Computational method of inverse elastostatics for anisotropic hyperelastic solids

Jia Lu, Xianlian Zhou, Madhavan L. Raghavan

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


The paper presents a computational method for predicting the initial geometry of a finitely deforming anisotropic elastic body from a given deformed state. The method is imperative for a class of problem in stress analysis, particularly in biomechanical applications. While the basic idea has been established elsewhere Comput. Methods Appl. Mech. Eng. 1996; 136:47-57; Int. J. Numer. Meth. Engng 1998; 43: 821-838), the implementation in general anisotropic solids is not a trivial exercise, but comes after a systematic development of Eulerian representations of constitutive equations. In this paper, we discuss the general representation in the context of fibrous hyperelastic solids, and provide explicit stress functions for some commonly used soft tissue models including the Fung model and the Holzapfel model. A three-field mixed formulation is introduced to enforce quasi-incompressibility constraints. The practical utility of this method is demonstrated using an example of aneurysm stress analysis.

Original languageEnglish (US)
Pages (from-to)1239-1261
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
StatePublished - Feb 5 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • Aneurysm stress analysis
  • Anisotropic solids
  • Finite element method
  • Inverse elastostatics
  • Tissue mechanics


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