Strength assessment of a strip with circular cut in tension taking into account material local defect of the material

Using a product digital prototype appears to be an advanced approach in calculating the composite material strength, since it makes it possible to take into account the real product technological features. The paper considers the problem of assessing strength of a fastening element made of the composite material under operation conditions to determine the fastening parameters that affect its load-bearing capacity. The highest initial principal stresses in tension of a strip with circular cut in the presence of the material defect were assessed. Local alteration in its Young’s modulus was considered as such a defect. It was assumed that the defect had the shape of a strip symmetrically located near the hole center. Calculations resulted in finding a multiplier function from the parameters characterizing the Young’s modulus in the defect area and the defect geometric size. The multiplier function makes it possible to assess the product strength, since it is a multiplier for the highest initial principal stresses arising in a sample without defect. The paper shows that the resulting solution could be used in practice with the computer tomography data and the known empirical relationships for Young’s modulus, tensile strength and Hounsfield numbers.

EDN: BGIKHS

References

[1] Kharin N.V., Vorobyev O.V., Berezhnoy D.V. et al. Construction of a representative model based on computed tomography. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin], 2018, vol. 3, pp. 95–102, doi: https://doi.org/10.15593/perm.mech/2018.3.10 (in Russ.).

[2] Schwen L.O., Wolfram U., Wilke H.-J. et al. Determining effective elasticity parameters of microstructured materials. 15th Workshop on the Finite Element Method in Biomedical Engineering, 2008, pp. 41–62.

[3] Kayumov R.A. Structure of nonlinear elastic relationships for the highly anisotropic layer of a nonthin shell. Mech. Compos. Mater., 1999, vol. 35, no. 5, pp. 409–418, doi: https://doi.org/10.1007/BF02329327

[4] Kasiviswanathan V., Arockiarajan A. Analytical, numerical and experimental studies on effective properties of layered (2-2) multiferroiccomposites. Sens. Actuator A Phys., 2015, vol. 236, pp. 380–393, doi: https://doi.org/10.1016/j.sna.2015.11.010

[5] Mohammadi Shah M., Komeili M., Phillion A.B. et al. Toward better understanding of the effect of fiber distribution on effective elastic properties of unidirectional composite yarns. Comput. Struct., 2016, vol. 163, pp. 29–40, doi: https://doi.org/10.1016/j.compstruc.2015.10.002

[6] Vilchevskaya E., Sevostianov I. Effective elastic properties of a particulate composite with transversely-isotropic matrix. Int. J. Eng. Sci., 2015, vol. 94, pp. 139–149, doi: https://doi.org/10.1016/j.ijengsci.2015.05.006

[7] Vahterova Y.A., Min Y.N. Effect of shape of armoring fibers on strength of composite materials. TURCOMAT, 2021, vol. 12, no. 2, pp. 2703–2708, doi: https://doi.org/10.17762/turcomat.v12i2.2295

[8] Vanlenthe G., Hagenmuller H., Bohner M. wet al. Nondestructive micro-computed tomography for biological imaging and quantification of scaffold–bone interaction in vivo. Biomaterials, 2007, vol. 28, no. 15, pp. 2479–2490, doi: https://doi.org/10.1016/j.biomaterials.2007.01.017

[9] Viceconti M., Qasim M., Bhattacharya P. et al. Are CT-based finite element model predictions of femoral bone strengthening clinically useful? Curr. Osteoporos. Rep., 2018, vol. 16, no. 3, pp. 216–223, doi: https://doi.org/10.1007/s11914-018-0438-8

[10] Semenova E., Gerasimov O., Koroleva E. et al. Automatic processing and analysis of the quality healing of derma injury. In: Biomechanics 2018. Springer, 2019, pp. 107–113, doi: https://doi.org/10.1007/978-3-319-97286-2_10

[11] Silva-Henao J., Synek A., Pahr D.H. et al. Selection of animal bone surrogate samples for orthopaedic screw testing based on human radius CT-derived bone morphology. Med. Eng. Phys., 2022, vol. 103, art. 103786, doi: https://doi.org/10.1016/j.medengphy.2022.103786

[12] Donnik A.M., Kossovich L.Yu., Olenko E.S. Biomechanics of the spine in fracture of the spine before and after surgical treatment. Biomechanical experiment. Rossiyskiy zhurnal biomekhaniki [Russian Journal of Biomechanics], 2022, vol. 26, no. 1, pp. 25–39. (In Russ.).

[13] Maslov L.B., Dmitryuk A.Yu., Zhmaylo M.A. et al. Study of the strength of a hip endoprosthesis made of polymeric material. Rossiyskiy zhurnal biomekhaniki [Russian Journal of Biomechanics], 2022, no. 4, pp. 19–33. (In Russ.).

[14] Moreno R., Borga M., Smedby Ö. Techniques for computing fabric tensors: a review. In: Visualization and processing of tensors and higher order descriptors for multi-valued data. Springer, 2014, pp. 271–292, doi: https://doi.org/10.1007/978-3-642-54301-2_12

[15] Moreno R., Smedby Ö., Borga M. On the efficiency of the mean intercept length tensor. SSBA Symposium, 2011. URL: http://liu.diva-portal.org/smash/get/diva2:533443/FULLTEXT01.pdf (accessed: 30.08.2023).

[16] Smit T.H., Schneider E., Odgaard A. Star length distribution: a volume-based concept for the characterization of structural anisotropy. J. Microsc., 1998, vol. 191, no. 3, pp. 249–257, doi: https://doi.org/10.1046/j.1365-2818.1998.00394.x

[17] Carniel T.A., Klahr B., Fancello E.A. On multiscale boundary conditions in the computational homogenization of an RVE of tendon fascicles. J. Mech. Behav. Biomed. Mater., 2019, vol. 91, pp. 131–138, doi: https://doi.org/10.1016/j.jmbbm.2018.12.003

[18] Marcián P., Lošák P., Kaiser J. et al. Estimation of orthotropic mechanical properties of human alveolar bone. ICEM, 2016, pp. 399–402.

[19] Gueguen Y., Ravalec M.L., Ricard L. Upscaling: effective medium theory, numerical methods and the fractal dream. Pure Appl. Geophys., 2006, vol. 163, no. 5–6, pp. 1175–1192, doi: https://doi.org/10.1007/s00024-006-0053-y

[20] Hollister S.J., Kikuchi N. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput. Mech., 1992, vol. 10, no. 2, pp. 73–95, doi: https://doi.org/10.1007/BF00369853

[21] Marcián P., Florian Z., Horáčková L. et al. Microstructural finite-element analysis of influence of bone density and histomorphometric parameters on mechanical behavior of mandibular cancellous bone structure. Solid State Phenom., 2016, vol. 258, pp. 362–365, doi: https://doi.org/10.4028/www.scientific.net/SSP.258.362

[22] Kayumov R.A., Muhamedova I.Z., Tazyukov B.F. et al. Parameter determination of hereditary models of deformation of composite materials based on identification method. J. Phys. Conf. Ser., 2018, vol. 973, art. 012006, doi: https://doi.org/10.1088/1742-6596/973/1/012006

[23] Sachenkov O.A., Gerasimov O.V., Koroleva E.V. et al. Building the inhomogeneous finite element model by the data of computed tomography. Rossiyskiy zhurnal biomekhaniki [Russian Journal of Biomechanics], 2018, vol. 22, no. 3, pp. 332–344. (In Russ.).

[24] Gerasimov O.V., Kharin N.V., Fedyanin A.O. et al. Bone stress-strain state evaluation using CT based FEM. Front. Mech. Eng., 2021, vol. 7, art. 688474, doi: https://doi.org/10.3389/fmech.2021.688474

[25] Maquer G., Musy S.N., Wandel J. et al. Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables. J. Bone Miner. Res., 2015, vol. 30, no. 6, pp. 1000–1008, doi: https://doi.org/10.1002/jbmr.2437

[26] Zienkiewicz O.C., Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng., 1987, vol. 24, no. 2, pp. 337–357, doi: https://doi.org/10.1002/nme.1620240206

[27] Grassi L., Schileo E., Taddei F. et al. Accuracy of finite element predictions in sideways load configurations for the proximal human femur. J. Biomech., 2012, vol. 45, no. 2, pp. 394–399, doi: https://doi.org/10.1016/j.jbiomech.2011.10.019

[28] Giovannelli L., Ródenas J.J., Navarro-Jiménez J.M. et al. Direct medical image-based Finite Element modelling for patient-specific simulation of future implants. Finite Elem. Anal. Des., 2017, vol. 136, pp. 37–57, doi: https://doi.org/10.1016/j.finel.2017.07.010

[29] Gerasimov O.V., Berezhnoy D.V., Bolshakov P.V. et al. Mechanical model of a heterogeneous continuum based on numerical-digital algorithm processing computer tomography data. Rossiyskiy zhurnal biomekhaniki [Russian Journal of Biomechanics], 2019, vol. 23, no. 1, pp. 104–116, doi: https://doi.org/10.15593/RJBiomech/2019.1.10 (in Russ.).

[30] Gerasimov O., Kharin N., Statsenko E. et al. Patient-specific bone organ modeling using CT based FEM. In: Mesh methods for boundary-value problems and applications. Springer, 2022, pp. 125–139, doi: https://doi.org/10.1007/978-3-030-87809-2_10

[31] Vorobyev O.V., Semenova E.V., Mukhin D.A. et al. The image-based finite element evaluation of the deformed state. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin], 2021, no. 2, pp. 44–54, doi: https://doi.org/10.15593/perm.mech/2021.2.05 (in Russ.).

[32] Gerasimov O., Sharafutdinova K., Rakhmatullin R. et al. Application of a digital prototype for CT-based bone strength analysis. ITNT, 2022, doi: https://doi.org/10.1109/ITNT55410.2022.9848693

[33] Gerasimov O., Kharin N., Yaikova V. et al. Direct image-based micro finite element modelling of bone tissue. MATEC Web Conf., 2020, vol. 329, art. 03072, doi: https://doi.org/10.1051/matecconf/202032903072

[34] Rho J.Y., Hobatho M.C., Ashman R.B. Relations of mechanical properties to density and CT numbers in human bone. Med. Eng. Phys., 1995, vol. 17, no. 5, pp. 347–355, doi: https://doi.org/10.1016/1350-4533(95)97314-f

[35] Kieser D.C., Kanade S., Waddell N.J. et al. The deer femur — a morphological and biomechanical animal model of the human femur. Biomed. Mater. Eng., 2014, vol. 24, no. 4, pp. 1693–1703, doi: https://doi.org/10.3233/BME-140981

[36] Shakirzyanov F.R., Kayumov R.A., Paymushin V.N. et al. About the causes of the bearing capacity loss of a composite beam under three-point bending. Uchenye zapiski Kazanskogo universiteta. Ser. Fiziko-matematicheskie nauki, 2022, vol. 164, no. 2–3, pp. 221–243. (In Russ.).

[37] Crenshaw T.D., Peo Jr.E.R., Lewis A.J. et al. Bone strength as a trait for assessing mineralization in swine: a critical review of techniques involved. J. Anim. Sci., 1981, vol. 53, no. 3, pp. 827–835, doi: https://doi.org/10.2527/JAS1981.533827X

[38] Imai K. Computed tomography-based finite element analysis to assess fracture risk and osteoporosis treatment. World J. Exp. Med., 2015, vol. 5, no. 3, pp. 182–187, doi: https://doi.org/10.5493/wjem.v5.i3.182