An extension of Hill's three-component model to include different fibre types in finite element modelling of muscle

B. Stojanovic, M. Kojic, M. Rosic, Chi Pong Tsui, Chak Yin Tang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

20 Citations (Scopus)


Most of the proposed versions of the Hill's model use a sliding-element theory, considering a single sarcomere. However, a muscle represents a collection of different fibre types with a large range in contractile properties among them. An extension of Hill's three-component model is proposed here to take into account different fibre types. We present a model consisting of a number of sarcomeras of different types coupled in parallel with the connective tissue. Each sarcomere is modelled by one non-linear elastic element connected in series with one non-linear contractile element. Using the finite element method, in an incremental-iterative scheme of calculating equilibrium configurations of a muscle, the key step is the determination of stresses corresponding to strain increments. The stress calculation procedure for the extended Hill's model is reduced to the solution of a number of independent non-linear equations with respect to the stretch increments of the serial elastic elements in each sarcomere. Since the distribution of the specific fibre type is non-uniform over the muscle volume, we have material heterogeneity which we modelled by using the so-called 'Generalized Isoparametric Element Formulation' for functionally graded materials (FGMs). The proposed computational scheme is built in our FE package PAK, so that muscles of complex three-dimensional shapes can be modelled. In numerical examples, we illustrate the main characteristics of the developed numerical model and some possibilities of realistic modelling of muscle functioning.
Original languageEnglish
Pages (from-to)801-817
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Issue number7
Publication statusPublished - 13 Aug 2007


  • Biceps muscle
  • Finite element method
  • Functionally graded materials
  • Hill's muscle model
  • Muscle modelling

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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