Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads
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We discuss the finite element modeling of porous materials such as bones using the linear micropolar elasticity. In order to solve static boundary-value problems, we developed new finite elements, which capture the micropolar behavior of the material. Developed elements were implemented in the commercial software ABAQUS. The modeling of a femur bone with and without implant under various stages of healing is discussed in details.
Keywordsbone implant Cosserat continuum micropolar elasticity numerical simulation finite element method
The research leading to these results has received funding from the People Program (Marie Curie Curie ITN transfer) of the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement No. PITN-GA-2013-606878.
- 1.S. Cowin (Ed.), Bone Mechanics Handbook, CRC Press LLC, Boca Raton (2001).Google Scholar
- 2.Y. H. An and R. A. Draughn (Eds.), Mechanical Testing of Bone and the Bone- Implant Interface, CRC Press LLC, Boca Raton (2000).Google Scholar
- 13.I. Goda, F. Dos Reis, and J. F. Ganghoffer, “Limit analysis of lattices based on the asymptotic homogenization method and prediction of size effects in bone plastic collapse,” in: H. Altenbach and S. Forest (Eds.), Generalized Continua as Models for Classical and Advanced Materials, Springer International Publishing (2016), pp. 179– 211.Google Scholar
- 15.F. Dell’Isola F., D. Steigmann, and A. Della Corte, “Synthesis of fibrous complex structures: Designing microstructure to deliver targeted macroscale response,” Appl. Mech. Rev., 67, No. 6, 060804–060804-21 (2016).Google Scholar
- 16.F. Dell’Isola, I. Giorgio, M. Pawlikowski, and N. L. Rizzi, “Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical examples of equilibrium,” Proc. Roy. Soc. A, 472, No. 2185 (2016), DOI: https://doi.org/10.1098/rspa.2015.0790.
- 17.D. Scerrato, I. Giorgio, and N. L. Rizzi, “Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations,” Z. Angew. Math. Phys., 67, No. 3, Article No. 53 (2016).Google Scholar
- 18.F. Dell’Isola, I. Giorgio, M. Pawlikowski, and N. L. Rizzi, “Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium,” Proc. R. Soc. A, 472, No. 2185 (2016), DOI: https://doi.org/10.1098/rspa.2015.0790.
- 20.M. Cuomo, F. Dell’Isola, L. Greco, and N. L. Rizzi, “First versus second gradient energies for planar sheets with two families of inextensible fibres: Investigation on deformation boundary layers, discontinuities and geometrical instabilities,” Compos. Part B - Eng., 115, 423–448 (2017).CrossRefGoogle Scholar
- 21.L. Placidi, L. Greco, S. Bucci, et al., “A second gradient formulation for a 2D fabric sheet with inextensible fibres,”Z. Angew. Math. Phys., 67, No. 5, 114 (2016), doi.org/ https://doi.org/10.1007/s00033-016-0701-8.
- 24.I. Giorgio, U. Andreaus, D. Scerrato, and P. Braidotti, “Modeling of a non-local stimulus for bone remodeling process under cyclic load: Application to a dental implant using a bioresorbable porous material,” Math. Mech. Solids (2016), DOI: https://doi.org/10.1177/1081286516644867.
- 25.I. Giorgio, U. Andreaus, T. Lekszycki, and A. Della Corte, “The influence of different geometries of matrix/scaffold on the remodeling process of a bone and bio-resorbable material mixture with voids,” Math. Mech. Solids (2015), DOI: https://doi.org/10.1177/ 1081286515616052.Google Scholar
- 26.G. Mishuris, “Models of an interaction between two elastic media one of which is weakened by a symmetrical angular cut,” Vestn. Leningrad Univ. Math., 62–66 (1985).Google Scholar
- 32.L. Morini, A. Piccolroaz, and G. Mishuris, “Dynamic energy release rate in couple- stress elasticity,” J. Phys. Conf. Ser., 451, No. 1, 012014 (2013).Google Scholar
- 34.V. A. Eremeyev, A. Skrzat, and F. Stachowicz, “On finite element computations of contact problems in micropolar elasticity,” Adv. Mater. Sci. Eng., Article ID 9675604, 1–9 (2016).Google Scholar
- 36.V. A. Eremeyev, A. Skrzat, and F. Stachowicz, “On FEM evaluation of stress concentration in micropolar elastic materials,” Nanomech. Sci. Technol., 7, No. 4, 297–304 (2016).Google Scholar
- 37.E. Cosserat and F. Cosserat, Théorie des Corps Déformables, Herman et Fils, Paris (1909).Google Scholar