journal-title":"Eng. Comput."},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0350","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.compstruct.2005.10.007","article-title":"Nonlinear analysis of plates and laminates using the element free Galerkin method","volume":"78","author":"Belinha","year":"2007","journal-title":"Compos. Struct."},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0355","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.enganabound.2007.08.006","article-title":"Analysis of plates and laminates using the natural neighbour radial point interpolation method","volume":"32","author":"Dinis","year":"2008","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"8","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0360","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1108\/02644400910996835","article-title":"The natural neighbour radial point interpolation method: dynamic applications","volume":"26","author":"Belinha","year":"2009","journal-title":"Eng. Comput."},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0365","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1080\/15376490903249925","article-title":"An unconstrained third-order plate theory applied to functionally graded plates using a meshless method","volume":"17","author":"Dinis","year":"2010","journal-title":"Mech. Adv. Mater. Struct."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0370","doi-asserted-by":"crossref","unstructured":"L.M.J.S. Dinis, R.M. Natal Jorge, J. Belinha, Static and dynamic analysis of laminated plates based on an unconstrained third order theory and using a radial point interpolator meshless method, Comput. Struct. (19) 1771\u20131784, 10.1016\/j.compstruc.2010.10.015.","DOI":"10.1016\/j.compstruc.2010.10.015"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0375","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ijmecsci.2013.08.011","article-title":"Analysis of thick plates by the natural radial element method","volume":"76","author":"Belinha","year":"2013","journal-title":"Int. J. Mech. Sci."},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0380","first-page":"108","article-title":"An\u00e1lise de vigas laminadas utilizando o natural neighbour radial point interpolation method","volume":"30","author":"Moreira","year":"2014","journal-title":"Rev. Internac. Metod. Numer. Calc. Disen. Ingr."},{"issue":"6","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0385","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1080\/15502287.2015.1103819","article-title":"The axisymmetric analysis of circular plates using the radial point interpolation method","volume":"16","author":"Farahani","year":"2015","journal-title":"Int. J. Comput. Methods Eng. Sci. Mech."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0390","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.enganabound.2017.08.010","article-title":"On the optimal shape parameters of distinct versions of RBF meshless methods for the bending analysis of plates","volume":"84","author":"Farahani","year":"2017","journal-title":"Eng. Anal. Bound. Elem."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0395","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1016\/j.prostr.2017.07.018","article-title":"An optimized RBF analysis of an isotropic Mindlin plate in bending","volume":"5","author":"Farahani","year":"2017","journal-title":"Proc. Struct. Integr."},{"issue":"13\u201316","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0400","doi-asserted-by":"crossref","first-page":"2009","DOI":"10.1016\/j.cma.2006.11.002","article-title":"Analysis of 3D solids using the natural neighbour radial point interpolation method","volume":"196","author":"Dinis","year":"2007","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0405","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1016\/j.compstruct.2009.10.014","article-title":"A 3D shell-like approach using a natural neighbour meshless method: isotropic and orthotropic thin structures","volume":"92","author":"Dinis","year":"2010","journal-title":"Compos. Struct."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0410","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.compstruct.2013.03.018","article-title":"Composite laminated plate analysis using the natural radial element method","volume":"103","author":"Belinha","year":"2013","journal-title":"Compos. Struct."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0415","doi-asserted-by":"crossref","DOI":"10.1016\/j.enganabound.2017.12.012","article-title":"Homogenization technique for heterogeneous composite materials using meshless methods","author":"Rodrigues","year":"2018","journal-title":"Eng. Anal. Bound. Elem."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0420","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.enganabound.2015.06.001","article-title":"Crack path prediction using the natural neighbour radial point interpolation method","volume":"59","author":"Azevedo","year":"2015","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0425","doi-asserted-by":"crossref","first-page":"1650006","DOI":"10.1142\/S175882511650006X","article-title":"The natural neighbor radial point interpolation method extended to the crack growth simulation","volume":"8","author":"Belinha","year":"2016","journal-title":"Int. J. Appl. Mech."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0430","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1016\/j.prostr.2017.07.147","article-title":"A GTN failure analysis of an AA6061-T6 Bi-failure specimen","volume":"5","author":"Farahani","year":"2017","journal-title":"Proc. Struct. Integr."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0435","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.matcom.2015.09.002","article-title":"The analysis of the bone remodelling around femoral stems: a meshless approach","volume":"121","author":"Belinha","year":"2016","journal-title":"Math. Comput. Simul."},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0440","doi-asserted-by":"crossref","first-page":"1550059","DOI":"10.1142\/S0219519415500591","article-title":"The mandible remodeling induced by dental implants: a meshless approach","volume":"15","author":"Belinha","year":"2015","journal-title":"J. Mech. Med. Biol."},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0445","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1080\/15376494.2014.987410","article-title":"Numerical analysis of dental implants using a new advanced discretization technique","volume":"23","author":"Duarte","year":"2015","journal-title":"Mech. Adv. Mater. Struct."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0450","first-page":"37","article-title":"The elasto-plastic response of the bone tissue due to the insertion of dental implants","volume":"vol. 110","author":"Tavares","year":"2015"},{"issue":"25\u201328","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0455","doi-asserted-by":"crossref","first-page":"1691","DOI":"10.1016\/j.cma.2010.01.022","article-title":"A comparison of implicit and explicit natural element methods in large strains problems: application to soft biological tissues modeling","volume":"199","author":"Doweidar","year":"2010","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0460","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1177\/0954411917751559","article-title":"A brain impact stress analysis using advanced discretization meshless techniques","volume":"232","author":"Marques","year":"2018","journal-title":"Proc. Inst. Mech. Eng. H"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0465","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.piutam.2017.08.040","article-title":"Biomechanical study of the vestibular system of the inner ear using a numerical method","volume":"24","author":"Santos","year":"2017","journal-title":"Proc. IUTAM"},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0470","doi-asserted-by":"crossref","DOI":"10.1016\/j.enganabound.2018.01.002","article-title":"The free vibrations analysis of the cupula in the inner ear using a natural neighbor meshless method","author":"Santos","year":"2018","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"6\u20138","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0475","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/j.cma.2004.06.031","article-title":"On the employ of meshless methods in biomechanics","volume":"194","author":"Doblar\u00e9","year":"2005","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0480","first-page":"11","article-title":"Simulation of bone internal remodeling by means of the \u03b1-shape-based natural element method","author":"Garc\u00eda","year":"2000"},{"issue":"5","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0485","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1007\/s00466-002-0303-5","article-title":"Meshless method for modeling of human proximal femur: treatment of nonconvex boundaries and stress analysis","volume":"28","author":"Liew","year":"2002","journal-title":"Comput. Mech."},{"issue":"2\u20138","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0490","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.ijengsci.2007.03.007","article-title":"Modeling and simulation of osteoporosis and fracture of trabecular bone by meshless method","volume":"45","author":"Lee","year":"2007","journal-title":"Int. J. Eng. Sci."},{"issue":"9","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0495","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1016\/j.clinbiomech.2008.06.009","article-title":"A new meshless approach for subject-specific strain prediction in long bones: evaluation of accuracy","volume":"23","author":"Taddei","year":"2008","journal-title":"Clin. Biomech."},{"issue":"C","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0500","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.entcs.2010.12.003","article-title":"Bone remodelling in BioShape","volume":"268","author":"Buti","year":"2010","journal-title":"Electron. Notes Theor. Comput. Sci."},{"issue":"11","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0505","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1016\/j.enganabound.2012.05.009","article-title":"Bone tissue remodelling analysis considering a radial point interpolator meshless method","volume":"36","author":"Belinha","year":"2012","journal-title":"Eng. Anal. Bound. Elem."},{"key":"10.1016\/B978-0-12-816390-0.00010-8_bb0510","first-page":"1","article-title":"A meshless microscale bone tissue trabecular remodelling analysis considering a new anisotropic bone tissue material law","volume":"5842","author":"Belinha","year":"2012","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"issue":"3","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0515","first-page":"151","article-title":"A global numerical analysis of the \u201ccentral incisor\/local maxillary bone\u201d system using a meshless method","volume":"11","author":"Moreira","year":"2014","journal-title":"MCB Mol. Cell. Biomech."},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0520","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1142\/S1756973711000509","article-title":"Multiscale continuous and discontinuous modeling of heterogeneous materials: a review on recent developments","volume":"03","author":"Nguyen","year":"2011","journal-title":"J. Multiscale Model."},{"issue":"1","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0525","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1109\/TSMC.1979.4310076","article-title":"A threshold selection method from gray-level histograms","volume":"9","author":"Otsu","year":"1979","journal-title":"IEEE Trans. Syst. Man Cybern."},{"issue":"2","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0530","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1111\/j.1365-2818.1974.tb03878.x","article-title":"The quantitative morphology of anisotropic trabecular bone","volume":"101","author":"Whitehouse","year":"1974","journal-title":"J. Microsc."},{"issue":"7","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0535","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1109\/TUFFC.2008.823","article-title":"Effects of structural anisotropy of cancellous bone on speed of ultrasonic fast waves in the bovine femur","volume":"55","author":"Mizuno","year":"2008","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"issue":"4","key":"10.1016\/B978-0-12-816390-0.00010-8_bb0540","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/S8756-3282(97)00007-0","article-title":"Three-dimensional methods for quantification of cancellous bone architecture","volume":"20","author":"Odgaard","year":"1997","journal-title":"Bone"}],"container-title":["Advances in Biomechanics and Tissue Regeneration"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:B9780128163900000108?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:B9780128163900000108?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T17:25:24Z","timestamp":1565976324000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/B9780128163900000108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9780128163900"],"references-count":107,"URL":"https:\/\/doi.org\/10.1016\/b978-0-12-816390-0.00010-8","relation":{},"subject":[],"published":{"date-parts":[[2019]]}}}