Mechanical response of an artery using a standard nonlinear solid

Alexander I. Veress, Peter M. Anderson, J. Fredrick Cornhill, James D. Thomas

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Introduction. The stress and deformation in an artery are determined from an axisymmetric analysis of thick-walled clyinder with a time-dpendent internal pressure. The purpose is to understand how different constitutive, loading, and geometric conditions affect the stress and deformation state within the artery. Materials and Methods. The equilibrium, compatibility, and constitutive equations are applied at N discretized points in the arterial wall, in an efficient scheme using Mathcad software on a desktop computer. The constitutive equations are a modification to a standard linear solid, so that one of the linear elements is nonlinear, and so that the 3-D response is anisotropic and dissipates energy only under deviatoric (shearing) stress states. Solution at each successive time increment requires inversion of a 6N by 6N matrix. Results. The model reproduces experimental stress relaxation data with a correlation coefficient of 0.985 and can reproduce quasi-static stress strain data with equal accuracy. Features such as conditioning of the tissue are understood in terms of the time-dependent properties of the tissue. Conclusion. The program can produce transient and steady-state responses that closely mimic tissue response. The analysis allows for quick and stable determination of the stress and strain states for a variety of loading conditions.

Original languageEnglish (US)
Pages (from-to)212-217
Number of pages6
JournalBiomedical Sciences Instrumentation
StatePublished - Dec 1 1997


  • Artery
  • Computer simulation
  • Mathematical model
  • Thick-walled cylinder
  • Viscoelasticity

ASJC Scopus subject areas

  • Hardware and Architecture


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