Modeling the Plastic Deformation of Dense and Porous Biomaterials Using Modified Yield Criteria by Lode Angle

[1] Rho, J. Y., Kuhn-Spearing, L., & Zioupos, P. (1998). Mechanical properties and the hierarchical structure of bone. Medical Engineering & Physics, 20(2), 92-102. https://doi.org/10.1016/s1350-4533(98)00007-1

[2] Hamed, E., Novitskaya, E., Li, J., Chen, P. Y., Jasiuk, I., & McKittrick, J. (2012). Elastic moduli of untreated, demineralized and deproteinized cortical bone: validation of a theoretical model of bone as an interpenetrating composite material. Acta Biomaterialia, 8(3), 1080-1092. https://doi.org/10.1016/j.actbio.2011.11.010

[3] Orías, A. A. E. (2005). The relationship between the mechanical anisotropy of human cortical bone tissue and its microstructure [Doctoral dissertation, University of Notre Dame]. https://doi.org/10.7274/9k41zc79t6t

[4] Pithioux, M., Lasaygues, P., & Chabrand, P. (2002). An alternative ultrasonic method for measuring the elastic properties of cortical bone. Journal of Biomechanics, 35 (7), 961-968. https://doi.org/10.1016/S00219290(02)00027-1

[5] Lasaygues, P., & Pithioux, M. (2002). Ultrasonic characterization of orthotropic elastic bovine bones. Ultrasonics, 39(8), 567-573. https://doi.org/10.1016/S0041-624X(02)00261-5

[6]  Mercer, C., He, M., Wang, R., & Evans, A. (2006). Mechanisms governing the inelastic deformation of cortical bone and application to trabecular bone. Acta Biomaterialia, 2(1), 59-68. https://doi.org/10.1016/j.actbio.2005.08.004

[7]  Chen, P. Y., & McKittrick, J. (2011). Compressive mechanical properties of demineralized and deproteinized cancellous bone. Journal of the Mechanical Behavior of Biomedical Materials, 4(7), 961-973. https://doi.org/10.1016/j.jmbbm.2011.02.006

[8] Chen, P. Y., Stokes, A., & McKittrick, J. J. A. B. (2009). Comparison of the structure and mechanical properties of bovine femur bone and antler of the North American elk (Cervus elaphus canadensis). Acta Biomaterialia, 5(2), 693-706. https://doi.org/10.1016/j.actbio.2008.09.011

[9] Alam, K., Mitrofanov, A. V., Bäker, M., & Silberschmidt, V. V. (2009, August). Stresses in ultrasonically assisted bone cutting. In Journal of Physics: Conference Series (Vol. 181, No. 1, p. 012014). IOP Publishing. https://doi.org/10.1088/1742-6596/181/1/012014

[10] Huang, J., Rapoff, A. J., & Haftka, R. T. (2006). Attracting cracks for arrestment in bone-like composites. Materials & Design, 27(6), 461-469. https://doi.org/10.1016/j.matdes.2004.11.022

[11] Sugita, N., Osa, T., Aoki, R., & Mitsuishi, M. (2009). A new cutting method for bone based on its crack propagation characteristics. CIRP Annals, 58(1), 113-118. https://doi.org/10.1016/j.cirp.2009.03.057

[12] Roberts, A. P., & Garboczi, E. J. (2000). Elastic properties of model porous ceramics. Journal of the American Ceramic Society, 83(12), 3041-3048. https://doi.org/10.1111/j.1151-2916.2000.tb01680.x

[13] Nakajima, H., & Ide, T. (2018). Fabrication, properties and applications of porous metals with directional pores. Materials Science Forum, 933, 49-54. https://doi.org/10.1016/j.pmatsci.2006.09.001

[14] Gibson, L., & Ashby, M. (1997). Cellular solids: structure and properties. Cambridge University Press. 

[15] Tvergaard, V. (1981). Influence of voids on shear band instabilities under plane strain conditions. International Journal of Fracture, 17(4), 389-407. https://doi.org/10.1007/BF00036191

[16] Tvergaard, V., & Needleman, A. (1984). Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica, 32(1), 157-69. https://doi.org/10.1016/0001-6160(84)90213-X

[17] Benallal, A. (2017). Constitutive equations for porous solids with matrix behaviour dependent on the second and third stress invariants. International Journal of Impact Engineering, 108, 47-62. https://doi.org/10.1016/j.ijimpeng.2017.05.004

[18] Dæhli, L. E., Morin, D., Børvik, T., & Hopperstad, O. S. (2018). A Lode-dependent Gurson model motivated by unit cell analyses. Engineering Fracture Mechanics, 190, 299-318. https://doi.org/10.1016/j.engfracmech.2017.12.023

[19] Dæhli, L. E. B., Hopperstad, O. S., & Benallal, A. (2019). Effective behaviour of porous ductile solids with a non-quadratic isotropic matrix yield surface. Journal of the Mechanics and Physics of Solids, 130, 56-81. https://doi.org/10.1016/j.jmps.2019.05.014

[20] Huang, S., Li, Z., Chen, Z., Chen, Q., & Pugno, N. (2013). Study on the elastic–plastic behavior of a porous hierarchical bioscaffold used for bone regeneration. Materials Letters, 112, 43-46. https://doi.org/10.1016/j.matlet.2013.08.114

[21] Kelly, N., & McGarry, J. P. (2012). Experimental and numerical characterization of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue. Journal of the Mechanical Behavior of Biomedical Materials, 9, 184-97. https://doi.org/10.1016/j.jmbbm.2011.11.013

[22] Cazacu, O., & Revil-Baudard, B. (2015). New three-dimensional plastic potentials for porous solids with a von Mises matrix. Comptes Rendus Mécanique, 343(2), 77-94. https://doi.org/10.1016/j.crme.2014.12.001

[23] Willam, K. J., & Warnke, E. (1975). Constitutive model for the triaxial behaviour of concrete. International Association for Bridge and Structural Engineering Proceedings, 19, 1-30. https://sid.ir/paper/600004/en

[24] Ansari Basir, E., & Narooei, K. (2016). Simulation of deformation behavior of porous titanium using modified Gurson yield function. Iranian Journal of Materials Forming, 3(2), 26-38. https://doi.org/10.22099/ijmf.2016.3861

[25] Dong, Y., & Jia, L. J. (2021). Plasticity model for structural steel with Lode angle dependence. Journal of Bridge Engineering, 26(12), 04021087. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001784

[26] Milone, A., Foti, P., Berto, F., & Landolfo, R. (2024). Post-necking and damage modelling of steel structural components: A comprehensive state of the art. Engineering Structures, 321, 118931. https://doi.org/10.1016/j.engstruct.2024.118931

[27] Liu, J., Li, X., Wang, C., Xu, Y., & Xia, K. (2024). A three-dimensional elastoplastic constitutive model incorporating Lode angle dependence. Geomechanics for Energy and the Environment, 38, 100567. https://doi.org/10.1016/j.gete.2024.100567