Identification of material parameters based on Mohr-Coulomb failure criterion for bisphosphonate treated canine vertebral cancellous bone

Xiang Wang, Matthew Allen, David Burr, Enrique J. Lavernia, Boris Jeremić, David P. Fyhrie

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Nanoindentation has been widely used to study bone tissue mechanical properties. The common method and equations for analyzing nanoindentation, developed by Oliver and Pharr, are based on the assumption that the material is linearly elastic. In the present study, we adjusted the constraint of linearly elastic behavior and use nonlinear finite element analysis to determine the change in cancellous bone material properties caused by bisphosphonate treatment, based on an isotropic form of the Mohr-Coulomb failure model. Thirty-three canine lumbar vertebrae were used in this study. The dogs were treated daily for 1 year with oral doses of alendronate, risedronate, or saline vehicle at doses consistent, on a mg/kg basis, to those used clinically for the treatment of post-menopausal osteoporosis. Two sets of elastic modulus and hardness values were calculated for each specimen using the Continuous Stiffness Measurement (CSM) method (ECSM and HCSM) from the loading segment and the Oliver-Pharr method (EO-P and HO-P) from the unloading segment, respectively. Young's modulus (EFE), cohesion (c), and friction angle (φ{symbol}) were identified using a finite element model for each nanoindentation. The bone material properties were compared among groups and between methods for property identification. Bisphosphonate treatment had a significant effect on several of the material parameters. In particular, Oliver-Pharr hardness was larger for both the risedronate- and alendronate-treated groups compared to vehicle and the Mohr-Coulomb cohesion was larger for the risedronate-treated compared to vehicle. This result suggests that bisphosphonate treatment increases the hardness and shear strength of bone tissue. Shear strength was linearly predicted by modulus and hardness measured by the Oliver-Pharr method (r2 = 0.99). These results show that bisphosphonate-induced changes in Mohr-Coulomb material properties, including tissue shear cohesive strength, can be accurately calculated from Oliver-Pharr measurements of Young's modulus and hardness.

Original languageEnglish
Pages (from-to)775-780
Number of pages6
JournalBone
Volume43
Issue number4
DOIs
StatePublished - Oct 2008

Fingerprint

Hardness
Diphosphonates
Canidae
Shear Strength
Elastic Modulus
Alendronate
Bone and Bones
Lumbar Vertebrae
Finite Element Analysis
Postmenopausal Osteoporosis
Friction
Cancellous Bone
Dogs
Risedronate Sodium

Keywords

  • Finite element method
  • Material parameter identification
  • Mohr-Coulomb failure criterion
  • Nanoindentation
  • Trabecular bone

ASJC Scopus subject areas

  • Physiology
  • Hematology
  • Endocrinology, Diabetes and Metabolism
  • Histology

Cite this

Identification of material parameters based on Mohr-Coulomb failure criterion for bisphosphonate treated canine vertebral cancellous bone. / Wang, Xiang; Allen, Matthew; Burr, David; Lavernia, Enrique J.; Jeremić, Boris; Fyhrie, David P.

In: Bone, Vol. 43, No. 4, 10.2008, p. 775-780.

Research output: Contribution to journalArticle

Wang, Xiang ; Allen, Matthew ; Burr, David ; Lavernia, Enrique J. ; Jeremić, Boris ; Fyhrie, David P. / Identification of material parameters based on Mohr-Coulomb failure criterion for bisphosphonate treated canine vertebral cancellous bone. In: Bone. 2008 ; Vol. 43, No. 4. pp. 775-780.
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AB - Nanoindentation has been widely used to study bone tissue mechanical properties. The common method and equations for analyzing nanoindentation, developed by Oliver and Pharr, are based on the assumption that the material is linearly elastic. In the present study, we adjusted the constraint of linearly elastic behavior and use nonlinear finite element analysis to determine the change in cancellous bone material properties caused by bisphosphonate treatment, based on an isotropic form of the Mohr-Coulomb failure model. Thirty-three canine lumbar vertebrae were used in this study. The dogs were treated daily for 1 year with oral doses of alendronate, risedronate, or saline vehicle at doses consistent, on a mg/kg basis, to those used clinically for the treatment of post-menopausal osteoporosis. Two sets of elastic modulus and hardness values were calculated for each specimen using the Continuous Stiffness Measurement (CSM) method (ECSM and HCSM) from the loading segment and the Oliver-Pharr method (EO-P and HO-P) from the unloading segment, respectively. Young's modulus (EFE), cohesion (c), and friction angle (φ{symbol}) were identified using a finite element model for each nanoindentation. The bone material properties were compared among groups and between methods for property identification. Bisphosphonate treatment had a significant effect on several of the material parameters. In particular, Oliver-Pharr hardness was larger for both the risedronate- and alendronate-treated groups compared to vehicle and the Mohr-Coulomb cohesion was larger for the risedronate-treated compared to vehicle. This result suggests that bisphosphonate treatment increases the hardness and shear strength of bone tissue. Shear strength was linearly predicted by modulus and hardness measured by the Oliver-Pharr method (r2 = 0.99). These results show that bisphosphonate-induced changes in Mohr-Coulomb material properties, including tissue shear cohesive strength, can be accurately calculated from Oliver-Pharr measurements of Young's modulus and hardness.

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