Effect of different helmet shell configurations on the protection against head trauma

[EN] Head trauma following a ballistic impact in a helmeted head is assessed in this work by means of finite element models. Both the helmet and the head models employed were validated against experimental high-rate impact tests in a previous work. Four different composite ply configurations were tested on the helmet shell, and the energy absorption and the injury outcome resulting from a high-speed impact with full metal jacket bullets were computed. Results reveal that hybrid aramid-polyethylene configurations do not prevent bullet penetration at high velocities, while 16-layer aramid configurations are superior in dissipating the energy absorbed from the impact. The fabric orientation of these laminates proved to be determinant for the injury outcome, as maintaining the same orientations for all the layers led to basilar skull fractures (dangerous), while alternating orientation of the adjacent plies resulted in an undamaged skull. To the authors knowledge, no previous work in the literature has analysed numerically the influence of different stack configurations on a single combat helmet composite shell on human head trauma.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The study received the funding support from the Spanish Ministry of Economy and Competitiveness in the framework of the projects DPI2013-46641-R and DPI2017-89197-C2-2-R and the Generalitat Valenciana in the context of the Programme PROMETEO 2016/007.Palomar-Toledano, M.; Belda R.; Giner Maravilla, E. (2019). Effect of different helmet shell configurations on the protection against head trauma. Journal of Strain Analysis for Engineering Design. 54(7-8):408-415. https://doi.org/10.1177/0309324719835706S408415547-

The minimum shear stress range criterion and its application to crack orientation prediction in incomplete contact fretting problems

[EN] A proper prediction of crack paths is required when assessing accurately the fatigue crack propagation life. Recently, some authors have pointed out that the criterion of minimum shear stress range leads to inconsistent results when predicting fretting crack paths under incomplete contacts. In this paper, different fretting experiments with cylinder-to-flat contact found in the literature are reviewed, and the corresponding crack path prediction using the extended finite element method and the minimum shear stress range crack orientation criterion is performed. Results show the applicability of the criterion to predict the crack orientation during stage II in incomplete contact fretting problems.The authors gratefully acknowledge the financial support given by the Spanish Ministry of Economy and Competitiveness and the FEDER program through the project DPI2017-89197-C2-1-R, DPI2017-89197-C2-2-R and DPI2014-56137-C2-2-R and the FPI subprogram associated to the project with the reference BES-2015-072070. The support of the Generalitat Valenciana, Programme PROMETEO 2016/007, is also acknowledged. The financial support given by the Eusko Jaurlaritza under "Programa de apoyo a la investigacion colaborativa en areas estrategicas" (Project MEDECA: Ref. KK-2017/00053, and MEDECA2: Ref. KK-2018/00013) programs is also acknowledged.Infante, D.; Llavori, I.; Zabala, A.; Giner Maravilla, E. (2019). The minimum shear stress range criterion and its application to crack orientation prediction in incomplete contact fretting problems. International Journal of Fatigue. 129:1-9. https://doi.org/10.1016/j.ijfatigue.2019.105223S1912

A comparison between some fracture modelling approaches in 2D LEFM using finite elements

[EN] The finite element method has been widely used to solve different problems in the field of fracture mechanics. In the last two decades, new methods have been developed to improve the accuracy of the solution in 2D linear elastic fracture mechanics problems, such as the extended finite element method (XFEM) or the phantom node method (PNM). The goal of this work is to quantify the differences between some numerical approaches: standard finite element method (FEM), mechanical property degradation, interelemental crack method with multi-point constraints, XFEM and PNM. We explain the different techniques analysed together with their advantages and disadvantages. We compare these numerical techniques to model fracture using problems of reference with known solutions, evaluating their behaviour in terms of convergence with respect to the element size and accuracy of the stress intensity factor (SIF), stresses ahead the crack tip and crack propagation prediction. Some of the new techniques have shown a better accuracy in SIF calculation or stress fields ahead the crack tip and other lead to high errors in local results estimations. However, all methods reviewed here can predict crack propagation for the problems of reference of this work, showing good accuracy in crack orientation prediction.The authors gratefully acknowledge the funding support received from the Spanish Ministerio de Ciencia, Innovacion y Universidades and the FEDER operation program in the framework of the projects DPI2017-89197-C2-1-R and DPI2017-89197-C2-2-R and the FPI subprograms BES-2014-068473 and BES-2015-072070. The financial support of the Generalitat Valenciana through the Programme PROMETEO 2016/007 is also acknowledged.Marco, M.; Infante-García, D.; Belda, R.; Giner Maravilla, E. (2020). A comparison between some fracture modelling approaches in 2D LEFM using finite elements. International Journal of Fracture. 223(1-2):151-171. https://doi.org/10.1007/s10704-020-00426-6S1511712231-2Agwai A, Guven I, Madenci E (2010) Comparison of XFEM, CZM and PD for predicting crack initiation and propagation. In: Collection of technical papers—AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conferenceAreias PMA, Belytschko T (2005) Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int J Numer Methods Eng 63(8):760–788Argyris JH, Kelsey S (1954) Energy theorems and structural analysis. Aircraft Eng 26(12):410–422Banks-Sills L (1991) Application of the finite element method to linear elastic fracture mechanics. Appl Mech Rev 44(10):447–461Banks-Sills L, Sherman D (1986) Comparison of methods for calculating stress intensity factors with quarter point elements. Int J Fract 32:127–140Banks-Sills L, Sherman D (1992) On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods. Int J Fract 53:1–20Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620Bittencourt TN, Barry A, Ingraffea AR (1992) Comparison of mixed-mode stress intensity factors obtained through displacement correlation, J-integral formulation and modified crack-closure integral. In: Fracture mechanics: 22nd Symposium. Atluri SN, Newman,JC Jr, Raju IS, Epstein JS, editors, number II, ASTM STP, Philadelphia, pp 69-82Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL (1996) Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng Fract Mech 55(2):321–334Bobet A, Einstein HH (1998) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92:221–252Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48:797–826Clough RW (1960) The finite element method in plane stress analysis, Conference on matrix methods in structural mechanics, ASCE, Pittsburgh, PA: 345-378Clough RW (1962) The stress distribution of Norfork Dam, structures and materials research. Department of civil engineering, University of California: Series 100, Issue 19, BerkeleyDuflot M (2007) A study of the representation of cracks with level sets. Int J Numer Methods Eng 70(11):1261–1302Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342Gallagher RH (1978) A review of finite element techniques in fracture mechanics. In: Proceedings of the first international conference on numerical methods in fracture mechanics (Luxmoore AR, Owen DRJ, Hrsg S) Swansea: Pineridge Press, pp 1–25Gdoutos EE (1993) Fracture mechanics: an introduction. Solid mechanics and its applications. Kluwer Academic Publishers, Dordrecht, HollandGiner E, Fuenmayor FJ, Baeza L, Tarancón JE (2005) Error estimation for the finite element evaluation of G$$_{{\rm I}}$$ and G$$_{{\rm II}}$$ in mixed-mode linear elastic fracture mechanics. Finite Elem Anal Des 41:1079–1104Giner E, Sukumar N, Tarancón JE, Fuenmayor FJ (2009) An Abaqus implementation of the extended finite element method. Eng Fract Mech 76(3):347–368Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 19(33):3523–3540Henshell RD, Shaw KG (1975) Crack tip elements are unnecessary. Int J Numer Methods Eng 9:495–507Hibbitt, Karlsson, Sorensen (2004) Inc. ABAQUS/standard user’s manual, Pawtucket, Rhode IslandIngraffea AR (2004) Computational fracture mechanics. In: Encyclopedia of computational mechanics, 1$$^{{\rm st}}$$ edn. Wiley, pp 375-405Jäger P, Steinmann P, Kuhl E (2008) Modelling three-dimensional crack propagation—a comparison of crack path tracking strategies. Int J Numer Methods Eng 76(9):1328–1352Jirásek M (2011) Damage and smeared crack models. In: Hofstetter G, Meschke G (eds) Numerical modelling of concrete cracking. Springer, Berlin, pp 1–49Kanninen MF, Popelar CH (1985) Advanced fracture mechanics. Oxford University Press, Oxford (UK)Kuna M (2013) Finite elements in fracture mechanics. Theory—numerics—applications. Springer, BerlinMarco M, Belda R, Miguélez MH, Giner E (2018a) A heterogeneous orientation criterion for crack modelling in cortical bone using a phantom-node approach. Finite Elem Anal Des 146:107–117Marco M, Giner E, Larraínzar-Garijo R, Caeiro JR, Miguélez MH (2018b) Modelling of femur fracture using finite element procedures. Eng Fract Mech 196:157–167Moës N, Gravouil A (2002) Non-planar 3D crack growth by the extended finite element method and level sets—part I: mechanical model. Int J Numer Methods Eng 53(11):2549–2568Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150Oliver J, Huespe AE, Samaniego E, Chaves EWV (2002) On strategies for tracking strong discontinuities in computational failure mechanics. In: Fifth world congress on computational mechanics. Mang HA, Rammerstorfer FC, Eberhardsteiner J. Vienna, Austria, pp 7-12Ooi ET, Man H, Natarajan S, Song C (2015) Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling. Eng Fract Mech 144:101–117Owen DRJ, Fawkes AJ (1983) Engineering fracture mechanics: numerical methods and applications. Pineridge Press Ltd., SwanseaQian G, Wang M (1996) Symmetric branching of mode II and mixed-mode fatigue crack growth in a stainless steel. J Eng Mater Technol 118:356–361Qian G, González-Albuixech VF, Niffenegger M, Giner E (2016) Comparison of KI calculation methods. Eng Fract Mech 156:52–67Rashid YR (1968) Analysis of prestressed concrete reactor vessels. Nucl Eng Des 7:334–334Rice JR, Tracey DM (1973) Computational fracture mechanics. In: Numerical and computer methods in structural mechanics. Fenves SJ, Perrone N, Robinson AR, Schnobrich WC, Academic Press, New York, pp 585-623Saouma VE, Ingraffea AR (1981) Fracture mechanics analysis of discrete cracking. In: Proceedings, IABSE colloquium on advanced mechanics of reinforced concrete, Delft 393Song JH, Wang H, Belytschko T (2008) A comparative study on finite element methods for dynamic fracture. 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Analysis of the effect of out-of-phase biaxial fatigue loads on crack paths in cruciform specimens using XFEM

[EN] In the present research work, a numerical crack growth analysis using linear elastic fracture mechanics is carried out paying attention to the crack paths that grow in the central part of cruciform specimens under biaxial fatigue loads. The crack propagation in this type of specimens has been studied using the extended finite element method (XFEM). The objective is to analyse the effect of different phase angles under biaxial fatigue loads and to assess the different orientation criteria for nonproportional loading, benefiting from the advantages of XFEM. The crack path and the stress intensity factor range of a crack either aligned or inclined to the load directions have been investigated using different crack orientation criteria. Symmetrical branching is predicted for an initial crack inclined at 45 degrees with phase angle of loading equal to 90 degrees and 180 degrees. Numerical results are in good agreement with the experimental observations found in the literature, although the study reveals important differences in the crack path predictions depending on the orientation criteria.The authors gratefully acknowledge the financial support given by the Spanish Ministry of Economy and Competitiveness and the FEDER program through the project DPI2017-89197-C2-1-R, DPI2017-89197-C2-2-R and DPI2014-56137-C2-2-11 and the FPI subprogram associated to the project with the reference BES-2015-072070. The support of the Generalitat Valenciana, Programme PROMETEO 2016/007, is also acknowledged. Guian Qian is grateful for the financial support by the National Natural Science Foundation of China (No.11872364).Infante, D.; Qian, G.; Miguélez, MH.; Giner Maravilla, E. (2019). Analysis of the effect of out-of-phase biaxial fatigue loads on crack paths in cruciform specimens using XFEM. International Journal of Fatigue. 123:87-95. https://doi.org/10.1016/j.ijfatigue.2019.01.019S879512

A heterogeneous orientation criterion for crack modelling in cortical bone using a phantom-node approach

[EN] Cortical bone can be considered as a heterogeneous composite at microscopic scale, composed of osteons that act as reinforcement fibres embedded in interstitial matrix. Cement lines constitute the interface between osteons and matrix, and they often behave as the weakest links along which microcracks tend to propagate. However, current simulations of crack growth using XFEM combined with usual orientation criteria as implemented in commercial codes do not capture this behaviour: they predict crack paths that do not follow the cement lines surrounding osteons. The reason is that the orientation criterion used in the implementation of XFEM does not take into account the heterogeneity of the material, leading to simulations that differ from experimental results. In this work, a crack orientation criterion for heterogeneous materials based on interface damage prediction in composites is proposed and a phantom node approach has been implemented to model crack propagation. The method has been validated by means of linear elastic fracture mechanics (LEFM) problems obtaining accurate results. The procedure is applied to different problems including several osteons with simplified geometry and an experimental test reported in the literature leading to satisfactory predictions of crack paths.The authors gratefully acknowledge the funding support received from the Spanish Ministry of Economy and Competitiveness and the FEDER operation program in the framework of the projects DPI2013-46641-R, DPI2017-89197-C2 and RTC-2015-3887-8 and also from the Generalitat Valenciana through the Programme PROMETEO 2016/007.Marco, M.; Belda, R.; Miguélez, MH.; Giner Maravilla, E. (2018). A heterogeneous orientation criterion for crack modelling in cortical bone using a phantom-node approach. Finite Elements in Analysis and Design. 146:107-117. https://doi.org/10.1016/j.finel.2018.04.009S10711714

Relevant factors affecting the direction of crack propagation in complete contact problems under fretting fatigue

[EN] In fatigue problems, an accurate estimation of the propagation direction is important for life prediction. We identify the most relevant factors that affect the crack orientation during the propagation stage of fretting fatigue cracks, arising from complete contacts. Contrary to what initially expected, parameters such as normal load, cyclic bulk load, etc. do not have a noticeable influence on the orientation. However the relative Young's moduli of indenter/specimen materials, the indenter width and the surface coefficient of friction are the most influencing factors. Analyses are performed through the extended finite element method (X-FEM) and an orientation criterion for non-proportional loading proposed by the authors. Experimental fretting fatigue tests confirm the predicted trends. An explanation of this behaviour is also given.The authors gratefully acknowledge the financial support given by the Spanish Ministry of Economy and Competitiveness and the FEDER program through the projects DPI2017-89197-C2-1-R and DPI2017-89197-C2-2-R. The support of the Generalitat Valenciana, Programme PROMETEO 2016/007, is also acknowledged. The authors thank the collaboration of Mr. Francisco Gelardo RodriguezMarco, M.; Infante-Garcia, D.; Diaz-Alvarez, J.; Giner Maravilla, E. (2019). Relevant factors affecting the direction of crack propagation in complete contact problems under fretting fatigue. Tribology International. 131:343-352. https://doi.org/10.1016/j.triboint.2018.10.048S34335213

An Experimental and Numerical Investigation to Characterize an Aerospace Composite Material with Open-Hole Using Non-Destructive Techniques

[EN] In this study, the open-hole quasi-static tensile and fatigue loading behavior of a multidirectional CFRP thick laminate, representative of laminates used in the aerospace industry, is studied. Non-destructive techniques such as infrared thermographic (IRT) and digital image correlation (DIC) are used to analyze the behavior of this material. We aim at characterizing the influence of the manufacturing defects and the stress concentrator through the temperature variation and strain distribution during fatigue and quasi-static tests. On the one hand, the fatigue specimens were tested in two main perpendicular directions of the laminate. The results revealed that manufacturing defects such as fiber waviness can have a major impact than open-hole stress concentrator on raising the material temperature and causing fracture. In addition, the number of plies with fibers oriented in the load direction can drastically reduce the temperature increment in the laminate. On the other hand, the quasi-static tensile tests showed that the strain distribution around the hole is able to predict the crack initiation and progression in the external plies. Finally, the experimental quasi-static tests were numerically simulated using the finite element method showing good agreement between the numerical and experimental results.This research was funded by the FEDER programme and the Spanish Ministerio de Ciencia, Innovacion y Universidades, projects DPI2017-89197-C2-1-R and DPI2017-89197-C2-2-R. The funding of the Generalitat Valenciana, Programme PROMETEO 2016/007 is also acknowledged.Feito-Sánchez, N.; Calvo, JV.; Belda, R.; Giner Maravilla, E. (2020). An Experimental and Numerical Investigation to Characterize an Aerospace Composite Material with Open-Hole Using Non-Destructive Techniques. Sensors. 20(15):1-18. https://doi.org/10.3390/s20154148S118201

3D analysis of the influence of specimen dimensions on fretting stresses

[EN] In this paper, the contact conditions and stresses that arise in a fretting test have been analyzed by means of a three-dimensional finite element model of the contact between a sphere and a flat surface. An h-adaptive process, based on element subdivision, has been used in order to obtain a low discretization error at a reasonable computational cost. The influence of finite dimensions of the specimen in the stress fields has been evaluated. The results have been compared with the classical Cattaneo-Mindlin solution.The authors wish to thank the financial support received from CICYT by means of the project PB97-0696-C02-02.Tur Valiente, M.; Fuenmayor Fernández, F.; J.J. Ródenas; Giner Maravilla, E. (2003). 3D analysis of the influence of specimen dimensions on fretting stresses. Finite Elements in Analysis and Design. 39(10):933-949. https://doi.org/10.1016/S0168-874X(02)00139-7S933949391

Numerical analysis of the influence of micro-voids on fretting fatigue crack initiation lifetime

[EN] In this paper, the influence of the heterogeneity in the predicted crack initiation lifetime under fretting fatigue conditions is analysed for a regular and a random distribution of micro-voids. A critical plane analysis with two multiaxial damage criteria is performed to assess the crack initiation lifetime. The predicted initiation lifetime in the heterogeneous material is compared with the results obtained in the homogeneous case. The numerical results show that the heterogeneity has a noticeable influence on the predicted initiation lifetime. Furthermore, the numerical model suggests that a crack may firstly initiate at the upper edge of the micro-voids located close to the contact edge, leading to a mean reduction of the predicted crack initiation lifetime. However, in some cases, the introduction of micro-voids reduces the stress intensity at the contact edge and thus decreasing the predicted crack initiation lifetime.The authors gratefully acknowledge the financial support given by the Spanish Ministry of Economy and Competitiveness and the FEDER program through the projects DPI2017-89197-C2-1-R, DPI2017-89197-C2-2-R and the FPI subprogram with the reference BES-2015-072070. The support of the Generalitat Valenciana, Programme PROMETEO 2016/007, is also acknowledged.r The last author would like to acknowledge the financial support of the Research Foundation-Flanders (FWO), The Luxembourg National Research Fund (FNR) and Slovenian Research Agency (ARRS) in the framework of the FWO Lead Agency project: G018916N 'Multi-analysis of fretting fatigue using physical and virtual experiments'.Infante-García, D.; Giner Maravilla, E.; Miguélez, MH.; Wahab, MA. (2019). Numerical analysis of the influence of micro-voids on fretting fatigue crack initiation lifetime. Tribology International. 135:121-129. https://doi.org/10.1016/j.triboint.2019.02.032S121129135Hills, D. A., & Nowell, D. (2014). Mechanics of fretting fatigue—Oxford’s contribution. Tribology International, 76, 1-5. doi:10.1016/j.triboint.2013.09.015Hojjati-Talemi, R., Wahab, M. A., Giner, E., & Sabsabi, M. (2013). Numerical Estimation of Fretting Fatigue Lifetime Using Damage and Fracture Mechanics. Tribology Letters, 52(1), 11-25. doi:10.1007/s11249-013-0189-8Nowell, D., Dini, D., & Hills, D. A. (2006). Recent developments in the understanding of fretting fatigue. Engineering Fracture Mechanics, 73(2), 207-222. doi:10.1016/j.engfracmech.2005.01.013Amargier, R., Fouvry, S., Chambon, L., Schwob, C., & Poupon, C. (2010). Stress gradient effect on crack initiation in fretting using a multiaxial fatigue framework. International Journal of Fatigue, 32(12), 1904-1912. doi:10.1016/j.ijfatigue.2010.06.004PROUDHON, H., FOUVRY, S., & BUFFIERE, J. (2005). A fretting crack initiation prediction taking into account the surface roughness and the crack nucleation process volume. International Journal of Fatigue, 27(5), 569-579. doi:10.1016/j.ijfatigue.2004.09.001Pereira, K., & Abdel Wahab, M. (2017). Fretting fatigue crack propagation lifetime prediction in cylindrical contact using an extended MTS criterion for non-proportional loading. Tribology International, 115, 525-534. doi:10.1016/j.triboint.2017.06.026Hojjati-Talemi, R., Abdel Wahab, M., De Pauw, J., & De Baets, P. (2014). Prediction of fretting fatigue crack initiation and propagation lifetime for cylindrical contact configuration. Tribology International, 76, 73-91. doi:10.1016/j.triboint.2014.02.017Noraphaiphipaksa, N., Manonukul, A., & Kanchanomai, C. (2017). Fretting Fatigue with Cylindrical-On-Flat Contact: Crack Nucleation, Crack Path and Fatigue Life. Materials, 10(2), 155. doi:10.3390/ma10020155NAVARRO, C., MUNOZ, S., & DOMINGUEZ, J. (2008). On the use of multiaxial fatigue criteria for fretting fatigue life assessment. International Journal of Fatigue, 30(1), 32-44. doi:10.1016/j.ijfatigue.2007.02.018Bhatti, N. A., & Abdel Wahab, M. (2017). A numerical investigation on critical plane orientation and initiation lifetimes in fretting fatigue under out of phase loading conditions. Tribology International, 115, 307-318. doi:10.1016/j.triboint.2017.05.036Sabsabi, M., Giner, E., & Fuenmayor, F. J. (2011). Experimental fatigue testing of a fretting complete contact and numerical life correlation using X-FEM. International Journal of Fatigue, 33(6), 811-822. doi:10.1016/j.ijfatigue.2010.12.012Szolwinski, M. P., & Farris, T. N. (1998). Observation, analysis and prediction of fretting fatigue in 2024-T351 aluminum alloy. Wear, 221(1), 24-36. doi:10.1016/s0043-1648(98)00264-6Gong, H., Rafi, K., Gu, H., Starr, T., & Stucker, B. (2014). Analysis of defect generation in Ti–6Al–4V parts made using powder bed fusion additive manufacturing processes. Additive Manufacturing, 1-4, 87-98. doi:10.1016/j.addma.2014.08.002RAJASEKARAN, B., GANESHSUNDARARAMAN, S., JOSHI, S., & SUNDARARAJAN, G. (2009). Effect of grinding on plain fatigue and fretting fatigue behaviour of detonation gun sprayed Cu–Ni–In coating on Al–Mg–Si alloy. International Journal of Fatigue, 31(4), 791-796. doi:10.1016/j.ijfatigue.2008.03.003Chan, L. C., Lu, X. Z., & Yu, K. M. (2015). Multiscale approach with RSM for stress–strain behaviour prediction of micro-void-considered metal alloy. Materials & Design, 83, 129-137. doi:10.1016/j.matdes.2015.05.064Bhatti, N. A., & Abdel Wahab, M. (2018). Fretting fatigue crack nucleation: A review. Tribology International, 121, 121-138. doi:10.1016/j.triboint.2018.01.029Marco, M., Infante-García, D., Díaz-Álvarez, J., & Giner, E. (2019). Relevant factors affecting the direction of crack propagation in complete contact problems under fretting fatigue. Tribology International, 131, 343-352. doi:10.1016/j.triboint.2018.10.048Muñoz, S., Navarro, C., & Domínguez, J. (2007). Application of fracture mechanics to estimate fretting fatigue endurance curves. Engineering Fracture Mechanics, 74(14), 2168-2186. doi:10.1016/j.engfracmech.2006.10.010Giner, E., Sabsabi, M., Ródenas, J. J., & Javier Fuenmayor, F. (2014). Direction of crack propagation in a complete contact fretting-fatigue problem. International Journal of Fatigue, 58, 172-180. doi:10.1016/j.ijfatigue.2013.03.001Kumar, D., Biswas, R., Poh, L. H., & Wahab, M. A. (2017). Fretting fatigue stress analysis in heterogeneous material using direct numerical simulations in solid mechanics. Tribology International, 109, 124-132. doi:10.1016/j.triboint.2016.12.033Mayer, H., Papakyriacou, M., Zettl, B., & Stanzl-Tschegg, S. . (2003). Influence of porosity on the fatigue limit of die cast magnesium and aluminium alloys. International Journal of Fatigue, 25(3), 245-256. doi:10.1016/s0142-1123(02)00054-3Taylor, D. (2008). The theory of critical distances. Engineering Fracture Mechanics, 75(7), 1696-1705. doi:10.1016/j.engfracmech.2007.04.007Araújo, J. (2002). The effect of rapidly varying contact stress fields on fretting fatigue. International Journal of Fatigue, 24(7), 763-775. doi:10.1016/s0142-1123(01)00191-8McDiarmid, D. L. (1991). A GENERAL CRITERION FOR HIGH CYCLE MULTIAXIAL FATIGUE FAILURE. Fatigue & Fracture of Engineering Materials and Structures, 14(4), 429-453. doi:10.1111/j.1460-2695.1991.tb00673.xSocie, D. (1987). Multiaxial Fatigue Damage Models. Journal of Engineering Materials and Technology, 109(4), 293-298. doi:10.1115/1.3225980Gates, N., & Fatemi, A. 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International Journal of Fatigue, 23(8), 703-711. doi:10.1016/s0142-1123(01)00029-

Explicit expressions for elastic constants of osteoporotic lamellar tissue and damage assessment using Hashin failure criterion

[EN] In this work, we have derived explicit expressions to estimate the orthotropic elastic constants of lamellar tissue as a function of the porosity at tissue level (microporosity) and the bone mineral density. Our results reveal that the terms of the main diagonal of the stiffness matrix fit an exponential equation, while the cross terms of the matrix fit a polynomial expression. Regarding to bone damage, failure onset assessed by Hashin criterion is mainly due to matrix elements failure. Finally, a linear relationship was found between bone mineral density (BMD) and cancellous bone stiffness at the macro scale.The authors acknowledge the Generalitat Valenciana for the financial support received through Plan FDGENT 2018. The authors also ackowledge the Ministerio de Ciencia e Innovacin and the ERDF-FEDER programme through the project DPI2017-89197-C2-2-R.Megías Díaz, R.; Belda González, R.; Vercher Martínez, A.; Giner Maravilla, E. (2022). Explicit expressions for elastic constants of osteoporotic lamellar tissue and damage assessment using Hashin failure criterion. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 150-158. https://doi.org/10.4995/YIC2021.2021.12442OCS15015