INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2007; 69:1239–1261 Published online 31 July 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1807 Computational method of inverse elastostatics for anisotropic hyperelastic solids Jia Lu 1, ∗, † , Xianlian Zhou 1, ‡ and Madhavan L. Raghavan 2, § 1 Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, The University of Iowa, Iowa City, IA 52242-1527, U.S.A. 2 Department of Biomedical Engineering, The University of Iowa, Iowa City, IA 52242, U.S.A. SUMMARY 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. Copyright 2006 John Wiley & Sons, Ltd. Received 23 December 2005; Revised 22 May 2006; Accepted 23 May 2006 KEY WORDS: inverse elastostatics; finite element method; anisotropic solids; tissue mechanics; aneurysm stress analysis 1. INTRODUCTION In the analysis of finitely deforming elastic bodies, there is a class of problem in which the deformed geometry and the applied load are known while the initial geometry or the stress in ∗ Correspondence to: Jia Lu, Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, The University of Iowa, Iowa City, IA 52242-1527, U.S.A. † E-mail: jia-lu@uiowa.edu ‡ E-mail: xianzhou@engineering.uiowa.edu § E-mail: raghavan@engineering.uiowa.edu Contract/grant sponsor: National Science Foundation; contract/grant number: CMS 03-48194 Copyright 2006 John Wiley & Sons, Ltd.