Abstract

A theoretical and experimental investigation of the transverse load sensitivity of Bragg gratings in birefringent fibers to conforming contact is presented. A plane elasticity model is used to predict the contact dimensions between a conforming material and optical fiber and the principal stresses, indicating birefringence, created as a result of this contact. The transverse load sensitivity of commercially available birefringent fiber is experimentally measured for two cases of conforming contact. Theoretical and experimental results show that birefringent optical fiber can be used to make modulus-independent measurements of contact load. Therefore, Bragg gratings could be applied to conforming contact load measurements while avoiding some of the complications associated with existing contact sensors: specifically, the necessity to precalibrate by using materials with mechanical properties identical to those found in situ.

© 2010 Optical Society of America

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  1. E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
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    [CrossRef]
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2008

E. R. Komi, J. R. Roberts, and S. J. Rothberg, “Measurement and analysis of grip force during a golf shot,” Proc. Inst. Mech. Eng. Part P J. Sports Eng. Technol. 222, 23-35 (2008).

2007

M. M. Krishna, M. S. Shunmugam, and N. S. Prasad, “A study on the sealing performance of bolted flange joints with gaskets using finite element analysis,” Int. J. Pressure Vessels Piping 84, 349-357 (2007).
[CrossRef]

2006

I. Abe, O. Frazao, M. W. Schiller, R. N. Noqueira, H. J. Kalinowski, and J. L. Pinto, “Bragg gratings in normal and reduced diameter high birefringence fibre optics,” Meas. Sci. Technol. 17, 1477-1484 (2006).
[CrossRef]

2005

S.-K. Han, S. Federico, M. Epstein, and W. Herzog, “An articular cartilage contact model based on real surface geometry,” J. Biomech. 38, 179-184 (2005).
[CrossRef]

2004

G. Chen, L. Liu, H. Jia, J. Yu, L. Xu, and W. Wang, “Simultaneous strain and temperature measurements with fiber Bragg grating written in novel Hi-Bi optical fiber,” IEEE Photonics Technol. Lett. 16, 221-223 (2004).
[CrossRef]

E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
[CrossRef]

2003

P. Wierzba and B. B. Kosmowski, “Application of polarisation-maintaining side-hole fibres to direct force measurement,” Opto-Electron. Rev. 11, 305-312 (2003).

2002

C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatum, “A polarization-maintaining fibre Bragg grating interrogation system for multi-axis strain sensing,” Meas. Sci. Technol. 13, 1446-1449 (2002).
[CrossRef]

2001

M. K. Barker and B. B. Seedhom, “The relationship of the compressive modulus of articular cartilage: does cartilage optimize its modulus so as to minimize the strains arising in it due to the prevalent loading regime?” Rheumatology 40, 274-284 (2001).
[CrossRef] [PubMed]

M. Ciavarella and P. Decuzzi, “The state of stress induced by the plane frictionless cylindrical contact. I. The case of elastic similarity,” Int. J. Solids Struct. 38, 4507-4523 (2001).
[CrossRef]

M. Ciavarella and P. Decuzzi, “The state of stress induced by plane frictionless cylindrical contact. II. The general case (elastic dissimilarity),” Int. J. Solids Struct. 38, 4525-4533(2001).
[CrossRef]

2000

S. Ferguson, J. Bryant, R. Ganz, and K. Ito, “The acetabular labrum seal: a poroelastic finite element model,” Clin. Biomech. (Bristol, Avon) 15, 463-468 (2000).
[CrossRef]

1998

J. Z. Wu, W. Herzog, and M. Epstein, “Effects of inserting a Pressensor film into articular joints on the actual contact mechanics,” J. Biomech. Eng. 120, 655-659 (1998).
[CrossRef]

K. Yokoyama, M. Okazaki, and T. Komito, “Effect of contact pressure and thermal degradation on the sealibility of O-ring,” JSAE Rev. 19, 123-128 (1998).
[CrossRef]

P. Niemczyk, K. Cummings, A. Sarvazyan, E. Bancila, W. Ward, and R. Weiss, “Correlation of mechanical imaging and histopathology of radical prostatectomy specimens: a pilot study for detecting prostate cancer,” J. Urol. (Baltimore) 160, 797-801 (1998).
[CrossRef]

1996

E. Udd, D. Nelson, and C. Lawrence, “Three axis strain and temperature fiber optic grating sensor,” Proc. SPIE 2718, 104-109 (1996).
[CrossRef]

1995

1993

M. Ferguson-Pell and M. Cardi, “Prototype development and comparative evaluation of wheelchair pressure mapping system,” Assist. Technol. 5(2), 78-91 (1993).
[CrossRef]

1986

W. A. Hodge, R. S. Fuan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann, “Contact pressures in the human hip joint measured in vivo,” Proc. Natl. Acad. Sci. USA 83, 2789-2883 (1986).
[CrossRef]

S. L. A. Carrara, B. Y. Kim, and H. J. Shaw, “Elasto-optic alignment of birefringent axes in polarization-holding fiber,” Opt. Lett. 11, 470-472 (1986).
[CrossRef] [PubMed]

1983

A. J. Barlow and D. Payne, “The stress-optic effect in optical fibers,” IEEE J. Quantum Electron. 19, 834-839 (1983).
[CrossRef]

1981

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17, 2123-2129 (1981).
[CrossRef]

1978

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

1959

G. Hondros, “The evaluation of Poisson's ratio and the modulus of materials of a low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete,” Aust. J. Appl. Sci. 10, 243-268 (1959).

Abe, I.

I. Abe, O. Frazao, M. W. Schiller, R. N. Noqueira, H. J. Kalinowski, and J. L. Pinto, “Bragg gratings in normal and reduced diameter high birefringence fibre optics,” Meas. Sci. Technol. 17, 1477-1484 (2006).
[CrossRef]

Bancila, E.

P. Niemczyk, K. Cummings, A. Sarvazyan, E. Bancila, W. Ward, and R. Weiss, “Correlation of mechanical imaging and histopathology of radical prostatectomy specimens: a pilot study for detecting prostate cancer,” J. Urol. (Baltimore) 160, 797-801 (1998).
[CrossRef]

Barker, M. K.

M. K. Barker and B. B. Seedhom, “The relationship of the compressive modulus of articular cartilage: does cartilage optimize its modulus so as to minimize the strains arising in it due to the prevalent loading regime?” Rheumatology 40, 274-284 (2001).
[CrossRef] [PubMed]

Barlow, A. J.

A. J. Barlow and D. Payne, “The stress-optic effect in optical fibers,” IEEE J. Quantum Electron. 19, 834-839 (1983).
[CrossRef]

Bingjun, F.

F. Bingjun, S. Wang, and L. Zhonkui, Frontiers of Rock Mechanics and Sustainable Development in the 21st Century (Swets and Zeitlinger, 2001).

Bryant, J.

S. Ferguson, J. Bryant, R. Ganz, and K. Ito, “The acetabular labrum seal: a poroelastic finite element model,” Clin. Biomech. (Bristol, Avon) 15, 463-468 (2000).
[CrossRef]

Burgess, R. G.

W. A. Hodge, R. S. Fuan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann, “Contact pressures in the human hip joint measured in vivo,” Proc. Natl. Acad. Sci. USA 83, 2789-2883 (1986).
[CrossRef]

Cardi, M.

M. Ferguson-Pell and M. Cardi, “Prototype development and comparative evaluation of wheelchair pressure mapping system,” Assist. Technol. 5(2), 78-91 (1993).
[CrossRef]

Carlson, K. L.

W. A. Hodge, R. S. Fuan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann, “Contact pressures in the human hip joint measured in vivo,” Proc. Natl. Acad. Sci. USA 83, 2789-2883 (1986).
[CrossRef]

Carrara, S. L. A.

Chehura, E.

E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
[CrossRef]

Chen, G.

G. Chen, L. Liu, H. Jia, J. Yu, L. Xu, and W. Wang, “Simultaneous strain and temperature measurements with fiber Bragg grating written in novel Hi-Bi optical fiber,” IEEE Photonics Technol. Lett. 16, 221-223 (2004).
[CrossRef]

Ciavarella, M.

M. Ciavarella and P. Decuzzi, “The state of stress induced by the plane frictionless cylindrical contact. I. The case of elastic similarity,” Int. J. Solids Struct. 38, 4507-4523 (2001).
[CrossRef]

M. Ciavarella and P. Decuzzi, “The state of stress induced by plane frictionless cylindrical contact. II. The general case (elastic dissimilarity),” Int. J. Solids Struct. 38, 4525-4533(2001).
[CrossRef]

Cummings, K.

P. Niemczyk, K. Cummings, A. Sarvazyan, E. Bancila, W. Ward, and R. Weiss, “Correlation of mechanical imaging and histopathology of radical prostatectomy specimens: a pilot study for detecting prostate cancer,” J. Urol. (Baltimore) 160, 797-801 (1998).
[CrossRef]

Decuzzi, P.

M. Ciavarella and P. Decuzzi, “The state of stress induced by plane frictionless cylindrical contact. II. The general case (elastic dissimilarity),” Int. J. Solids Struct. 38, 4525-4533(2001).
[CrossRef]

M. Ciavarella and P. Decuzzi, “The state of stress induced by the plane frictionless cylindrical contact. I. The case of elastic similarity,” Int. J. Solids Struct. 38, 4507-4523 (2001).
[CrossRef]

Edahiro, T.

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17, 2123-2129 (1981).
[CrossRef]

Epstein, M.

S.-K. Han, S. Federico, M. Epstein, and W. Herzog, “An articular cartilage contact model based on real surface geometry,” J. Biomech. 38, 179-184 (2005).
[CrossRef]

J. Z. Wu, W. Herzog, and M. Epstein, “Effects of inserting a Pressensor film into articular joints on the actual contact mechanics,” J. Biomech. Eng. 120, 655-659 (1998).
[CrossRef]

Federico, S.

S.-K. Han, S. Federico, M. Epstein, and W. Herzog, “An articular cartilage contact model based on real surface geometry,” J. Biomech. 38, 179-184 (2005).
[CrossRef]

Ferguson, S.

S. Ferguson, J. Bryant, R. Ganz, and K. Ito, “The acetabular labrum seal: a poroelastic finite element model,” Clin. Biomech. (Bristol, Avon) 15, 463-468 (2000).
[CrossRef]

Ferguson-Pell, M.

M. Ferguson-Pell and M. Cardi, “Prototype development and comparative evaluation of wheelchair pressure mapping system,” Assist. Technol. 5(2), 78-91 (1993).
[CrossRef]

Frazao, O.

I. Abe, O. Frazao, M. W. Schiller, R. N. Noqueira, H. J. Kalinowski, and J. L. Pinto, “Bragg gratings in normal and reduced diameter high birefringence fibre optics,” Meas. Sci. Technol. 17, 1477-1484 (2006).
[CrossRef]

Fuan, R. S.

W. A. Hodge, R. S. Fuan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann, “Contact pressures in the human hip joint measured in vivo,” Proc. Natl. Acad. Sci. USA 83, 2789-2883 (1986).
[CrossRef]

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Ganz, R.

S. Ferguson, J. Bryant, R. Ganz, and K. Ito, “The acetabular labrum seal: a poroelastic finite element model,” Clin. Biomech. (Bristol, Avon) 15, 463-468 (2000).
[CrossRef]

Han, S.-K.

S.-K. Han, S. Federico, M. Epstein, and W. Herzog, “An articular cartilage contact model based on real surface geometry,” J. Biomech. 38, 179-184 (2005).
[CrossRef]

Harris, W. H.

W. A. Hodge, R. S. Fuan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann, “Contact pressures in the human hip joint measured in vivo,” Proc. Natl. Acad. Sci. USA 83, 2789-2883 (1986).
[CrossRef]

Herzog, W.

S.-K. Han, S. Federico, M. Epstein, and W. Herzog, “An articular cartilage contact model based on real surface geometry,” J. Biomech. 38, 179-184 (2005).
[CrossRef]

J. Z. Wu, W. Herzog, and M. Epstein, “Effects of inserting a Pressensor film into articular joints on the actual contact mechanics,” J. Biomech. Eng. 120, 655-659 (1998).
[CrossRef]

Hill, K. O.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Hodge, W. A.

W. A. Hodge, R. S. Fuan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann, “Contact pressures in the human hip joint measured in vivo,” Proc. Natl. Acad. Sci. USA 83, 2789-2883 (1986).
[CrossRef]

Hondros, G.

G. Hondros, “The evaluation of Poisson's ratio and the modulus of materials of a low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete,” Aust. J. Appl. Sci. 10, 243-268 (1959).

Hosaka, T.

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17, 2123-2129 (1981).
[CrossRef]

Huang, S.

Ito, K.

S. Ferguson, J. Bryant, R. Ganz, and K. Ito, “The acetabular labrum seal: a poroelastic finite element model,” Clin. Biomech. (Bristol, Avon) 15, 463-468 (2000).
[CrossRef]

James, S. W.

E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
[CrossRef]

C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatum, “A polarization-maintaining fibre Bragg grating interrogation system for multi-axis strain sensing,” Meas. Sci. Technol. 13, 1446-1449 (2002).
[CrossRef]

Jia, H.

G. Chen, L. Liu, H. Jia, J. Yu, L. Xu, and W. Wang, “Simultaneous strain and temperature measurements with fiber Bragg grating written in novel Hi-Bi optical fiber,” IEEE Photonics Technol. Lett. 16, 221-223 (2004).
[CrossRef]

Johnson, D. C.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Johnson, K. L.

K. L. Johnson, Contact Mechanics (Cambridge U. Press, 1987).

Kalinowski, H. J.

I. Abe, O. Frazao, M. W. Schiller, R. N. Noqueira, H. J. Kalinowski, and J. L. Pinto, “Bragg gratings in normal and reduced diameter high birefringence fibre optics,” Meas. Sci. Technol. 17, 1477-1484 (2006).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647-649 (1978).
[CrossRef]

Kim, B. Y.

Komi, E. R.

E. R. Komi, J. R. Roberts, and S. J. Rothberg, “Measurement and analysis of grip force during a golf shot,” Proc. Inst. Mech. Eng. Part P J. Sports Eng. Technol. 222, 23-35 (2008).

Komito, T.

K. Yokoyama, M. Okazaki, and T. Komito, “Effect of contact pressure and thermal degradation on the sealibility of O-ring,” JSAE Rev. 19, 123-128 (1998).
[CrossRef]

Kosmowski, B. B.

P. Wierzba and B. B. Kosmowski, “Application of polarisation-maintaining side-hole fibres to direct force measurement,” Opto-Electron. Rev. 11, 305-312 (2003).

Krishna, M. M.

M. M. Krishna, M. S. Shunmugam, and N. S. Prasad, “A study on the sealing performance of bolted flange joints with gaskets using finite element analysis,” Int. J. Pressure Vessels Piping 84, 349-357 (2007).
[CrossRef]

Lawrence, C.

E. Udd, D. Nelson, and C. Lawrence, “Three axis strain and temperature fiber optic grating sensor,” Proc. SPIE 2718, 104-109 (1996).
[CrossRef]

LeBlanc, M.

Liu, L.

G. Chen, L. Liu, H. Jia, J. Yu, L. Xu, and W. Wang, “Simultaneous strain and temperature measurements with fiber Bragg grating written in novel Hi-Bi optical fiber,” IEEE Photonics Technol. Lett. 16, 221-223 (2004).
[CrossRef]

Mann, R. W.

W. A. Hodge, R. S. Fuan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann, “Contact pressures in the human hip joint measured in vivo,” Proc. Natl. Acad. Sci. USA 83, 2789-2883 (1986).
[CrossRef]

Measures, R. M.

Nelson, D.

E. Udd, D. Nelson, and C. Lawrence, “Three axis strain and temperature fiber optic grating sensor,” Proc. SPIE 2718, 104-109 (1996).
[CrossRef]

Niemczyk, P.

P. Niemczyk, K. Cummings, A. Sarvazyan, E. Bancila, W. Ward, and R. Weiss, “Correlation of mechanical imaging and histopathology of radical prostatectomy specimens: a pilot study for detecting prostate cancer,” J. Urol. (Baltimore) 160, 797-801 (1998).
[CrossRef]

Noqueira, R. N.

I. Abe, O. Frazao, M. W. Schiller, R. N. Noqueira, H. J. Kalinowski, and J. L. Pinto, “Bragg gratings in normal and reduced diameter high birefringence fibre optics,” Meas. Sci. Technol. 17, 1477-1484 (2006).
[CrossRef]

Ohn, M. M.

Okamoto, K.

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. 17, 2123-2129 (1981).
[CrossRef]

Okazaki, M.

K. Yokoyama, M. Okazaki, and T. Komito, “Effect of contact pressure and thermal degradation on the sealibility of O-ring,” JSAE Rev. 19, 123-128 (1998).
[CrossRef]

Pal, B. P.

B. P. Pal, Fundamentals of Fibre Optics in Telecommunication and Sensor Systems (New Age International, 1992).

Payne, D.

A. J. Barlow and D. Payne, “The stress-optic effect in optical fibers,” IEEE J. Quantum Electron. 19, 834-839 (1983).
[CrossRef]

Pinto, J. L.

I. Abe, O. Frazao, M. W. Schiller, R. N. Noqueira, H. J. Kalinowski, and J. L. Pinto, “Bragg gratings in normal and reduced diameter high birefringence fibre optics,” Meas. Sci. Technol. 17, 1477-1484 (2006).
[CrossRef]

Prasad, N. S.

M. M. Krishna, M. S. Shunmugam, and N. S. Prasad, “A study on the sealing performance of bolted flange joints with gaskets using finite element analysis,” Int. J. Pressure Vessels Piping 84, 349-357 (2007).
[CrossRef]

Roberts, J. R.

E. R. Komi, J. R. Roberts, and S. J. Rothberg, “Measurement and analysis of grip force during a golf shot,” Proc. Inst. Mech. Eng. Part P J. Sports Eng. Technol. 222, 23-35 (2008).

Rothberg, S. J.

E. R. Komi, J. R. Roberts, and S. J. Rothberg, “Measurement and analysis of grip force during a golf shot,” Proc. Inst. Mech. Eng. Part P J. Sports Eng. Technol. 222, 23-35 (2008).

Sarvazyan, A.

P. Niemczyk, K. Cummings, A. Sarvazyan, E. Bancila, W. Ward, and R. Weiss, “Correlation of mechanical imaging and histopathology of radical prostatectomy specimens: a pilot study for detecting prostate cancer,” J. Urol. (Baltimore) 160, 797-801 (1998).
[CrossRef]

Schiller, M. W.

I. Abe, O. Frazao, M. W. Schiller, R. N. Noqueira, H. J. Kalinowski, and J. L. Pinto, “Bragg gratings in normal and reduced diameter high birefringence fibre optics,” Meas. Sci. Technol. 17, 1477-1484 (2006).
[CrossRef]

Seedhom, B. B.

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M. M. Krishna, M. S. Shunmugam, and N. S. Prasad, “A study on the sealing performance of bolted flange joints with gaskets using finite element analysis,” Int. J. Pressure Vessels Piping 84, 349-357 (2007).
[CrossRef]

Staines, S. E.

E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
[CrossRef]

C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatum, “A polarization-maintaining fibre Bragg grating interrogation system for multi-axis strain sensing,” Meas. Sci. Technol. 13, 1446-1449 (2002).
[CrossRef]

Tatam, R. P.

E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
[CrossRef]

Tatum, R. P.

C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatum, “A polarization-maintaining fibre Bragg grating interrogation system for multi-axis strain sensing,” Meas. Sci. Technol. 13, 1446-1449 (2002).
[CrossRef]

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P. Niemczyk, K. Cummings, A. Sarvazyan, E. Bancila, W. Ward, and R. Weiss, “Correlation of mechanical imaging and histopathology of radical prostatectomy specimens: a pilot study for detecting prostate cancer,” J. Urol. (Baltimore) 160, 797-801 (1998).
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P. Wierzba and B. B. Kosmowski, “Application of polarisation-maintaining side-hole fibres to direct force measurement,” Opto-Electron. Rev. 11, 305-312 (2003).

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J. Z. Wu, W. Herzog, and M. Epstein, “Effects of inserting a Pressensor film into articular joints on the actual contact mechanics,” J. Biomech. Eng. 120, 655-659 (1998).
[CrossRef]

Xu, L.

G. Chen, L. Liu, H. Jia, J. Yu, L. Xu, and W. Wang, “Simultaneous strain and temperature measurements with fiber Bragg grating written in novel Hi-Bi optical fiber,” IEEE Photonics Technol. Lett. 16, 221-223 (2004).
[CrossRef]

Ye, C.-C.

E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
[CrossRef]

C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatum, “A polarization-maintaining fibre Bragg grating interrogation system for multi-axis strain sensing,” Meas. Sci. Technol. 13, 1446-1449 (2002).
[CrossRef]

Yokoyama, K.

K. Yokoyama, M. Okazaki, and T. Komito, “Effect of contact pressure and thermal degradation on the sealibility of O-ring,” JSAE Rev. 19, 123-128 (1998).
[CrossRef]

Yu, J.

G. Chen, L. Liu, H. Jia, J. Yu, L. Xu, and W. Wang, “Simultaneous strain and temperature measurements with fiber Bragg grating written in novel Hi-Bi optical fiber,” IEEE Photonics Technol. Lett. 16, 221-223 (2004).
[CrossRef]

Zhonkui, L.

F. Bingjun, S. Wang, and L. Zhonkui, Frontiers of Rock Mechanics and Sustainable Development in the 21st Century (Swets and Zeitlinger, 2001).

Appl. Opt.

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[CrossRef]

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G. Chen, L. Liu, H. Jia, J. Yu, L. Xu, and W. Wang, “Simultaneous strain and temperature measurements with fiber Bragg grating written in novel Hi-Bi optical fiber,” IEEE Photonics Technol. Lett. 16, 221-223 (2004).
[CrossRef]

Int. J. Pressure Vessels Piping

M. M. Krishna, M. S. Shunmugam, and N. S. Prasad, “A study on the sealing performance of bolted flange joints with gaskets using finite element analysis,” Int. J. Pressure Vessels Piping 84, 349-357 (2007).
[CrossRef]

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[CrossRef]

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S.-K. Han, S. Federico, M. Epstein, and W. Herzog, “An articular cartilage contact model based on real surface geometry,” J. Biomech. 38, 179-184 (2005).
[CrossRef]

J. Biomech. Eng.

J. Z. Wu, W. Herzog, and M. Epstein, “Effects of inserting a Pressensor film into articular joints on the actual contact mechanics,” J. Biomech. Eng. 120, 655-659 (1998).
[CrossRef]

J. Urol. (Baltimore)

P. Niemczyk, K. Cummings, A. Sarvazyan, E. Bancila, W. Ward, and R. Weiss, “Correlation of mechanical imaging and histopathology of radical prostatectomy specimens: a pilot study for detecting prostate cancer,” J. Urol. (Baltimore) 160, 797-801 (1998).
[CrossRef]

JSAE Rev.

K. Yokoyama, M. Okazaki, and T. Komito, “Effect of contact pressure and thermal degradation on the sealibility of O-ring,” JSAE Rev. 19, 123-128 (1998).
[CrossRef]

Meas. Sci. Technol.

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[CrossRef]

C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatum, “A polarization-maintaining fibre Bragg grating interrogation system for multi-axis strain sensing,” Meas. Sci. Technol. 13, 1446-1449 (2002).
[CrossRef]

Opt. Lett.

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P. Wierzba and B. B. Kosmowski, “Application of polarisation-maintaining side-hole fibres to direct force measurement,” Opto-Electron. Rev. 11, 305-312 (2003).

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[CrossRef]

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[CrossRef]

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M. K. Barker and B. B. Seedhom, “The relationship of the compressive modulus of articular cartilage: does cartilage optimize its modulus so as to minimize the strains arising in it due to the prevalent loading regime?” Rheumatology 40, 274-284 (2001).
[CrossRef] [PubMed]

Smart Mater. Struct.

E. Chehura, C.-C. Ye, S. E. Staines, S. W. James, and R. P. Tatam, “Characterization of the response of fiber Bragg gratings fabricated in stress and geometrically induced high birefringence fibers to temperature and transverse load,” Smart Mater. Struct. 13, 888-895 (2004).
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Figures (11)

Fig. 1
Fig. 1

Schematic showing uniform pressure P, distributed over the contact length a, or contact angle 2 θ , of the optical fiber (disk of radius R). Coordinate axes are also shown. The arbitrary radius r originates from disk center O. Square elements labeled A and B show principal stress directions along O y and O x axes, respectively.

Fig. 2
Fig. 2

Schematic showing geometry of contact between optical fiber (body 1) and conforming material (body 2). Applied force F is expressed per unit of fiber length supporting the contact load and can be located anywhere along the line of action shown. Contact angle θ is the half-angle of contact as measured from the vertical axis of symmetry. Body 1 (body 2) has Young’s modulus E 1 ( E 2 ) and Poisson ratio v 1 ( ν 2 ) .

Fig. 3
Fig. 3

Schematic showing relevant features of transverse loading apparatus. Transverse loads are created by manually compressing a calibrated spring. Load is then transmitted through the load cell, to the top gauge block, through the fibers, and then to the bottom block. Both gauge blocks are constrained to allow only vertical motion by guide blocks. Optical fibers are shown between steel gauge blocks. Bow Tie fiber fast and slow axes are also shown.

Fig. 4
Fig. 4

(a) Contact model predicted values of the contact angle θ between the fiber and the conforming body, for various values of the conforming body Young’s modulus, versus applied transverse load F. Numeric values shown near curves represent the Young’s modulus specific to that curve. To preserve clarity, modulus values for 6 MPa (dotted), 8 MPa (dashed) and 10 MPa (dotted–dashed) are not shown. (b) Model predicted variation of maximum contact angle θ MAX , at 3 N / mm , versus Young’s modulus of conforming body over the range of values found in cartilage.

Fig. 5
Fig. 5

Principal stresses along the O y axis of the fiber. Each curve corresponds to a different contact angle (Young’s modulus of body 2). The outside radius of the fiber core is also noted. An asterisk (*) indicates that stress magnitudes are normalized to the stresses found for the case of E = 20 MPa .

Fig. 6
Fig. 6

Principal stresses along the O x axis of the fiber. Each curve corresponds to a different contact angle (Young’s modulus of body 2). An asterisk (*) indicates that stress magnitudes are normalized to the stresses found for the case of E = 20 MPa .

Fig. 7
Fig. 7

Example wavelength shift versus transverse load data obtained from protocol 1. Data are shown for transverse loading of both the fast axis (F) and the slow axis (S). Horizontal error bars ( ± 0.0185 N / mm ) are not clearly visible at this scale but are based on published nonrepeatability of load cell. Vertical error bars ( ± 0.005 mm ), also not shown, correspond to published reproducibility of optical spectrum analyzer.

Fig. 8
Fig. 8

Typical Bragg wavelength shift versus load data measured for the slow axis in protocol 2. Lines A and B through data points were obtained through linear-regression calculations. Q * was estimated by calculating the intersection of lines A and B, which have differing slopes due to the elastomer–steel contact described previously.

Fig. 9
Fig. 9

(a) Wavelength shift for increasing absolute load data obtained from protocol 2, trial 2. The load was applied along the fast axis of the fiber. Horizontal error bars ( ± 0.45 N ) were not clearly visible at the given scale and are not shown. (b) Typical wavelength shift for increasing transverse load, expressed per unit of fiber length. “Slow” and “fast” indicate that data correspond to either the slow axis or fast axis Bragg wavelength, respectively.

Fig. 10
Fig. 10

(a) Close-up view (scaled for clarity) showing optical fiber compressed between conforming elastomer and gauge block. Fiber fast and slow axes are noted. D is the distance between points of elastomer contact on the gauge block. (b) Close-up view showing fiber compressed between two layers of conforming elastomer.

Fig. 11
Fig. 11

(a) Wavelength shift for increasing absolute load data obtained from protocol 3, trial 1. The load was applied along the fast axis of the fiber. (b) Wavelength shift for increasing transverse load, expressed per unit of fiber length. (c) Spectral separation calculated from fast and slow axis data. The dashed line represents the linear regression fit for plotted data. “Slow” and “fast” indicate that data correspond to either the slow axis or the fast axis Bragg wavelength, respectively.

Tables (3)

Tables Icon

Table 1 Normalized Principal Stress Magnitudes for Lowest ( 0.5 MPa ) and Highest ( 20 MPa ) Body 2 Modulus

Tables Icon

Table 2 Linear-Regression-Calculated Sensitivities, from Bragg Wavelength versus Load Data for Protocol 1 and for Load Applied along Both the Fast and the Slow Axes a

Tables Icon

Table 3 Linear-Regression-Calculated Sensitivities, Based on Spectral Separation, from Bragg Wavelength versus Load Data for Protocols 2 and 3

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

λ B = 2 Λ n 0 ,
B = n x n y = ( n x o n y o ) + C ( σ x σ y ) ,
λ f = 2 n f Λ , λ s = 2 n s Λ ,
B = 2 k o n o 3 ( p 11 p 12 ) ( 1 + ν ) F π r E ,
σ x = 2 P π [ ( 1 r 2 / R 2 ) sin 2 θ ( 1 2 r 2 / R 2 cos 2 θ + r 4 / R 4 ) ( tan 1 1 + r 2 / R 2 1 r 2 / R 2 ) tan θ ] , σ y = 2 P π [ ( 1 r 2 / R 2 ) sin 2 θ ( 1 2 r 2 / R 2 cos 2 θ + r 4 / R 4 ) + ( tan 1 1 + r 2 / R 2 1 r 2 / R 2 ) tan θ ] ,
σ y = 2 P π [ ( 1 r 2 / R 2 ) sin 2 θ ( 1 + 2 r 2 / R 2 cos 2 θ + r 4 / R 4 ) + ( tan 1 1 r 2 / R 2 1 + r 2 / R 2 ) tan θ ] , σ x = 2 P π [ ( 1 r 2 / R 2 ) sin 2 θ ( 1 + 2 r 2 / R 2 cos 2 θ + r 4 / R 4 ) ( tan 1 1 r 2 / R 2 1 + r 2 / R 2 ) tan θ ] .
O y : σ x = 2 P θ π , σ y = 2 P θ π [ 1 4 ( 1 r 2 / R 2 ) 2 ] ; O x : σ y = 2 P θ π [ 1 4 ( 1 + r 2 / R 2 ) 2 ] , σ x = 2 P θ π [ 1 4 r 2 / R 2 ( 1 + r 2 / R 2 ) 2 ] .
E 1 * Δ R F = ( α 1 ) ( log [ b 2 + 1 ] + 2 b 4 ) + 2 π ( 1 + α ) ( b 2 + 1 ) b 2 4 β π ( 1 + α ) .
b = tan ( θ / 2 ) .
η = E 1 * / E 2 * , ς = ( 1 ν 1 * ) η ( 1 ν 2 * ) ,
α = 1 η 1 + η , β = 1 2 ς 1 + η .
F = ( Q i Q * ) D w l + Q * l ,

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