Constitutive framework optimized for myocardium and other high-strain, laminar materials with one fiber family

John C. Criscione, Andrew D. McCulloch, William C. Hunter

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


Central to this analysis is the identification of six rotation invariant scalars α1-6 that succinctly define the strain in materials that have one family of parallel fibers arranged in laminae. These scalars were chosen so as to minimize covariance amongst the response terms in the hyperelastic limit, and they are termed strain attributes because it is necessary to distinguish them from strain invariants. The Cauchy stress t is expressed as the sum of six response terms, almost all of which are mutually orthogonal for finite strain (i.e. 14 of the 15 inner products vanish). For small deformations, the response terms are entirely orthogonal (i.e. all 15 inner products vanish). A response term is the product of a response function with its associated kinematic tensor. Each response function is a scalar partial derivative of the strain energy W with respect to a strain attribute. Applications for this theory presently include myocardium (heart muscle) which is often modeled as having muscle fibers arranged in sheets. Utility for experimental identification of strain energy functions is demonstrated by showing that common tests on incompressible materials can directly determine terms in W. Since the described set of strain attributes reduces the covariance amongst response terms, this approach may enhance the speed and precision of inverse finite element methods.

Original languageEnglish (US)
Pages (from-to)1681-1702
Number of pages22
JournalJournal of the Mechanics and Physics of Solids
Issue number8
StatePublished - Aug 2002

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


  • A. Finite strain
  • B. Anisotropic material
  • B. Constitutive behavior
  • B. Elastic material


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