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Strength of Materials
Erschienen in: Strength of Materials 4/2017

15.11.2017

Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads

verfasst von: V. A. Eremeyev, A. Skrzat, F. Stachowicz

Erschienen in: Strength of Materials | Ausgabe 4/2017

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Abstract

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.
Vorheriger Artikel Experimental and Numerical Analysis of Springback Behavior of Aluminum Alloys
Nächster Artikel Deep-Drawing Process Simulation for Tailor-Welded Blanks with an Elastic Blankholder

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Literatur
1.
S. Cowin (Ed.), Bone Mechanics Handbook, CRC Press LLC, Boca Raton (2001).
2.
Y. H. An and R. A. Draughn (Eds.), Mechanical Testing of Bone and the Bone- Implant Interface, CRC Press LLC, Boca Raton (2000).
3.
S. C. Cowin and D. H. Hegedus, “Bone remodeling I: theory of adaptive elasticity,” J. Elasticity, 6, No. 3, 313–326 (1976).CrossRef
4.
D. H. Hegedus and S. C. Cowin, “Bone remodeling II: small strain adaptive elasticity,” J. Elasticity, 6, No. 4, 337–352 (1976).CrossRef
5.
R. S. Lakes and J. F. Yang, “Transient study of couple stress effects in compact bone: torsion,” J. Biomech. Eng., 103, 275–279 (1981).CrossRef
6.
J. F. C. Yang and R. S. Lakes, “Experimental study of micropolar and couple stress elasticity in compact bone in bending,” J. Biomech., 15, No 2, 91–98 (1982).CrossRef
7.
H. C. Park and R. S. Lakes, “Cosserat micromechanics of human bone: strain redistribution by a hydration sensitive constituent,” J. Biomech., 19, No. 5, 385–397 (1986).CrossRef
8.
R. S. Lakes, “Experimental microelasticity of two porous solids,” Int. J. Solids Struct., 22, No. 1, 55–63 (1986).CrossRef
9.
R. S. Lakes, “Experimental micro mechanics methods for conventional and negative Poisson’s ratio cellular solids as Cosserat continua,” J. Eng. Mater. Technol., 113, No. 1, 148–155 (1991).CrossRef
10.
I. Goda, M. Assidi, S. Belouettar, and J. F. Ganghoffer, “A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization,” J. Mech. Behav. Biomed., 16, 87–108 (2012).CrossRef
11.
I. Goda, M. Assidi, and J. F. Ganghoffer, “3D elastic micropolar model of vertebral trabecular bone from lattice homogenization of the bone microstructure,” Biomech. Model. Mechan., 13, No. 1, 53–83 (2014).CrossRef
12.
I. Goda and J. F. Ganghoffer, “Identification of couple-stress moduli of vertebral trabecular bone based on the 3D internal architectures,” J. Mech. Behav. Biomed., 51, 99–118 (2015).CrossRef
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.
14.
I. Goda, R. Rahouadj, J. F. Ganghoffer, et al., “3D couple-stress moduli of porous polymeric biomaterials using μCT image stack and FE characterization,” Int. J. Eng. Sci., 100, 25–44 (2016).CrossRef
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).
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).
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.
19.
E. Turco, F. Dell’Isola, A. Cazzani, and N. L. Rizzi, “Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models,” Z. Angew. Math. Phys., 67, No. 4, 1–28 (2016).CrossRef
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).CrossRef
21.
22.
T. Lekszycki and F. Dell’Isola, “A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio- resorbable materials,” Z. Angew. Math. Mech., 92, No. 6, 426–444 (2012).CrossRef
23.
I. Giorgio, U. Andreaus, D. Scerrato, and F. Dell’Isola, “A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials,” Biomech. Model. Mechan., 15, No. 5, 1325-1343 (2016).CrossRef
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.
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).
27.
E. Radi, “Effects of characteristic material lengths on mode III crack propagation in couple stress elastic–plastic materials,” Int. J. Plasticity, 23, No. 8, 1439–1456 (2007).CrossRef
28.
E. Radi, “On the effects of the characteristic lengths in bending and torsion on Mode III crack in couple stress elasticity,” Int. J. Solids Struct., 45, No. 10, 3033–3058 (2008).CrossRef
29.
A. Piccolroaz, G. Mishuris, and E. Radi, “Mode III interfacial crack in the presence of couple-stress elastic materials,” Eng. Fract. Mech., 80, 60–71 (2012).CrossRef
30.
G. Mishuris, A. Piccolroaz, and E. Radi, “Steady-state propagation of a Mode III crack in couple stress elastic materials,” Int. J. Eng. Sci., 61, 112–128 (2012).CrossRef
31.
L. Morini, A. Piccolroaz, G. Mishuris, and E. Radi, “On fracture criteria for dynamic crack propagation in elastic materials with couple stresses,” Int. J. Eng. Sci., 71, 45–61 (2013).CrossRef
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).
33.
L. Morini, A. Piccolroaz, and G. Mishuris, “Remarks on the energy release rate for an antiplane moving crack in couple stress elasticity,” Int. J. Solids Struct., 51, No. 18, 3087–3100 (2014).CrossRef
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).
35.
V. A. Eremeyev, A. Skrzat, and A. Vinakurava, “Application of the micropolar theory to the strength analysis of bioceramic materials for bone reconstruction,” Strength Mater., 48, No. 4, 573–582 (2016).CrossRef
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).
37.
E. Cosserat and F. Cosserat, Théorie des Corps Déformables, Herman et Fils, Paris (1909).
38.
A. C. Eringen, Microcontinuum Field Theories: I. Foundations and Solids, Springer Science&Business Media, New York (1999).CrossRef
39.
V. A. Eremeyev, L. P. Lebedev, and H. Altenbach, Foundations of Micropolar Mechanics, Springer Science&Business Media, Berlin (2013).CrossRef
40.
W. Pietraszkiewicz and V. A. W Eremeyev, “On natural strain measures of the non-linear micropolar continuum,” Int. J. Solids Struct., 46, No. 3, 774–787 (2009).CrossRef
41.
W. Pietraszkiewicz and V. A. Eremeyev, “On vectorially parameterized natural strain measures of the non-linear Cosserat continuum,” Int. J. Solids Struct., 46, No. 11, 2477–2480 (2009).CrossRef
42.
V. A. Eremeyev and W. Pietraszkiewicz, “Material symmetry group of the non-linear polar-elastic continuum,” Int. J. Solids Struct., 49, No. 14, 1993–2005 (2012).CrossRef
43.
V. A. Eremeyev and W. Pietraszkiewicz, “Material symmetry group and constitutive equations of micropolar anisotropic elastic solids,” Math. Mech. Solids, 21, No. 2, 210–221 (2016).CrossRef
Metadaten
Titel
Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads
verfasst von
V. A. Eremeyev
A. Skrzat
F. Stachowicz
Publikationsdatum
15.11.2017
Verlag
Springer US
Erschienen in
Strength of Materials / Ausgabe 4/2017
Print ISSN: 0039-2316
Elektronische ISSN: 1573-9325
DOI
https://doi.org/10.1007/s11223-017-9901-5

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