Parametric model for the simulation of the railway catenary system static equilibrium problem

Dynamic simulations of pantograph catenary interaction are nowadays essential for improving the performance of railway locomotives, by achieving better current collection at higher speeds and lower wear of thecollecting parts.The first step in performing these simulations is to compute the static equilibrium of the overhead line.The initial dropper lengths play an important role in hanging the contact wire at an appropriate height. From a classical point of view, if one wants to obtain the static equilibrium configuration of the system for different combinations of dropper lengths, one static pro- blem must be solved for each combination of lengths, which involves a prohibitive computational cost. In this paper we propose a parametric model of the catenary, including the undeformed dropper lengths as extra-coordinates of the problem. This multidimensional problem is efficiently solved by means of the Proper Generalized Decomposition (PGD) technique, avoiding the curse of dimensionality issue. The capabilities and performance of the proposed method are shown by numerical examples.The authors would like to acknowledge the financial support of the FPU program offered by the Ministerio de Educacion, Cultura y Deporte under Grant number FPU13/04191. The funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged.Gregori Verdú, S.; Tur Valiente, M.; Nadal, E.; Fuenmayor Fernández, FJ.; Chinesta, F. (2016). Parametric model for the simulation of the railway catenary system static equilibrium problem. Finite Elements in Analysis and Design. 115:21-32. https://doi.org/10.1016/j.finel.2016.02.007S213211

A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework

[EN] Today industries do not only require fast simulation techniques but also verification techniques for the simulations. The proper generalized decomposition (PGD) has been situated as a suitable tool for fast simulation for many physical phenomena. However, so far, verification tools for the PGD are under development. The PGD approximation error mainly comes from two different sources. The first one is related with the truncation of the PGD approximation and the second one is related with the discretization error of the underlying numerical technique. In this work we propose a fast error indicator technique based on recovery techniques, for the discretization error of the numerical technique used by the PGD technique, for refinement purposes.Authors 5 and 6 thank the financial support of the research Project DPI2013-46317-R of the Ministerio de Economia y Competitividad (Spain). The funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged. These authors also thank the support of the Framework Programme 7 Initial Training Network Funding under Grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology".Nadal, E.; Leygue, A.; Chinesta, F.; Beringhier, M.; Ródenas, J.; Fuenmayor Fernández, FJ. (2015). A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. Computational Mechanics. 55(2):251-266. https://doi.org/10.1007/s00466-014-1097-yS251266552Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newton Fluid Mech 139:153–176Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. J Non-Newton Fluid Mech 144:98–121Chinesta F, Ladeveze P, Cueto E (2011) A short review on model order reduction based on proper generalized decomposition. Arch Comput Methods Eng 18:395–404Giner E, Bognet B, Ródenas JJ, Leygue A, Fuenmayor FJ, Chinesta F (2013) The proper generalized decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics. Int J Solids Struct 50:1710–1720Chinesta F, Ammar A, Leygue A, Keunings R (2011) An overview of the proper generalized decomposition with applications in computational rheology. J Non-Newton Fluid Mech 166(11):578–592Ammar A, Chinesta F, Diez P, Huerta A (2010) An error estimator for separated representations of highly multidimensional models. Comput Methods Appl Mech Eng 199(25–28):1872–1880Moitinho de Almeida JP (2013) A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics. Int J Numer Methods Eng 94:961–984Ladevèze P, Chamoin L (2011) On the verification of model reduction methods based on the proper generalized decomposition. Comput Methods Appl Mech Eng 200:2032–2047Ladevèze P, Leguillon D (1983) Error estimate procedure in the finite element method and applications. SIAM J Numer Anal 20(3):485–509Babuška I, Rheinboldt WC (1978) A-posteriori error estimates for the finite element method. Int J Numer Methods Eng 12(10):1597–1615Ródenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70(6):705–727Díez P, Parés N, Huerta A (2003) Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates. Int J Numer Methods Eng 56(10):1465–1488Bognet B, Bordeu F, Chinesta F, Leygue A, Poitou A (2012) Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity. Comput Methods Appl Mech Eng 201–204:1–12Bognet B, Leygue A, Chinesta F (2014) Separated representations of 3D elastic solutions in shell geometries. Adv Model Simul Eng Sci 1(1):1–4Ghnatios C, Chinesta F, Binetruy C (2013) 3D modeling of squeeze flows occurring in composite laminates. Int J Mater Form 9(1):1–11Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2):337–357Chinesta F, Keunings R, Leygue A (2013) The proper generalized decomposition for advanced numerical simulations: a primer. Springer Publishing Company, New York IncorporatedDonea J, Huerta A (2002) Finite element methods for flow problems. Wiley, New YorkGonzalez D, Cueto E, Chinesta F, Diez P, Huerta A (2013) SUPG-based stabilization of proper generalized decompositions for high-dimensional advection-diffusion equations. Int J Numer Methods Eng 94(13):1216–1232Chinesta F, Ammar A, Cueto E (2010) Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models. Arch Comput Methods Eng 17(4):327–350Chinesta F, Leygue A, Bordeu F, Aguado JV, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A (2013) PGD-based computational vademecum for efficient design, optimization and control. Arch Comput Methods Eng 20:31–59Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33(7):1331–1364Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33(7):1365–1382Kvamsdal T, Okstad KM (1998) Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int J Numer Methods Eng 42(3):443–472Wiberg NE, Abdulwahab F (1993) Patch recovery based on superconvergent derivatives and equilibrium. Int J Numer Methods Eng 36(16):2703–2724Wiberg NE, Abdulwahab F, Ziukas S (1994) Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. Int J Numer Methods Eng 37(20):3417–3440Blacker T, Belytschko T (1994) Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37(3):517–536Ródenas JJ, González-Estrada OA, Tarancón JE, Fuenmayor FJ (2008) A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting. Int J Numer Methods Eng 76(4):545–571Ródenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2010) Accurate recovery-based upper error bounds for the extended finite element framework. Comput Methods Appl Mech Eng 199(37–40):2607–2621Nadal E, (2014) Cartesian grid FEM (cgFEM): high performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization. PhD thesis, Universitat Politècnica de ValènciaKarihaloo BL, Xiao QZ (2003) Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct 81(3):119–129González-Estrada OA, Ródenas JJ, Chinesta F, Fuenmayor FJ (2013) Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM. Comput Mech 52:321–344Fuenmayor FJ, Oliver JL (1996) Criteria to achieve nearly optimal meshes in the h-adaptive finite element mehod. Int J Numer Methods Eng 39(23):4039–4061Fuenmayor F, Restrepo J, Tarancón J, Baeza L (2001) Error estimation and h-adaptive refinement in the analysis of natural frequencies. Finite Elem Anal Des 38:137–15

Fast simulation of the pantograph-catenary dynamic interaction

Simulation of the pantograph-catenary dynamic interaction has now become a useful tool for designing and optimizing the system. In order to perform accurate simulations, including system non-linearities, the Finite Element Method is commonly employed combined with a time integration scheme, even though the computational time required may be longer than with the use of other simpler approaches. In this paper we propose a two-stage methodology (Offline/Online) which notably reduces the computational cost without any loss in accuracy and makes it possible to successfully carry out very efficient optimizations or even Hardware in the Loop simulations with real-time requirements.The authors would like to acknowledge the financial support received from the FPU program offered by the Ministerio de Educacion, Cultura y Deporte under grant number (FPU13/04191), and also funding from the Universitat Politecnica de Valencia and the Generalitat Valenciana (PROMETEO/2016/007).Gregori Verdú, S.; Tur Valiente, M.; Nadal Soriano, E.; Aguado, J.; Fuenmayor Fernández, FJ.; Chinesta, F. (2017). Fast simulation of the pantograph-catenary dynamic interaction. Finite Elements in Analysis and Design. 129:1-13. https://doi.org/10.1016/j.finel.2017.01.007S11312

Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method

The computation of stress intensity factors (SIFS) in curved and non-planar cracks using domain integrals introduces some difficulties related to the use of curvilinear gradients. Several approaches exist in the literature that consider curvilinear corrections within a finite element framework, but these depend on each particular crack configuration and they are not general. In this work, we introduce the curvilinear gradient correction within the extended finite element method framework (XFEM), based only on the level set information used for the crack description and the local coordinate system definition. Our formulation depends only on the level set coordinates and, therefore, an explicit analytical description of the crack is not needed. It is shown that this curvilinear correction improves the results and enables the study of generic cracks. In addition, we have introduced a simple error indicator for improving the SIF computed via the interaction integral, thanks to the better behavior of the J-integral as it does not need auxiliary extraction fields.This work has been carried out within the framework of the research projects DPI2007-66995-C03-02 and DPI2010-20990 financed by the Ministerio de Economia y Competitividad. The support of the Generalitat Valenciana, Programme PROMETEO 2012/023 is also acknowledged.González Albuixech, VF.; Giner Maravilla, E.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ.; Gravouil, A. (2013). Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method. Computer Methods in Applied Mechanics and Engineering. 264:129-144. https://doi.org/10.1016/j.cma.2013.05.016S12914426

Calculation of the critical energy release rate Gc of the cement line in cortical bone combining experimental tests and finite element models

[EN] In this work, a procedure is proposed to estimate the critical energy release rate Gc of the so-called cement line in cortical bone tissue. Due to the difficulty of direct experimental estimations, relevant elastic and toughness material properties at bone microscale have been inferred by correlating experimental tests and finite element simulations. In particular, three-point bending tests of ovine cortical bone samples have been performed and modeled by finite elements. The initiation and growth of microcracks in the tested samples are simulated through finite elements using a damage model based on a maximum principal strain criterion, showing a good correlation with the experimental results. It is observed that microcracks evolve mainly along the cement lines and through the interstitial material but without crossing osteons. The numerical model allows the calculation of the cement line critical energy release rate Gc by approximating its definition by finite differences. This way, it is possible to estimate this property poorly documented in the literature.The authors wish to thank the Ministerio de Economia y Competitividad for the support received in the framework of the project DPI2013-46641-R and to the Generalitat Valenciana, Programme PROMETEO 2016/007. The authors also thank Dr. Jose Luis Peris, from Instituto de Biomecanica de Valencia (IBV) and Carlos Tudela Desantes for their collaboration within the context of the project.Giner Maravilla, E.; Belda, R.; Arango-Villegas, C.; Vercher Martínez, A.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ. (2017). Calculation of the critical energy release rate Gc of the cement line in cortical bone combining experimental tests and finite element models. Engineering Fracture Mechanics. 184:168-182. https://doi.org/10.1016/j.engfracmech.2017.08.026S16818218

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. Biomechanics and Modeling in Mechanobiology. 13(2):1-21. https://doi.org/10.1007/s10237-013-0507-yS121132Akiva 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. Anat Rec 158:375–386Ascenzi A, Bonucci E (1968) The compressive properties of single osteons. Anat Rec 161:377–392Ashman RB, Cowin SC, van Buskirk WC, Rice JC (1984) A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech 17:349–361Bar-On B, Wagner HD (2012) Elastic modulus of hard tissues. J Biomech 45:672–678Bondfield W, Li CH (1967) Anisotropy of nonelastic flow in bone. J Appl Phys 38:2450–2455Cowin SC (2001) Bone mechanics handbook, 2nd edn. CRC Press Boca Raton, FloridaCowin SC, van Buskirk WC (1986) Thermodynamic restrictions on the elastic constant of bone. J Biomech 19:85–86Currey JD (1962) Strength of bone. Nature 195:513Cusack S, Miller A (1979) Determination of the elastic constants of collagen by brillouin light scattering. J Mol Biol 135:39–51Doty S, Robinson RA, Schofield B (1976) Morphology of bone and histochemical staining characteristics of bone cells. In: Aurbach GD (ed) Handbook of physiology. American Physiology Soc, Washington, pp 3–23Erts D, Gathercole LJ, Atkins EDT (1994) Scanning probe microscopy of crystallites in calcified collagen. J Mater Sci Mater Med 5:200–206Faingold A, Sidney RC, Wagner HD (2012) Nanoindentation of osteonal bone lamellae. J Mech Biomech Materials 9:198–206Franzoso G, Zysset PK (2009) Elastic anisotropy of human cortical bone secondary osteons measured by nanoindentation. J Biomech Eng 131:021001Gebhardt W (1906) Über funktionell wichtige Anordnungsweisen der eineren und grösseren Bauelemente des Wirbeltierknochens. II. Spezieller Teil. Der Bau der Haversschen Lamellensysteme und seine funktionelle Bedeutung. Arch Entwickl Mech Org 20:187–322Gibson RF (1994) Principles of composite material mechanics. McGraw-Hill, New YorkGiraud-Guille M (1988) Twisted plywood architecture of collagen fibrils in human compact bone osteons. Calcif Tissue Int 42:167–180Gurtin ME (1972) The linear theory of elasticity. Handbuch der Physik VIa/ 2:1–296Halpin JC (1992) Primer on composite materials: analysis, 2nd edn. CRC Press, Taylor & Francis, Boca Raton, FloridaHassenkam T, Fantner GE, Cutroni JA, Weaver JC, Morse DE, Hanma PK (2004) High-resolution AFM imaging of intact and fractured trabecular bone. Bone 35:4–10Hohe J (2003) A direct homogenization approach for determination of the stiffness matrix for microheterogeneous plates with application to sandwich panels. Composites Part B 34:615–626Hulmes DJS, Wess TJ, Prockop DJ, Fratzl P (1995) Radial packing, order, and disorder in collagen fibrils. Biophys J 68:1661–1670Jäger I, Fratzl P (2000) Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys J 79:1737–1746Ji B, Gao H (2004) Mechanical properties of nanostructure of biological materials. J Mech Phy Sol 52:1963–1990Landis WJ, Hodgens KJ, Aerna J, Song MJ, McEwen BF (1996) Structural relations between collagen and mineral in bone as determined by high voltage electron microscopic tomography. Microsc Res Tech 33:192–202Lekhnitskii SG (1963) Theory of elasticity of an anisotropic elastic body. Holden-Day, San FranciscoLempriere BM (1968) Poisson’s ratio in orthotropic materials. Am Inst Aeronaut Astronaut J J6:2226–2227Lowenstam HA, Weiner S (1989) On biomineralization. Oxford University, New YorkLusis J, Woodhams RT, Xhantos M (1973) The effect of flake aspect ratio on flexural properties of mica reinforced plastics. Polym Eng Sci 13:139–145Martínez-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 10:309–322Orgel JPRO, Miller A, Irving TC, Fischetti RF, Hammersley AP, Wess TJ (2001) The in situ supermolecular structure of type I collagen. Structure 9:1061–1069Padawer GE, Beecher N (1970) On the strength and stiffness of planar reinforced plastic resins. Polym Eng Sci 10:185–192Pahr DH, Rammerstofer FG (2006) Buckling of honeycomb sandwiches: periodic finite element considerations. Comput Model Eng Sci 12:229–242Reisinger AG, Pahr DH, Zysset PK (2010) Sensitivity analysis and parametric study of elastic properties of an 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 10:67–77Rezkinov N, Almany-Magal R, Shahar R, Weiner S (2013) Three-dimensional imaging of collagen fibril organization in rat circumferential lamellar bone using a dual beam electron microscope reveals ordered and disordered sub-lamellar structures. Bone 52(2):676–683Rho JY, Kuhn-Spearing L, Zioupos P (1998) Mechanical properties and the hierarchical structure of bone. Med Eng Phys 20:92–102Rubin 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 33:270–282Suquet P (1987) Lecture notes in physics-homogenization techniques for composite media. Chapter IV. Springer, BerlinWagermaier W, Gupta HS, Gourrier A, Burghammer M, Roschger P, Fratzl P (2006) Spiral twisting of fiber orientation inside bone lamellae. Biointerphases 1:1–5Wagner HD, Weiner S (1992) On the relationship between the microstructure of bone and its mechanical stiffness. J Biomech 25:1311–1320Weiner S, Wagner HD (1998) The material bone: structure-mechanical function relations. Annu Rev Mater Sci 28:271–298Weiner S, Traub W, Wagner H (1999) Lamellar bone: structure-function relations. J Struct Biol 126:241–255Yao H, Ouyang L, Ching W (2007) Ab initio calculation of elastic constants of ceramic crystals. J Am Ceram 90:3194–3204Yoon YJ, Cowin SC (2008b) The estimated elastic constants for a single bone osteonal lamella. Biomech Model Mechanobiol 7:1–11Yuan 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 10:147–160Zhang Z, Zhang YWF, Gao H (2010) On optimal hierarchy of load-bearing biological materials. Proc R Soc B 278:519–525Zuo S, Wei Y (2007) Effective elastic modulus of bone-like hierarchical materials. Acta Mechanica Solida Sinica 20:198–20

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

Clonal chromosomal mosaicism and loss of chromosome Y in elderly men increase vulnerability for SARS-CoV-2

The pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, COVID-19) had an estimated overall case fatality ratio of 1.38% (pre-vaccination), being 53% higher in males and increasing exponentially with age. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, we found 133 cases (1.42%) with detectable clonal mosaicism for chromosome alterations (mCA) and 226 males (5.08%) with acquired loss of chromosome Y (LOY). Individuals with clonal mosaic events (mCA and/or LOY) showed a 54% increase in the risk of COVID-19 lethality. LOY is associated with transcriptomic biomarkers of immune dysfunction, pro-coagulation activity and cardiovascular risk. Interferon-induced genes involved in the initial immune response to SARS-CoV-2 are also down-regulated in LOY. Thus, mCA and LOY underlie at least part of the sex-biased severity and mortality of COVID-19 in aging patients. Given its potential therapeutic and prognostic relevance, evaluation of clonal mosaicism should be implemented as biomarker of COVID-19 severity in elderly people. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, individuals with clonal mosaic events (clonal mosaicism for chromosome alterations and/or loss of chromosome Y) showed an increased risk of COVID-19 lethality

Computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths

[EN] The acoustic modelling of automotive exhaust devices, such as catalytic converters (CC) and diesel particulate filters (DPF), usually requires the use of multidimensional analytical and numerical techniques. The presence of higher order modes and three-dimensional waves in the expansion and contraction subdomains, as well as sound propagation within the monolith capillary ducts, can be considered through the finite element method (FEM), although this approach is traditionally thought to be very time consuming. With a view to overcome this limitation and to reduce the computational effort of the FEM, alternative modelling techniques are presented in the current work to speed up transmission loss calculations in exhaust devices incorporating monoliths. These approaches are based on the point collocation technique and the mode matching method. As shown in earlier studies, the sound attenuation of an exhaust device incorporating a monolith can be properly predicted if the latter is replaced by a plane wave four-pole transfer matrix providing a relationship between the acoustic fields at both sides of the monolithic region. Therefore, this work combines the presence of multidimensional higher order modes in the expansion and contraction regions with one-dimensional wave propagation within the capillary ducts of the central monolith. The point collocation technique and the mode matching method are applied to the compatibility conditions of the acoustic fields at all the subdomain interfaces to couple the solutions of the wave equation in the corresponding exhaust device subcomponents. For the particular case of rigid circular ducts, Bessel functions are considered as transversal pressure modes. The computational efficiency and accuracy of the results associated with the two analytical modelling techniques presented here are assessed, including the effect of the number of modes and collocation points, as well as their location. All the analytical approaches proposed in this work provide accurate predictions of the device attenuation performance and outperform the computational expenditure of a FE computation. Some differences are found, however, among the various analytical schemes in terms of computational speed and solution accuracy. From the results presented here, the mode matching method is the most efficient technique for the particular configurations under study, mainly due to the possibility of exploiting the orthogonality properties of the transverse pressure modes.This work has been supported by Ministerio de Economia y Competitividad and the European Regional Development Fund (project TRA2013-45596-C2-1-R), as well as Generalitat Valenciana (projects Prometeo/2016/007 and GV/2016/011 of Conselleria d'Educacio, Investigacio, Cultura i Esport).Denia, FD.; Martínez Casas, J.; Carballeira, J.; Nadal, E.; Fuenmayor Fernández, FJ. (2018). Computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths. Journal of Computational and Applied Mathematics. 330:995-1006. https://doi.org/10.1016/j.cam.2017.03.010S995100633