Three-dimensional Deformation and Stress Distribution of the Anterior Cruciate Ligament in the Knee (Constitutive Formulation and Finite Element Model of a Fiber-Reinforced Hyperelastic Material)

Shunji Hirokawa, Reiji Tsuruno

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Highly variable deformations of a human anterior cruciate ligament (ACL) cannot be adequately quantified by one-dimensional, localized measurements and/or analyses. This paper describes a new structurally-motivated phenomenological approach. Such assumption was made that the ACL ligament can be idealized as being composed of a homogeneous matrix in which two non-interacting families of densely distributed extensible fibers are embedded. A non-linear stress-strain characteristic exhibited by multiple collagen fibers was represented by the multi-linear curve. Then a constitutive equation for the ACL composite was formulated. Using the finite element method, finite deformation and stress distribution of the ACL as a function of knee flexion were introduced through simulation.

Original languageEnglish
Pages (from-to)2169-2177
Number of pages9
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume64
Issue number622
DOIs
Publication statusPublished - Jan 1 1998
Externally publishedYes

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Ligaments
Fiber reinforced materials
Stress concentration
Fibers
Constitutive equations
Collagen
Finite element method
Composite materials

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

Cite this

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AB - Highly variable deformations of a human anterior cruciate ligament (ACL) cannot be adequately quantified by one-dimensional, localized measurements and/or analyses. This paper describes a new structurally-motivated phenomenological approach. Such assumption was made that the ACL ligament can be idealized as being composed of a homogeneous matrix in which two non-interacting families of densely distributed extensible fibers are embedded. A non-linear stress-strain characteristic exhibited by multiple collagen fibers was represented by the multi-linear curve. Then a constitutive equation for the ACL composite was formulated. Using the finite element method, finite deformation and stress distribution of the ACL as a function of knee flexion were introduced through simulation.

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