Constitutive modeling of the anterior cruciate ligament bundles and patellar tendon with full-field methods

Callan M. Luetkemeyer, Ulrich Scheven, Jonathan B. Estrada, Ellen M. Arruda

Research output: Contribution to journalArticlepeer-review


Anterior cruciate ligament (ACL) injury rates are rising, and there is little consensus about what puts someone at risk for an ACL injury. Finite element models provide an effective platform for systemically determining the effect of possible injury risk factors on ACL strain concentrations. However, the accuracy of a finite element model relies on the accuracy of the material models used in its construction. Standard material characterization methods require an assumption of both deformation and material homogeneity, but our recent work has demonstrated that structural features like the shape of the ligament–bone attachment (enthesis) and collagen fiber splay (material direction heterogeneity) create unavoidable deformation heterogeneity. Hence, in this study, full-volume, full-field, finite deformation methods were used to build material models for the ovine ACL bundles and patellar tendon. Specifically, displacement-encoded magnetic resonance imaging (MRI) was used to measure five full-volume deformation fields of each ligament (n=5 specimens of each) under tension, and the virtual fields method (VFM) was used to determine material model parameters with these data. This method accounts for strain heterogeneity, principal material direction heterogeneity (fiber splay), and enthesis shape. While most constitutive parameters were consistent among all specimen groups, parameters describing the degree of anisotropy, or collagen fiber alignment, showed statistically significant differences between groups. This work demonstrates that (when strain heterogeneity and structural properties are accounted for) ligament material properties are deterministic and ligament material microstructure is detectable with mesoscale measures of mechanical function.

Original languageEnglish (US)
Article number104577
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Nov 2021
Externally publishedYes


  • ACL
  • Anisotropy
  • Collagen alignment
  • Displacement-encoded MRI
  • Full-field
  • Ligament
  • Material properties
  • Mechanics
  • Microstructure
  • Virtual fields method

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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