The material mismatch at the attachment of tendon to bone is among the most severe for any tensile connection in nature. Attaching dissimilar materials is a major challenge in engineering, and has proven to be a challenge in surgical practice as well. Here, we examine the material attachment schemes employed at this connection through the lens of solid mechanics. We identify four strategies that the body adopts to achieve effective load transfer between tendon and bone: (1) a shallow attachment angle at the insertion of transitional tissue and bone, (2) shaping of gross tissue morphology of the transitional tissue, (3) interdigitation of bone with the transitional tissue, and (4) functional grading of transitional tissue between tendon and bone. We provide solutions to model problems that highlight the first two mechanisms: discuss the third qualitatively in the context of engineering practice and provide a review of our earlier work on the fourth. We study these strategies both in terms of ways that biomimetic attachment might benefit engineering practice and of ways that engineering experience might serve to improve surgical healing outcomes.

1.
Delale
,
F.
, 1984, “
Stress Singularities in Bonded Anisotropic Materials
,”
Int. J. Solids Struct.
0020-7683,
20
(
1
), pp.
31
40
.
2.
Mittelstedt
,
C.
, and
Becker
,
W.
, 2007, “
Free-Edge Effects in Composite Laminates
,”
Appl. Mech. Rev.
0003-6900,
60
, pp.
217
245
.
3.
Wang
,
S. S.
, and
Choi
,
I.
, 1982, “
Boundary-Layer Effects in Composite Laminates: Part 1—Free-Edge Stress Singularities
,”
ASME J. Appl. Mech.
0021-8936,
49
, pp.
541
548
.
4.
Williams
,
M. L.
, 1952, “
Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
,”
ASME J. Appl. Mech.
0021-8936,
19
, pp.
526
528
.
5.
Genin
,
G. M.
,
Kent
,
A.
,
Birman
,
V.
,
Wopenka
,
B.
,
Pasteris
,
J. D.
,
Marquez
,
P. J.
, and
Thomopoulos
,
S.
, 2009, “
Functional Grading of Mineral and Collagen in the Attachment of Tendon to Bone
,”
Biophys. J.
0006-3495,
97
(
4
), pp.
976
985
.
6.
Thomopoulos
,
S.
,
Marquez
,
J. P.
,
Weinberger
,
B.
,
Birman
,
V.
, and
Genin
,
G. M.
, 2006, “
Collagen Fiber Orientation at the Tendon to Bone Insertion and Its Influence on Stress Concentrations
,”
J. Biomech.
0021-9290,
39
(
10
), pp.
1842
1851
.
7.
Thomopoulos
,
S.
,
Williams
,
G. R.
,
Gimbel
,
J. A.
,
Favata
,
M.
, and
Soslowsky
,
L. J.
, 2003, “
Variation of Biomechanical, Structural, and Compositional Properties Along the Tendon to Bone Insertion Site
,”
J. Orthop. Res.
0736-0266,
21
(
3
), pp.
413
419
.
8.
Wopenka
,
B.
,
Kent
,
A.
,
Pasteris
,
J. D.
,
Yoon
,
Y.
, and
Thomopoulos
,
S.
, 2008, “
The Tendon-to-Bone Transition of the Rotator Cuff: A Preliminary Raman Spectroscopic Study Documenting the Gradual Mineralization Across the Insertion in Rat Tissue Samples
,”
Appl. Spectrosc.
0003-7028,
62
(
12
), pp.
1285
1294
.
9.
Thomopoulos
,
S.
,
Williams
,
G. R.
, and
Soslowsky
,
L. J.
, 2003, “
Tendon to Bone Healing: Differences in Biomechanical, Structural, and Compositional Properties Due to a Range of Activity Levels
,”
ASME J. Biomech. Eng.
0148-0731,
125
(
1
), pp.
106
113
.
10.
Galatz
,
L. M.
,
Sandell
,
L. J.
,
Rothermich
,
S. Y.
,
Das
,
R.
,
Mastny
,
A.
,
Havlioglu
,
N.
,
Silva
,
M. J.
, and
Thomopoulos
,
S.
, 2006, “
Characteristics of the Rat Supraspinatus Tendon During Tendon-to-Bone Healing After Acute Injury
,”
J. Orthop. Res.
0736-0266,
24
(
3
), pp.
541
550
.
11.
Carpenter
,
J. E.
,
Thomopoulos
,
S.
,
Flanagan
,
C. L.
,
Debano
,
C. M.
, and
Soslowsky
,
L. J.
, 1998, “
Rotator Cuff Defect Healing: A Biomechanical and Histologic Analysis in an Animal Model
,”
J. Shoulder Elbow Surg.
1058-2746,
7
(
6
), pp.
599
605
.
12.
Galatz
,
L. M.
,
Ball
,
C. M.
,
Teefey
,
S. A.
,
Middleton
,
W. D.
, and
Yamaguchi
,
K.
, 2004, “
The Outcome and Repair Integrity of Completely Arthroscopically Repaired Large and Massive Rotator Cuff Tears
,”
J. Bone Joint Surg. Am.
,
86-A
(
2
), pp.
219
224
.
13.
Galatz
,
L. M.
,
Griggs
,
S.
,
Cameron
,
B. D.
, and
Iannotti
,
J. P.
, 2001, “
Prospective Longitudinal Analysis of Postoperative Shoulder Function: A Ten-Year Follow-Up Study of Full-Thickness Rotator Cuff Tears
,”
J. Bone Joint Surg. Am.
,
83-A
(
7
), pp.
1052
1056
.
14.
Chue
,
C. H.
, and
Liu
,
C. I.
, 2002, “
Disappearance of Free-Edge Stress Singularity in Composite Laminates
,”
Compos. Struct.
0263-8223,
56
(
1
), pp.
111
129
.
15.
Wu
,
Z.
, 2004, “
Design Free of Stress Singularities for Bi-Material Components
,”
Compos. Struct.
0263-8223,
65
(
3–4
), pp.
339
345
.
16.
Lekhnitskii
,
S. G.
, 1963,
Theory of Elasticity of an Anisotropic Elastic Body
,
Holden-Day
,
New York
.
17.
Maganaris
,
C. N.
, and
Paul
,
J. P.
, 1999, “
In Vivo Human Tendon Mechanical Properties
,”
J. Physiol.
,
521
, pp.
307
313
.
18.
Weiss
,
J. A.
,
Gardiner
,
J. C.
, and
Bonifasi-Lista
,
C.
, 2002, “
Ligament Material Behavior Is Nonlinear, Viscoelastic and Rate-Independent Under Shear Loading
,”
J. Biomech.
0021-9290,
35
(
7
), pp.
943
950
.
19.
Yin
,
L.
, and
Elliott
,
D. M.
, 2004, “
A Biphasic and Transversely Isotropic Mechanical Model for Tendon: Application to Mouse Tail Fascicles in Uniaxial Tension
,”
J. Biomech.
0021-9290,
37
(
6
), pp.
907
916
.
20.
Anderson
,
T. L.
, 2005,
Fracture Mechanics: Fundamentals and Applications
,
CRC
,
Boca Raton, FL
.
21.
Gürdal
,
Z.
,
Haftka
,
R. T.
, and
Hajela
,
P.
, 1999,
Design and Optimization of Laminated Composite Materials
,
Wiley-Interscience
,
New York
.
22.
Hurd
,
A. J.
, and
Truman
,
K. Z.
, 2006, “
Optimization Method of Pile Foundations
,”
Solid Mechanics and Its Applications
, Vol.
140
,
Springer
,
Amsterdam, The Netherlands
, p.
653
.
23.
Jakiela
,
M. J.
,
Chapman
,
C.
,
Duda
,
J.
,
Adewuya
,
A.
, and
Saitou
,
K.
, 2000, “
Continuum Structural Topology Design With Genetic Algorithms
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
186
(
2–4
), pp.
339
356
.
24.
Clark
,
J. M.
, and
Harryman
,
D. T.
, II
, 1992, “
Tendons, Ligaments, and Capsule of the Rotator Cuff. Gross and Microscopic Anatomy
,”
J. Bone Joint Surg. Am.
,
74
(
5
), pp.
713
725
.
25.
Curtis
,
A. S.
,
Burbank
,
K. M.
,
Tierney
,
J. J.
,
Scheller
,
A. D.
, and
Curran
,
A. R.
, 2006, “
The Insertional Footprint of the Rotator Cuff: An Anatomic Study
,”
Arthroscopy: J. Relat. Surg.
0749-8063,
22
(
6
), pp.
603
609
.
26.
Dugas
,
J. R.
,
Campbell
,
D. A.
,
Warren
,
R. F.
,
Robie
,
B. H.
, and
Millett
,
P. J.
, 2002, “
Anatomy and Dimensions of Rotator Cuff Insertions
,”
J. Shoulder Elbow Surg.
1058-2746,
11
(
5
), pp.
498
503
.
27.
Itoi
,
E.
,
Berglund
,
L. J.
,
Grabowski
,
J. J.
,
Schultz
,
F. M.
,
Growney
,
E. S.
,
Morrey
,
B. F.
, and
An
,
K. N.
, 1995, “
Tensile Properties of the Supraspinatus Tendon
,”
J. Orthop. Res.
0736-0266,
13
(
4
), pp.
578
584
.
28.
Minagawa
,
H.
,
Itoi
,
E.
,
Konno
,
N.
,
Kido
,
T.
,
Sano
,
A.
,
Urayama
,
M.
, and
Sato
,
K.
, 1998, “
Humeral Attachment of the Supraspinatus and Infraspinatus Tendons: An Anatomic Study
,”
Arthroscopy: J. Relat. Surg.
0749-8063,
14
(
3
), pp.
302
306
.
29.
Mochizuki
,
T.
,
Sugaya
,
H.
,
Uomizu
,
M.
,
Maeda
,
K.
,
Matsuki
,
K.
,
Sekiya
,
I.
,
Muneta
,
T.
, and
Akita
,
K.
, 2008, “
Humeral Insertion of the Supraspinatus and Infraspinatus. New Anatomical Findings Regarding the Footprint of the Rotator Cuff
,”
J. Bone Joint Surg. Am.
,
90
(
5
), pp.
962
969
.
30.
Ruotolo
,
C.
,
Fow
,
J. E.
, and
Nottage
,
W. M.
, 2004, “
The Supraspinatus Footprint: An Anatomic Study of the Supraspinatus Insertion
,”
Arthroscopy: J. Relat. Surg.
0749-8063,
20
(
3
), pp.
246
249
.
31.
Fung
,
Y. C.
, 1993,
Biomechanics: Mechanical Properties of Living Tissues
,
Springer
,
New York
.
32.
Benjamin
,
M.
,
Kumai
,
T.
,
Milz
,
S.
,
Boszczyk
,
B. M.
,
Boszczyk
,
A. A.
, and
Ralphs
,
J. R.
, 2002, “
The Skeletal Attachment of Tendons–Tendon ‘Entheses’
,”
Comp. Biochem. Physiol. A
0300-9629,
133
(
4
), pp.
931
945
.
33.
Comsol
,
I.
, 2006, COMSOL Multiphysics User’s Guide, COMSOL, Inc., Burlington, MA.
34.
The Mathworks, Inc.
, 2010; see http://www.mathworks.comhttp://www.mathworks.com, Natick, MA.
35.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
, 2007,
Numerical Recipes: The Art of Scientific Computing
,
Cambridge University Press
,
Cambridge, UK
.
36.
Huang
,
J.
,
Venkataraman
,
S.
,
Rapoff
,
A. J.
, and
Haftka
,
R. T.
, 2003, “
Optimization of Axisymmetric Elastic Modulus Distributions Around a Hole for Increased Strength
,”
Struct. Multidiscip. Optim.
1615-147X,
25
(
4
), pp.
225
236
.
37.
Lipton
,
R.
, 2002, “
Design of Functionally Graded Composite Structures in the Presence of Stress Constraints
,”
Int. J. Solids Struct.
0020-7683,
39
(
9
), pp.
2575
2586
.
38.
Wang
,
P.
, and
Xu
,
L. R.
, 2006, “
Convex Interfacial Joints with Least Stress Singularities in Dissimilar Materials
,”
Mech. Mater.
0167-6636,
38
(
11
), pp.
1001
1011
.
39.
Dines
,
J. S.
,
Bedi
,
A.
,
Elattrache
,
N. S.
, and
Dines
,
D. M.
, 2010, “
Single-Row Versus Double-Row Rotator Cuff Repair: Techniques and Outcomes
,”
J. Am. Acad. Orthop. Surg.
1067-151X,
18
(
2
), pp.
83
93
.
40.
Schneider
,
H.
, 1956, “
Zur Struktur Der Sehnenansatzzonen
,”
Anat. Embryol. (Berl)
0340-2061,
119
(
5
), pp.
431
456
.
41.
Birman
,
V.
, and
Byrd
,
L. W.
, 2007, “
Modeling and Analysis of Functionally Graded Materials and Structures
,”
Appl. Mech. Rev.
0003-6900,
60
(
5
), pp.
195
216
.
42.
Milz
,
S.
,
Rufai
,
A.
,
Buettner
,
A.
,
Putz
,
R.
,
Ralphs
,
J. R.
, and
Benjamin
,
M.
, 2002, “
Three-Dimensional Reconstructions of the Achilles Tendon Insertion in Man
,”
J. Anat.
0021-8782,
200
(
2
), pp.
145
152
.
43.
Birman
,
V.
, and
Byrd
,
L. W.
, 2005, “
Effect of Z-Pins on Fracture in Composite Cocured Double Cantilever Beams
,”
J. Aerosp. Eng.
0893-1321,
18
(
1
), pp.
51
59
.
44.
Byrd
,
L. W.
, and
Birman
,
V.
, 2005, “
The Estimate of the Effect of Z-Pins on the Strain Release Rate, Fracture and Fatigue in a Composite Co-Cured Z-Pinned Double Cantilever Beam
,”
Compos. Struct.
0263-8223,
68
(
1
), pp.
53
63
.
45.
Byrd
,
L. W.
, and
Birman
,
V.
, 2006, “
Effectiveness of Z-Pins in Preventing Delamination of Co-Cured Composite Joints on the Example of a Double Cantilever Test
,”
Composites, Part B
1359-8368,
37
(
4–5
), pp.
365
378
.
46.
Freitas
,
G.
,
Fusco
,
T.
,
Campbell
,
T.
,
Harris
,
J.
, and
Rosenberg
,
S.
, 1997, “
Z-Fiber Technology and Products for Enhancing Composite Design
,” p.
17
.
47.
Freitas
,
G.
,
Magee
,
C.
,
Dardzinski
,
P.
, and
Fusco
,
T.
, 1994, “
Fiber Insertion Process for Improved Damage Tolerance in Aircraft Laminates
,”
J. Adv. Mater.
1070-9789,
25
(
4
), pp.
36
43
.
48.
Tersoff
,
J.
, and
Legoues
,
F. K.
, 1994, “
Competing Relaxation Mechanisms in Strained Layers
,”
Phys. Rev. Lett.
0031-9007,
72
(
22
), pp.
3570
3573
.
49.
Suresh
,
S.
, and
Mortensen
,
A.
, 1998,
Fundamentals of Functionally Graded Materials: Processing and Thermomechanical Behaviour of Graded Metals and Metal-Ceramic Composites
,
IOM Communications Ltd.
,
London
.
You do not currently have access to this content.