Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences

We propose a new credibility portfolio selection model, in which a measure of loss aversion is introduced as an objective function, joint to the expected value of the returns and the below-mean absolute semi-deviation as a risk measure. The uncertainty of the future returns is directly approximated using the historical returns on the portfolios, so the uncertain return on a given portfolio is modeled as an LR-power fuzzy variable. Quantifying the uncertainty by means of a credibility distribution allows us to measure the investors’ loss aversion as the credibility of achieving a non-positive return, which is better perceived by investors than other measures of risk. Furthermore, we analyze the relationships between the three objective functions, showing that the risk measure and the loss aversion function are practically uncorrelated. Thus, the information provided by these criteria do not overlap each other. In order to generate several non-dominated portfolios taking into account the investor’s preferences and that the problem is non-linear and non-convex, we apply up to three preference-based EMO algorithms. These algorithms allow to approximate a part of the Pareto optimal front called region of interest. We analyze three investor profiles taking into account their loss-adverse attitudes: conservative, cautious and aggressive. A computational study is performed with data of the Spanish stock market, showing the important role played by the loss aversion function to generate a diversified set of non-dominated portfolios fitting the expectations of each investor

A new approach to portfolio selection based on forecasting

In this paper we analyze the portfolio selection problem from a novel perspective based on the analysis and prediction of the time series corresponding to the portfolio’s value. Namely, we define the value of a particular portfolio at the time of its acquisition. Using the time series of historical prices of the different financial assets, we calculate backward the value that said portfolio would have had in past time periods. A damped trend model is then used to analyze this time series and to predict the future values of the portfolio, providing estimates of the mean and variance for different forecasting horizons. These measures are used to formulate the portfolio selection problem, which is solved using a multi-objective genetic algorithm. To show the performance of this procedure, we use a data set of asset prices from the New York Stock Market

Efecto de cubiertas vegetales permanentes en la fertilidad del cultivo de cítricos ecológicos

Se han estudiado diferentes cubiertas vegetales permanentes en mandarinos ecológicos y convencionales de Alzira, en suelo arenoso, para comprobar su comportamiento fertilizante y su crecimiento. En plantación joven, con aspersión, se sembró alfalfa (Medicago sativa), sola y junto a ray-grass inglés (Lolium perenne), trévoles (Trifolium subterraneum+T. repens) y mielgas (Medicago rugosa+M. truncatula+M. polymorpha). En Clemenules adultos a goteo se estudiaron las silvestres en la conducción ecológica, y el no laboreo con herbicidas en la convencional. La evolución muestra como trévoles y mielgas degeraron muy deprisa, dando paso a silvestres (grama -Cynodon dactylon- en verano, y Bromus spp. y otras en invierno), descartándolos como coberturas en estas condiciones. La alfalfa es la que mejor ha resistido la competencia de las hierbas en condiciones de insolación alta y aspersión. En biomasa y cobertura no se han encontrado diferencias entre alfalfa y grama, mientras que las demás eran menores, sobre todo en los adultos, por su sombreado

Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach

[EN] In this work, explicit expressions to estimate all the transversely isotropic elastic constants of lamellar bone as a function of the volumetric bone mineral density (BMD) are provided. The methodology presented is based on the direct homogenization procedure using the finite element method, the continuum approach based on the Hill bounds, the least-square method and the mean field technique. Firstly, a detailed description of the volumetric content of the different components of bone is provided. The parameters defined in this step are related to the volumetric BMD considering that bone mineralization process occurs at the smallest scale length of the bone tissue. Then, a thorough description provides the details of the numerical models and the assumptions adopted to estimate the elastic behaviour of the forward scale lengths. The results highlight the noticeable influence of the BMD on the elastic modulus of lamellar bone. Power law regressions fit the Young's moduli, shear stiffness moduli and Poisson ratios. In addition, the explicit expressions obtained are applied to the estimation of the elastic constants of cortical bone. At this scale length, a representative unit cell of cortical bone is analysed including the fibril orientation pattern given by Wagermaier et al. (Biointerphases 1:1-5, 2006) and the BMD distributions observed by Granke et al. (PLoS One 8:e58043, 2012) for the osteon. Results confirm that fibril orientation arrangement governs the anisotropic behaviour of cortical bone instead of the BMD distribution. The novel explicit expressions obtained in this work can be used for improving the accuracy of bone fracture risk assessment.The authors acknowledge the Ministerio de Economia y Competitividad for the financial support received through the project DPI2013-46641-R and to the Generalitat Valenciana for Programme PROMETEO 2016/007. The authors declare that they have no conflict of interestVercher Martínez, A.; Giner Maravilla, E.; Belda, R.; Aigoun, A.; Fuenmayor Fernández, F. (2018). Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach. Biomechanics and Modeling in Mechanobiology. 17(2):449-464. https://doi.org/10.1007/s10237-017-0971-xS449464172Akiva U, Wagner HD, Weiner S (1998) Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone. J Mater Sci 33:1497–1509Ascenzi A, Bonucci E (1967) The tensile properties of single osteons. Ana Rec 158:375–386Barbour KE, Zmuda JM, Strotmeyer ES, Horwitz MJ, Boudreau R, Evans RW, Ensrud K, Petit MA, Gordon CL, Cauley JA (2013) Correlates of trabecular and cortical volumetric bone mineral density of the radius and tibia older men: the osteoporotic fractures in men study. J Bone Miner Res 25(5):1017–1028Bar-On B, Wagner HD (2013) Structural motifs and elastic properties of hierarchical biological tissues—a review. J Struct Biol 183:149–164Cowin SC (2000) How is a tissue built? J Biomech Eng 122:553–569Cowin SC (2001) Bone mechanics handbook, 2nd edn. CRC Press, Boca RatonCurrey JD (1986) Power law models for the mechanical properties of cancellous bone. Eng Med 15(3):153–154Currey JD (1988) The effect of porosity and mineral content on the Young’s modulus of elasticity of compact bone. J Biomech 21:131–139Daszkiewicz K, Maquer G, Zysset PK (2017) The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements. Biomech Model Mechanobiol 16:731–742Faingold A, Sidney RC, Wagner HD (2012) Nanoindentation of osteonal bone lamellae. J Mech Biomech Materials 9:198–206Fratzl P, Fratzl-Zelman N, Klaushofer K, Vogl G, Koller K (1991) Nucleation and growth of mineral crystals in bone studied by small-angle X-ray scattering. Calcif Tissue Int 48:407–413Fritsch A, Hellmich C (2007) ’Universal’ microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. J Theo Biol 24:597–620Grampp S, Genant HK, Mathur A, Lang P, Jergas M, Takada M, Glüer CC, Lu Y, Chavez M (1997) Comparisons of noninvasive bone mineral measurements in assessing age-related loss, fracture discrimination and diagnostic classification. J Bone Miner Res 12:697–711Grant CA, Langton C, Schuetz MA, Epari DR (2011) Determination of the material properties of ovine cortical bone. Poster No. 2226, 57th Orthopaedic Research Society (ORS) Annual meeting, Long Beach, CaliforniaGranke M, Gourrier A, Rupin F, Raum K, Peyrin F, Burghammer M, Saïd A, Laugier P (2012) Microfibril orientation dominates the microelastic properties of human bone tissue at the lamellar length scale. PLoS One 8:e58043Gurtin ME (1972) The linear theory of elasticity. Handbuch del Physik VIa 2:1–296Hamed E, Jasiuk I (2012) Elastic modeling of bone at nanostructural level. Mat Sci Eng R73:27–49Hernández CJ, Beaupré GS, Keller TS, Carter DR (2001a) The influence of bone volume fraction and ash fraction on bone strength and modulus. Bone 29:74–78Hill R (1952) The elastic behaviour of a crystalline aggregate. Proc Phys Soc Sec A 65:349–354Hodge AJ, Petruska JA (1963) Recent studies with the electron microscope on ordered aggregates of the tropocollagen macromolecule. In: Ramachandran GN (ed) Aspects of protein structure. Academic Press, New York, pp 289–300Jäger I, Fratzl P (2000) Mineralized collagen: a mechanical model with a staggered arrangement of mineral particles. Biophys J 78:1737–1746Kuhn JL, Goldstein SA, Choi K, London M, Feldkamp LA, Matthews LS (1989) Comparison of the trabecular and cortical tissue moduli from human iliac crests. J Orthop Res 7:876–884Landis WJ, Song MJ, Leith A, McEwen L, McEwen BF (1993) Mineral and organic matrix interaction in normally calcifying tendon visualized in three dimensions by high-voltage electron microscopic tomography and graphic image reconstruction. J Struct Biol 110:39–54Lees S, Heeley JD, Cleary PF (1979) A study of some properties of a sample of bovine cortical bone using ultrasound. Calcif Tissue Int 29:107–117Lekhnitskii SG (1963) Theory of elasticity of anisotropic elastic body. Holden-Day, San Francisco, pp 1–73Lempriere BM (1968) Poisson’s ratio in orthotropic materials. Am Inst Aeronaut Astronaut J J6:2226–2227Liu Y, Kim YK, Dai L, Li N, Khan SO, Pashley DH, Tay FR (2011) Hierarchical and non-hierarchical mineralization of collagen. Biomater 32:1291–1300Majumdar S, Kothari M, Augat P, Newitt DC, Link TM, Lin JC, Lang T, Lu Y, Genant HK (1998) High-resolution magnetic resonance imaging: three-dimensional trabecular bone architecture and biomechanical properties. Bone 22(5):445–454Martínez-Reina J, Domínguez J, García-Aznar JM (2011) Effect of porosity and mineral content on the elastic constants of cortical bone: a multiscale approach. Biomech Model Mechanobiol 10:309–322Nobakhti S, Limbert G, Thurner PJ (2014) Cement lines and interlamellar areas in compact bone as strain amplifiers—Contributors to elasticity, fracture toughness and mechanotransduction. J Mech Behav Biomed Mater 29:235–251Orgel JPRO, Irving TC, Miller A, Wess TJ (2006) Microfibrillar structure of type I collagen in situ. PNAS USA 103:9001–9005Reisinger AG, Pahr DH, Zysset PK (2010) Sensitivity analysis and parametric study of elastic properties of unidirectional mineralized bone fibril-array using mean field methods. Biomech Model Mechanobiol 9:499–510Reisinger AG, Pahr DH, Zysset PK (2011) Elastic anisotropy of bone lamellae as a function of fibril orientation pattern. Biomech Model Mechanobiol 10:67–77Rho JY, Kuhn-Spearing L, Zioupos P (1998) Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20:92–102Robinson RA, Rochester MD (1952) An electron-microscopic study of the crystalline inorganic component of bone and its relationship to the organic matrix. J Bone Joint Surg 34–a:389–435Roque WL, Arcaro K, Alberich-Bayarri A (2013) Mechanical competence of bone: a new parameter to grade trabecular bone fragility from tortuosity and elasticity. IEEE Trans Bio Eng 60:1363–1370Rubin MA, Jasiuk I, Taylor J, Rubin J, Ganey T, Apkarian RP (2003) TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. Bone 33:270–282Sasaki N, Tagami A, Goto T, Taniguchi M, Nakata M, Hikichi K (2002) Atomic force microscopic studies on the structure of bovine femoral cortical bone at the collagen fibril-mineral level. J Mater Sci Mater Med 13(3):333–337Schaffler MB, Burr DB (1988) Stiffness of compact bone: effects of porosity and density. J Biomech 21:13–16Silver FH, Landis WJ (2011) Deposition of apatite in mineralizing vertebrate extracellular matrices: a model of possible nucleation sites on type I collagen. Connect Tissue Res 52:242–254Tommasini SM, Nasser P, Hu B, Jepsen KJ (2008) Biological co-adaptation of morphological and composition traits contributes to mechanical functionality and skeletal fragility. J Bone Miner Res 23:236–246Ulrich D, Rietbergen B, Weinans H, Rüegsegger P (1998) Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech 31:1187–1192Ulrich D, Rietbergen B, Laib A, Rüegsegger P (1999) The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone 25:55–60Vercher A, Giner E, Arango C, Tarancón JE, Fuenmayor FJ (2014) Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models. Biomech Model Mechanobiol 13:437–449Vercher-Martínez A, Giner E, Arango C, Fuenmayor FJ (2015) Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone. J Mech Behav Biomed Mater 42:243–256Wagermaier W, Gupta HS, Gourrier A, Burghammer M, Roschger P, Fratzl P (2006) Spiral twisting of fiber orientation inside bone lamellae. Biointerphases 1:1–5Weiner S, Traub W (1986) Organization of hydroxiapatite within collagen fibrils. FEBS Lett 206:262–266Weiner S, Wagner HD (1998) The material bone: structure-mechanical function relations. Annu Rev Mater Sci 28:271–298Yang L, Palermo L, Black DM, Eastell R (2014) Prediction of incident hip fracture with the estimated femoral strength by finite element analysis of DXA scans in the study of osteoporotic fractures. JBMR 29:2594–2600Yuan YJ, Cowin SC (2008a) The estimated elastic constants for a single bone osteonal lamella. Biomech Model Mechanobiol 7:1–11Yu W, Glüer CC, Grampp S, Jergas M, Fuerst T, Wu CY, Lu Y, Fan B, Genant HK (1995) Spinal bone mineral assessment in postmenopausal women: a comparison between dual X-ray absorptiometry and quantitative computed tomography. Osteoporos Int 5:433–439Yang L, Palermo L, Black DM, Eastell R (2014) Prediction of incident hip fracture with the estimated femoral strength by finite element analysis of DXS Scans in the study of osteoporotic fractures. J Bone Miner Res 29(12):2594–2600Yuan F, Stock SR, Haeffner DR, Almer JD, Dunand DC, Brinson LC (2011) A new model to simulate the elastic properties of mineralized collagen fibril. Biomech Model Mechanobiol 10:147–16

Non-destructive Techniques Methodologies for the Detection of Ancient Structures under Heritage Buildings

[EN] Structures and elements buried beneath heritage buildings are frequent but are often unknown and inaccessible. Therefore, they are difficult to locate in general if an archaeological excavation is not carried out, with the economic cost and time involved. It is important to discover them in order to increase our knowledge of cultural heritage, as well as to know, recover and improve the state of conservation of the materials that make up these structures. This paper presents methodologies for locating old structures using a low-cost NDT approach, with a qualitative and quantitative analysis of GPR profiles in heritage buildings. Small perforations are performed at critical points and introducing an endoscope for verification. Various crypts have been located using the proposed methodologies in a real study case: The Church of the Asución of Llíria in Spain.Gil Benso, E.; Mas Tomas, MDLA.; Lerma Elvira, C.; Torner, ME.; Vercher Sanchis, J. (2021). Non-destructive Techniques Methodologies for the Detection of Ancient Structures under Heritage Buildings. International journal of architectural heritage (electronic). 15(10):1457-1473. https://doi.org/10.1080/15583058.2019.1700320S14571473151

Abundance, movements and biodiversity of flying predatory insects in crop and non-crop agroecosystems

[EN] Predatory insects are key natural enemies that can highly reduce crops pest damage. However, there is a lack of knowledge about the movements of flying predatory insects in agroecosystems throughout the year. In particular, it is still unclear how these predators move from crop to non-crop habitats, which are the preferred habitats to overwinter and to spread during the spring and if these predators leave or stay after chemical treatments. Here, the Neuroptera, a generalist, highly mobile, flying predator order of insects, was selected as model. We studied the effects of farming management and the efficiency of edge shelterbelts, ground cover vegetation, and fruit trees canopy on holding flying predatory insects in Mediterranean traditional agroecosystems. Seasonal movements and winter effects were also assessed. We evaluated monthly nine fruit agroecosystems, six organic, and three pesticides sprayed, of 0.5-1 ha in eastern Spain during 3 years using two complementary methods, yellow sticky traps and aspirator. Results show surprisingly that the insect abundance was highest in pesticide sprayed systems, with 3.40 insects/sample versus 2.32 insects/sample in organic systems. The biodiversity indices were highest in agroecosystems conducted under organic management, with S of 4.68 and D of 2.34. Shelterbelts showed highest biodiversity indices, S of 3.27 and D of 1.93, among insect habitats. Insect species whose adults were active during the winter preferred fruit trees to spend all year round. However, numerous species moved from fruit trees to shelterbelts to overwinter and dispersed into the orchard during the following spring. The ground cover vegetation showed statistically much lower attractiveness for flying predatory insects than other habitats. Shelterbelts should therefore be the first option in terms of investment in ecological infrastructures enhancing flying predators.Sorribas Mellado, JJ.; González Cavero, S.; Domínguez Gento, A.; Vercher Aznar, R. (2016). Abundance, movements and biodiversity of flying predatory insects in crop and non-crop agroecosystems. Agronomy for Sustainable Development. 36(2). doi:10.1007/s13593-016-0360-3S362Altieri MA, Letourneau DK (1982) Vegetation management and biological control in agroecosystems. Crop Prot 1:405–430. doi: 10.1016/0261-2194(82)90023-0Altieri MA, Schmidt LL (1986) The dynamics of colonizing arthropod communities at the interface of abandoned, organic and commercial apple orchards and adjacent woodland habitats. Agric Ecosyst Environ 16:29–43. doi: 10.1016/0167-8809(86)90073-3Bengtsson J, Ahnström J, Weibull A (2005) The effects of organic agriculture on biodiversity and abundance: a meta-analysis. J App Ecol 42:261–269. doi: 10.1111/j.1365-2664.2005.01005.xBianchi F, Booij CJH, Tscharntke T (2006) Sustainable pest regulation in agricultural landscapes: a review on landscape composition, biodiversity and natural pest control. Proc R Soc B 273:1715–1727. doi: 10.1098/rspb.2006.3530Chaplin-Kramer RM, Rourke E, Blitzer EJ, Kremen C (2011) A meta-analysis of crop pest and natural enemy response to landscape complexity. Ecol Lett 14:922–932. doi: 10.1111/j.1461-0248.2011.01642.xCrowder DW, Northfield TD, Strand MR, Snyder WE (2010) Organic agriculture promotes evenness and natural pest control. Nature 466:109–112. doi: 10.1038/nature09183Dogramaci M, DeBano SJ, Kimoto C, Wooster DE (2011) A backpack-mounted suction apparatus for collecting arthropods from various habitats and vegetation. Entomol Exp et Appl 139:86–90. doi: 10.1111/j.1570-7458.2011.01099.xDuelli P, Studer M, Marchland I, Jakob S (1990) Population movements of arthropods between natural and cultivated areas. Biol Conserv 54:193–207. doi: 10.1016/0006-3207(90)90051-PEilenberg J, Hajek A, Lomer C (2001) Suggestions for unifying the terminology in biological control. BioControl 46:387–400. doi: 10.1023/A:1014193329979Forman RTT, Baudry J (1984) Hedgerows and hedgerow networks in landscape ecology. Environ Manage 8:495–510. doi: 10.1007/BF01871575Gurr GM, Wratten SD, Luna JM (2003) Multi-function agricultural biodiversity: pest management and other benefits. Basic Appl Ecol 4:107–116. doi: 10.1078/1439-1791-00122Hole DG, Perkins AJ et al (2005) Does organic farming benefit biodiversity? Biol Conserv 122:113–130. doi: 10.1016/j.biocon.2004.07.018Landis DA, Wratten SD, Gurr GM (2000) Habitat management to conserve natural enemies of arthropod pests in agriculture. Annu Rev Entomol 45:175–201. doi: 10.1146/annurev.ento.45.1.175Long RF, Corbett A, Lamb C, Reberg-Horton C, Chandler J, Stimmann M (1998) Beneficial insects move from flowering plants to nearby crops. Calif Agr 52:23–26. doi: 10.3733/ca.v052n05p23Östman Ö, Ekbom B, Bengtsson J (2001) Landscape heterogeneity and farming practice influence biological control. Basic App Ecol 2:365–371. doi: 10.1078/1439-1791-00072Pantaleoni RA, Ticchiati V (1988) I Neurotteri delle colture agrarie: osservazioni sulle fluttuazioni stagionali di populazione in frutteti. Boll dell’Ist di Entomol 43:43–57Panzer R, Schwartz MW (1998) Effectiveness of a vegetation-based approach to insect conservation. Conserv Biol 12:693–702. doi: 10.1111/j.1523-1739.1998.97051.xParedes D, Cayuela L, Gurr G, Campos M (2013) Effect of non-crop vegetation types on conservation biological control of pests in olive groves. PeerJ 1:1–16. doi: 10.7717/peerj.116Pekar S, Michalko R, Loverre P, Líznarová E, Cernecká L (2015) Biological control in winter: novel evidence for the importance of generalist predators. J Appl Ecol 52:270–279. doi: 10.1111/1365-2664.12363Pollard KA, Holland JM (2006) Arthropods within the woody element of hedgerows and their distribution pattern. Agric Forest Entomol 8:203–211. doi: 10.1111/j.1461-9563.2006.00297.xRand TA, Tylianakis JM, Tscharntke T (2006) Spillover edge effects: the dispersal of agriculturally subsidized insect natural enemies into adjacent natural habitats. Ecol Lett 9:603–614. doi: 10.1111/j.1461-0248.2006.00911.xSilva EB, Franco JC, Vasconcelos T, Branco M (2010) Effect of ground cover vegetation on the abundance and diversity of beneficial arthropods in citrus orchards. Bull Entomol Res 100:489–499. doi: 10.1017/S0007485309990526Smukler SM, Sánchez-Moreno S et al (2010) Biodiversity and multiple ecosystem functions in an organic farmscape. Agric Ecosyst Environ 139:80–97. doi: 10.1016/j.agee.2010.07.004Stelzl M, Devetak D (1999) Neuroptera in agricultural ecosystems. Agric Ecosyst Environ 74:305–321. doi: 10.1016/S0167-8809(99)00040-7Straub CS, Finke DL, Snyder WE (2008) Are the conservation of natural enemy biodiversity and biological control compatible goals? Biol Control 45:225–237. doi: 10.1016/j.biocontrol.2007.05.013Thierry D, Deutsch B, Paulian M, Villenave J, Canard M (2005) Typifying ecosystems by using green lacewing assemblages. Agron Sustain Dev 25:473–479. doi: 10.1051/agro:2005047Thomas CFG, Parkinson L, Griffiths GJK, García AF, Marshall EJP (2001) Aggregation and temporal stability of carabid beetle distributions in field and hedgerow habitats. J App Ecol 38:100–116. doi: 10.1046/j.1365-2664.2001.00574.xVillenave J, Thierry D, Mamun A, Lode T, Rat-Morris E (2005) The pollens consumed by common green lacewings Chrysoperla spp. in cabbage crop environment in western France. 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Analysis of the residual safety level in R/C slabs with severe joist corrosion

An analysis until the failure on a series of one-way slabs with severe corrosion at the lower reinforcement of the R/C joists is presented. Different positions in the slab and number of damaged joists have been studied, obtaining the residual safety assessment in cases of slabs damaged by flexural failure mechanisms. Since the boundary conditions have proved decisive for obtaining the behavior, the damaged slab has been evaluated as part of the entire building, as precisely as possible, taking into account the different phases of the construction process and deterioration in time, and the complex behavior of concrete, steel and masonry. The results of the proposed methodology are consistent with the pathology of the observed cases. As a result of this study the authors propose practical recommendations to help in making decisions about the magnitude of the intervention, always necessary in this type of pathology.Vercher Sanchis, JM.; Gil Benso, E.; Mas Tomas, MDLA.; Cubel Arjona, FJ. (2014). Analysis of the residual safety level in R/C slabs with severe joist corrosion. Journal of Performance of Constructed Facilities. 1-14. doi:10.1061/(ASCE)CF.1943-5509.0000608S11

Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models

Mineralized collagen fibrils have been usually analyzed like a two phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that, when Halpin-Tsai equations are applied to estimate elastic constants from typical constituent properties, not all crystal dimensions yield a model that satisfy thermodynamic restrictions. We provide the ranges of platelet dimensions that lead to positive definite stiffness matrices. On the other hand, a finite element model of a mineralized collagen fibril unit cell under periodic boundary conditions is analyzed. By applying six canonical load cases, homogenized stiffness matrices are numerically calculated. Results show a monoclinic behavior of the mineralized collagen fibril. In addition, a 5-layer lamellar structure is also considered where crystals rotate in adjacent layers of a lamella. The stiffness matrix of each layer is calculated applying Lekhnitskii transformations and a new finite lement model under periodic boundary conditions is analyzed to calculate the homogenized 3D anisotropic stiffness matrix of a unit cell of lamellar bone. Results are compared with the rule-of-mixtures showing in general good agreement.The authors acknowledge the Ministerio de Economia y Competitividad the financial support given through the project DPI2010-20990 and the Generalitat Valenciana through the Programme Prometeo 2012/023. The authors thank Ms. Carla Gonzalez Carrillo by her help in the development of some of the numerical models.Vercher Martínez, A.; Giner Maravilla, E.; Arango Villegas, C.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ. (2014). Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models. 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