In this paper, a numerical method based on finite elements is used to study the phenomena of resorption and growth of bone tissue and resorption of the biomaterial in the neighborhood of a dental implant fixture of the type IntraMobil Zylinder. The mechanical stimulus that drives these processes is a linear combination of strain energy and viscous dissipation. To simulate the implant, an axisymmetric model has been used from the point of view of the geometry; the material behavior is described in the poro-visco-elastic frame. The external action is represented by a load variable with sinusoidal law characterized by different frequencies. Investigated aspects are the influence of the load frequency and of the lazy zone on the remodeling process.
SonciniMPietrabissaRRodriguez y BaenaR. Computational approach for the mechanical reliability of a dental implant. In: MiddletonJPandeGNJonesML (eds.) Computer methods in biomechanics and biomedical engineering. Philadelphia, PA: Gordon and Breach Science Publishers, 2001.
2.
AndreausUCollocaMIacovielloD.Coupling image processing and stress analysis for damage identification in a human premolar tooth. Comput Methods Programs Biomed2011; 103(2): 61–73.
3.
AncillaoAAndreausU.Finite element analysis of the stress state produced by an orthodontic skeletal anchorage system based on miniscrews. J Cranio Max Dis2013; 2(1): 28.
4.
MarangosOMisraASpencerPet al. Physico-mechanical properties determination using microscale homotopic measurements: application to sound and caries-affected primary tooth dentin. Acta Biomater2009; 5(4): 1338–1348.
5.
NiznickGA.Product profile-achieving osseointegration in soft bone: The search for improved results. Oral Health2000; 90(8): 27–34.
6.
BabbushCAKirschAMentagPJet al. Intramobile cylinder (IMZ) two-stage osteointegrated implant system with the intramobile element (IME): part I. Its rationale and procedure for use. Int J Oral Maxillofac Implants1987; 2(4): 203.
7.
ByrneG.Fundamentals of implant dentistry. Hoboken, NJ: John Wiley & Sons, 2014.
8.
Di EgidioALuongoAPaoloneA. Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams. Int J Non Linear Mech2007; 42(1): 88–98.
9.
LuongoAZulliDPiccardoG.On the effect of twist angle on nonlinear galloping of suspended cables. Comput Struct2009; 87(15): 1003–1014.
10.
RutaGCVaranoVPignataroMet al. A beam model for the flexural-torsional buckling of thin-walled members with some applications. Thin Wall Struct2008; 46(7-9): 816–822.
RizziNVaranoVGabrieleS.Initial postbuckling behavior of thin-walled frames under mode interaction. Thin Wall Struct2013; 68: 124–134.
13.
PignataroMRizziNRutaGVaranoV.The effects of warping constraints on the buckling of thin-walled structures. J Mech Mater Struct2010; 4(10): 1711–1727.
14.
GrilloAFedericoSWittumGet al. Evolution of a fibre-reinforced growing mixture. Nuovo Cimento C2009; 32(1): 97.
15.
PlacidiLdell’IsolaFIaniroNet al. Variational formulation of pre-stressed solid–fluid mixture theory, with an application to wave phenomena. Eur J Mech A2008; 27(4): 582–606.
16.
PlacidiLHutterK.Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity. Continuum Mech Thermodyn2006; 17(6): 409–451.
17.
GodaIAssidiMBelouettarSet al. A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization. J Mech Behav Biomed Mater2012; 16: 87–108.
18.
AltenbachHEremeyevV.Analysis of the viscoelastic behavior of plates made of functionally graded materials. Z Angew Math Mech2008; 88(5): 332–341.
19.
AltenbachHEremeyevVALebedevLPet al. Acceleration waves and ellipticity in thermoelastic micropolar media. Arch Appl Mech2010; 80(3): 217–227.
20.
AminpourHRizziN.A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis. Math Mech Solids2016; 21(2): 168–181.
21.
CowinSCNunziatoJW.Linear elastic materials with voids. J Elast1983; 13(2): 125–147.
22.
BiotMA.Mechanics of deformation and acoustic propagation in porous media. J Appl Phys1962; 33(4): 1482–1498.
23.
BiotMA.Generalized theory of acoustic propagation in porous dissipative media. J Acoust Soc Am1962; 34(9A): 1254–1264.
dell’IsolaFRosaLWoźniakC. A micro-structured continuum modelling compacting fluid-saturated grounds: The effects of pore-size scale parameter. Acta Mech1998; 127(1-4): 165–182.
26.
dell’IsolaFBatraRC.Saint-Venant’s problem for porous linear elastic materials. J Elast1997; 47(1): 73–81.
27.
MadeoAdell’IsolaFDarveF.A continuum model for deformable, second gradient porous media partially saturated with compressible fluids. J Mech Phys Solids2013; 61(11): 2196–2211.
28.
MadeoAdell’IsolaFIaniroNet al. A variational deduction of second gradient poroelasticity II: An application to the consolidation problem. J Mech Mater Struct2008; 3(4): 607–625.
29.
TomicAGrilloAFedericoS.Poroelastic materials reinforced by statistically oriented fibres—numerical implementation and application to articular cartilage. IMA J Appl Math2014; 79(5): 1027–1059.
30.
FedericoSGrilloAHerzogWet al. Possible approaches in modelling rearrangement in a microstructured material. In: Key engineering materials, vol. 340. Trans Tech Publ, Zurich, Switzerland: Kreuzstrasse, pp.137–142.
31.
GrilloAProhlRWittumG.A poroplastic model of structural reorganisation in porous media of biomechanical interest. Continuum Mech Thermodyn2016; 28(1): 579–601.
32.
dell’IsolaFRosaLWoźniakC. Dynamics of solids with microperiodic nonconnected fluid inclusions. Arch Appl Mech1997; 67: 215–228.
33.
GanghofferJF.A contribution to the mechanics and thermodynamics of surface growth. Application to bone external remodeling. Int J Eng Sci2012; 50(1): 166–191.
PlacidiLFariaSHHutterK.On the role of grain growth, recrystallization and polygonization in a continuum theory for anisotropic ice sheets. Ann Glaciol2004; 39(1): 49–52.
36.
PlacidiLHutterK.An anisotropic flow law for incompressible polycrystalline materials. Z Angew Math Phys2005; 57(1): 160–181.
37.
dell’IsolaFHutterK.What are the dominant thermomechanical processes in the basal sediment layer of large ice sheets?Proc R Soc Lond A1998; 454(1972): 1169–1195.
38.
dell’IsolaFRomanoA.A phenomenological approach to phase transition in classical field theory. Int J Eng Sci1987; 25(11): 1469–1475.
39.
dell’IsolaFWoźniakC. On phase transition layers in certain micro-damaged two-phase solids. Int J Fract1997; 83(2): 175–189.
40.
YeremeyevVAFreidinABSharipovaLL.The stability of the equilibrium of two-phase elastic solids. J Appl Math Mech2007; 71(1): 61–84.
41.
EremeyevVAPietraszkiewiczW.Phase transitions in thermoelastic and thermoviscoelastic shells. Arch Mech2009; 61(1): 41–67.
42.
AndreausUGiorgioIMadeoA.Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids. Z Angew Math Phys2015; 66(1): 209–237.
YangYMisraA.Higher-order stress-strain theory for damage modeling implemented in an element-free galerkin formulation. Comput Model Eng Sci2010; 64(1): 1–36.
45.
YangYChingWYMisraA.Higher-order continuum theory applied to fracture simulation of nanoscale intergranular glassy film. J Nanomech Micromech2011; 1(2): 60–71.
46.
PlacidiL.A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Continuum Mech Thermodyn2015; 27(4-5): 623–638.
47.
PlacidiL.A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Continuum Mech Thermodyn2016; 28: 119–137.
48.
RinaldiAPlacidiL.A microscale second gradient approximation of the damage parameter of quasi-brittle heterogeneous lattices. Z Angew Math Mech2014; 94(10): 862–877.
49.
AndreausUCeradiniGD’AsdiaPet al. Damage modelling and seismic response of simple degrading systems. Res Mech1987; 22(1): 79–100.
50.
CarcaterraAdell’IsolaFEspositoRet al. Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials. Arch Ration Mech Anal2015; 218(3): 1239–1262.
51.
LeeTCStainesATaylorD.Bone adaptation to load: microdamage as a stimulus for bone remodelling. J Anat2002; 201(6): 437–446.
52.
SedlinED.A rheologic model for cortical bone: a study of the physical properties of human femoral samples. Acta Orthop1965; 36(S83): 1–77.
53.
BargrenJHBassettCALGjelsvikA.Mechanical properties of hydrated cortical bone. J Biomech1974; 7(3): 239–245.
54.
CarcaterraAAkayA.Dissipation in a finite-size bath. Phys Rev E2011; 84(1): 011121.
55.
CarcaterraARoveriNPepeG.Fractional dissipation generated by hidden wave-fields. Math Mech Solids2015; 20(10): 1251–1262.
56.
LekszyckiT.Application of variational methods in analysis and synthesis of viscoelastic continuous systems. J Struct Mech1991; 19(2): 163–192.
dell’IsolaFSeppecherPDella CorteA.The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results. Proc R Soc Lond A2015; 471(2183): 20150415.
59.
GiorgioIAndreausUScerratoDet al. A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials. Biomech Model Mechanobiol. Epub ahead of print on 30 January 2016. DOI: 10.1007/s10237-016-0765-6.
60.
LekszyckiTdell’IsolaF.A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials. Z Angew Math Mech2012; 92(6): 426–444.
61.
MullenderMGHuiskesR.Proposal for the regulatory mechanism of Wolff’s law. J Orthop Res1995; 13(4): 503–512.
62.
MadeoALekszyckiTdell’IsolaF.A continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery. C R Mec2011; 339(10): 625–640.
63.
KumarCJasiukIDantzigJ.Dissipation energy as a stimulus for cortical bone adaptation. J Mech Mater Struct2011; 6(1): 303–319.
64.
TurnerCH.Homeostatic control of bone structure: an application of feedback theory. Bone1991; 12(3): 203–217.
HambliR.Connecting mechanics and bone cell activities in the bone remodeling process: an integrated finite element modeling. Front Bioeng Biotechnol. Epub ahead of print on 08 April 2014. DOI: 10.3389/fbioe.2014.00006.
67.
CowinSCHegedusDH.Bone remodeling I: theory of adaptive elasticity. J Elast1976; 6(3): 313–326.
68.
CarterDRCalerWE.A cumulative damage model for bone fracture. J Orthop Res1985; 3(1): 84–90.
LekszyckiT.Modelling of bone adaptation based on an optimal response hypothesis. Meccanica2002; 37(4-5): 343–354.
71.
JangIGKimIY.Application of design space optimization to bone remodeling simulation of trabecular architecture in human proximal femur for higher computational efficiency. Finite Elem Anal Des2010; 46(4): 311–319.
72.
AndreausUCollocaMIacovielloDet al. Optimal-tuning pid control of adaptive materials for structural efficiency. Struct Multidiscip Optim2011; 43(1): 43–59.
73.
AndreausUCollocaMIacovielloD.An optimal control procedure for bone adaptation under mechanical stimulus. Control Eng Pract2012; 20(6): 575–583.
74.
AndreausUCollocaMIacovielloD. Modeling of trabecular architecture as result of an optimal control procedure. In: IacovielloDAndreausU (eds.) Biomedical imaging and computational modeling in biomechanics, chapter II. Dordrecht: Springer, 2013, pp.19–37.
75.
AndreausUCollocaMIacovielloD.Optimal bone density distributions: Numerical analysis of the osteocyte spatial influence in bone remodeling. Comput Methods Programs Biomed2014; 113(1): 80–91.
76.
LanyonLERubinCT.Static vs dynamic loads as an influence on bone remodelling. J Biomech1984; 17(12): 897–905.
77.
TurnerCH.Three rules for bone adaptation to mechanical stimuli. Bone1998; 23(5): 399–407.
78.
AndreausUGiorgioILekszyckiT.A 2-D continuum model of a mixture of bone tissue and bio-resorbable material for simulating mass density redistribution under load slowly variable in time. Z Angew Math Mech2014; 94(12): 978–1000.
79.
GiorgioIAndreausUMadeoA.The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids. Continuum Mech Thermodyn2016; 28(1): 21–40.
80.
GiorgioIGalantucciLDella CorteAet al. Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: current and upcoming applications. Int J Appl Electromagnet Mech2015; 47(4): 1051–1084.
81.
GiorgioICullaADel VescovoD.Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network. Arch Appl Mech2009; 79(9): 859–879.
82.
PorfiriMdell’IsolaFSantiniE.Modeling and design of passive electric networks interconnecting piezoelectric transducers for distributed vibration control. Int J Appl Electromagnet Mech2005; 21(2): 69–87.
83.
MauriniCdell’IsolaFDel VescovoD.Comparison of piezoelectronic networks acting as distributed vibration absorbers. Mech Syst Sig Process2004; 18(5): 1243–1271.
84.
PagniniLCPiccardoG.The three-hinged arch as an example of piezomechanic passive controlled structure. Continuum Mech Thermodyn. Epub ahead of print on 27 August 2015. DOI: 10.1007/s00161-015-0474-x.
85.
Del VescovoDGiorgioI. Dynamic problems for metamaterials: review of existing models and ideas for further research. Int J Eng Sci2014; 80: 153–172.
86.
dell’IsolaFLekszyckiTPawlikowskiMet al. Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence. Z Angew Math Phys2015; 66(6): 3473–3498.
87.
dell’IsolaFDella CorteAGrecoLet al. Plane bias extension test for a continuum with two inextensible families of fibers: a variational treatment with Lagrange multipliers and a perturbation solution. Int J Solids Struct2016; 81: 1–12.
88.
AlibertJJDella CorteA.Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof. Z Angew Math Phys2015; 66(5): 2855–2870.
89.
MadeoADella CorteAGrecoLet al. Wave propagation in pantographic 2D lattices with internal discontinuities. Proc Est Acad Sci2015; 64(3S): 325–330.
90.
CazzaniAMalagùMTurcoE.Isogeometric analysis of plane-curved beams. Math Mech Solids. Epub ahead of print on April 20, 2014. DOI: 10.1177/1081286514531265.
CazzaniAMalagùMTurcoE.Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches. Continuum Mech Thermodyn2016; 28(1): 139–156.
93.
CazzaniAMalagùMTurcoEet al. Constitutive models for strongly curved beams in the frame of isogeometric analysis. Math Mech Solids2016; 21(2): 182–209.
94.
Della CorteABattistaAdell’IsolaF. Referential description of the evolution of a 2D swarm of robots interacting with the closer neighbors: Perspectives of continuum modeling via higher gradient continua. Int J Non Linear Mech2016; 80: 209–220.
95.
FedericoSGrilloAImataniSet al. An energetic approach to the analysis of anisotropic hyperelastic materials. Int J Eng Sci2008; 46(2): 164–181.
96.
SolariGPagniniLCPiccardoG.A numerical algorithm for the aerodynamic identification of structures. J Wind Eng Ind Aerodyn1997; 69: 719–730.
97.
GrecoLCuomoM.B-Spline interpolation of Kirchhoff–Love space rods. Comput Methods Appl Mech Eng2013; 256: 251–269.
98.
GrecoLCuomoM.An implicit G1 multi patch B-spline interpolation for Kirchhoff–Love space rod. Comput Methods Appl Mech Eng2014; 269: 173–197.
99.
GrecoLCuomoM.An isogeometric implicit G1 mixed finite element for Kirchhoff space rods. Comput Methods Appl Mech Eng2016; 298: 325–349.
100.
CuomoMContrafattoLGrecoL.A variational model based on isogeometric interpolation for the analysis of cracked bodies. Int J Eng Sci2014; 80: 173–188.
