INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2006; 68:836–860 Published online 27 April 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1726 On the numerical treatment of initial strains in biological soft tissues E. Peña, M. A. Martinez, B. Calvo and M. Doblaré ∗, † Group of Structural Mechanics and Materials Modeling, Aragón Institute of Engineering Research, University of Zaragoza, María de Luna, 3. E-50018 Zaragoza, Spain SUMMARY In this paper, different methodologies to enforce initial stresses or strains in finite strain problems are compared. Since our main interest relies on the simulation of living tissues, an orthotropic hyperelastic constitutive model has been used to describe their passive material behaviour. Different methods are presented and discussed. Firstly, the initial strain distribution is obtained after deformation from a previously assumed to be known stress-free state using an appropriate finite element approach. This approach usually involves important mesh distortions. The second method consists on imposing the initial strain field from the definition of an initial incompatible ‘deformation gradient’ field obtained from experimental data. This incompatible tensor field can be imposed in two ways, depending on the origin of the experimental tests. In some cases as ligaments, the experiment is carried out from the stress-free configuration, while in blood vessels the starting point is usually the load-free configuration with residual stresses. So the strain energy function would remain the same for the whole simulation or redefined from the new origin of the experiment. Some validation and realistic examples are pre- sented to show the performance of the strategies and to quantify the errors appearing in each of them. Copyright  2006 John Wiley & Sons, Ltd. KEY WORDS: finite element method; initial strains; orthotropic hyperelastic material; human ligaments; fibred materials 1. INTRODUCTION Biological soft tissues are usually exposed to a complex distribution of ‘in vivo’ initial strains. This state is a consequence of the continuous growth, remodelling, damage and viscoplastic strains that suffer these living materials along their whole life. Usually, the distinction between residual and initial strains or stresses refers to their origin. In the context of living tissues, ∗ Correspondence to: Manuel Doblaré, Mechanical Engineering Department, University of Zaragoza, Agustin de Betancourt Building, María de Luna, s/n. E-50018 Zaragoza, Spain. † E-mail: mdoblare@unizar.es Contract/grant sponsor: CICYT; contract/grant numbers: DPI2003-09110-C02-01, DPI2004-07410-C03-01 Received 21 November 2005 Copyright  2006 John Wiley & Sons, Ltd. Accepted 20 February 2006