“Homogenized trigonal models for biomechanical applications” Relatore: Ch.mo Prof. Ing. MASSIMILIANO FRALDI Correlatore: GIANPAOLO PERRELLA Candidato: CIERVO MARCO Matr. 691/939 Università degli Studi di Napoli Federico II FACOLTA’ DI INGEGNERIA CORSO DI LAUREA IN INGEGNERIA BIOMEDICA (CLASSE DELLE LAUREE IN INGEGNERIA DELL’INFORMAZIONE n.9)
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“Homogenized trigonal models for biomechanical applications”
Relatore:Ch.mo Prof. Ing.
MASSIMILIANO FRALDI
Correlatore:GIANPAOLO PERRELLA
Candidato:CIERVO MARCO
Matr. 691/939
Università degli Studi di Napoli Federico II
FACOLTA’ DI INGEGNERIA
CORSO DI LAUREA ININGEGNERIA BIOMEDICA
(CLASSE DELLE LAUREE IN INGEGNERIA DELL’INFORMAZIONE n.9)
Description
Ligaments: Anterior Cruciate Ligament (ACL)
Healing ACL ruptures: 6-cord wire-rope scaffold
Analytical model: George A. Costello’s theory of the wire rope
Homogenized Trigonal model: example of development
Hierarchical structures: importance in biomechanics
The AP displacement of the tibia was determined by the displacement of the origin of the tibial coor-dinate system on the APaxis of the tibia. Tibial rotation was determined by the projection of the medial–lateral (ML) axis of the tibia onto the
A. Guadagno,Relatore Ch.mo Prof. Ing. A. Pepino e Correlatore Ing. A. RanavoloNapoli, 2004/2005.
VALUTAZIONE DELLE FORZE COMPRESSIVE E DI TAGLIO ALL’ARTICOLAZIONE DEL GINOCCHIO CON SISTEMA DI ANALISI COMPUTERIZZATA MULTIFATTORIALE DEL MOVIMENTO,
J Biomech. 2010 July 20; 43(10): 2039–2042. doi:10.1016/j.jbiomech.2010.03.015.A Knee-Specific Finite Element Analysis of the Human Anterior
Cruciate Ligament Impingement against the FemoralIntercondylar Notch
Hyung-Soon Park1,†, Chulhyun Ahn,†, David T. Fung, Yupeng Ren, and Li-QunZhang
ACL Kinematics
Flexion: 46.3 deg.Abduction: 0 deg.
External rotation: 0 deg.
Flexion: 44.8 deg.Abduction: 10.0 deg.
External rotation: 29.1 deg.
ACL Kinematics
The AP displacement of the tibia was determined by the displacement of the origin of the tibial coor-dinate system on the APaxis of the tibia. Tibial rotation was determined by the projection of the medial–lateral (ML) axis of the tibia onto the
Journal of Biomechanics 38 (2005) 293–298Interactions between kinematics and loading during
walking for thenormal and ACL deficient knee
Thomas P. Andriacchia, Chris O. Dyrby
Altman’s Scaffold
Biomaterials 23 (2002) 4131–4141Silk matrix for tissue engineered anterior cruciate
ligamentsGregory H. Altmana, Rebecca L. Horana, Helen H.
Lua, Jodie Moreaua, Ivan Martinb,John C. Richmondc, David L. Kaplana
Analytical Model
h1 h3h2core wires
axial tension in the wiretwisting moment in the wireshear force in the wire, along the local cooordinates system directionsbending moment in the wire in x and y directions, along the local coordina-tes system curvature of the wire in x and y directions, along the local coordinates system twist per unit length of the wire
THN, N’G, G’
κ, κ’
т
Kinematics of a wire
Mechanical Engineering Series, Springer - Theory of Wke Rope, 2nd ed. - George A. Costello
3
//t
k kF AEk kM ERεε εβ
βε ββ
εβ
=
Simple straigth strand
Δαξw = ξc - Tg α
core radiusRcRwαR = Rc+2Rwr = Rc+RwEvξc = ε
ξwβr = Tg α - Δα + νr
Rc ξc + Rw ξwTg α
β т = r βr = R β
Δт’ = 1 - 2 Sin2αr
Δα + Rc ξc + Rw ξwr2ν Sin α Cos α
Δκ’ = - 2 Sin α Cos αr
Δα + Rc ξc + Rw ξwr2ν Cos2 α curve variation
Gw’ = E Rw4 Δκ’ �4
Hw = E Rw4 Δт’ �4 (1 + v)Nw’ = Hw Cos2 α
r- Gw’ Sin α Cos α
rTw = � E Rw2 ξw
Fw = mw (Tw Sin α + Nw’ Cos α) Mw = mw (Hw Sin α + Gw’ Cos α + r Tw Cos α + r Hw Sin α )
Fc = � E Rc2 ξc Mc = E Rc4 т’ �4 (1 + v)
Geometrical characteristics
Deformationscore axial strain
angle of twist per unit lenght
Material propertiesYoung ModulusPoisson’s ratio
Core Loads
Wire Loads
wire radiuswire helix anglestrand total radiusstrand helical radius
wire axial strain
helical rototional strain
total rototional strain
Costitutive assumptions
Hipothesis of small displacements: Δα<<1, ξ<<1
30 Fibers
1 Bundle
Rf = 10.4067 10-5 m Equivalent fiber radius
R1 = [19 ± 2.8]10-6 mSilk fibroin average radius
On the right pilot-scale manu-facturing equipment for the fabrication of silk wire-rope matrices
Two particluars (B) and (C) of (i) and (iii), showing the extraction of the fibroins
On the left a close-up view of (i): the twisting machines showing the motor controlled spring-loaded clamps.
Fwh1 = mh1 (Twh1 Sin αh1 + Nwh1’ Cos αh1)Mwh1 = mh1 (Hwh1 Sin αh1 + Gwh1’ Cos αh1 + rh1 Twh1 Cos αh1 + rh1 Hwh1 Sin αh1)
Awh1 = mh2 Awh1wh2Gywh1 = Awh1 Δκh1’
Hwh1 = Mh1Twh1 = Fh1 Loads
Deformationsξch1 = ε
Analytical model Results and validation
0.05 0.10 0.15 0.20 0.25
200
300
400
500
600
Calculated
G. Vunjak-Novakovic et al.
Displacement (%)
Load
(N)
Root Mean Square Error Percentage
2
0.023
ni i
i i
x xx
RMSEPn
− = =
∑
Annu. Rev. Biomed. Eng. 2004. 6:131–56 TISSUE ENGINEERING OF LIGAMENTS
G. Vunjak-Novakovic1, Gregory Altman2,3, Rebecca Horan2 and David L. Kaplan2
1 Massachusetts Institute of Technology, Harvard-MIT Division of Health Sciences and Technology, Cambridge, Massachusetts 02139; email: [email protected]
Displacements along the z-axis [m] Rotations around the z-axis [deg]
0.10 0.15 0.20 0.25
200
300
400
500
600 Analytical model
Homogenized model
Displacement (%)
Load
(N)
Homogenized model Results and validation
Root Mean Square Error Percentage
2
0.086
ni i
i i
x xx
RMSEPn
− = =
∑
Root Mean Square Error Percentage
2
0.028
ni i
i i
x xx
RMSEPn
− = =
∑
Displacement (%)R
otat
ion
(deg
)0.10 0.15 0.20 0.25
100
80
60
40
Analytical model
Homogenized model
Conclusions andfuture developments
NON LINEAR BEHAVIOUR DEVELOPMENT
3D FEM JOINT IMPLEMENTATION WITH ON-SITE TESTS
IMPROVEMENT OF CURRENT SCAFFOLDS
DESIGN OF NEW STRUCTURES
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