INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2007; 69:2036–2057 Published online 15 August 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1825 An uncoupled directional damage model for fibred biological soft tissues. Formulation and computational aspects B. Calvo, E. Pe˜ na, M. A. Martinez and M. Doblar´ e ∗, † Group of Structural Mechanics and Materials Modeling, Arag´ on Institute of Engineering Research, University of Zaragoza, Mar´ ıa de Luna, 3. E-50018 Zaragoza, Spain SUMMARY In this paper we present a fully three-dimensional finite-strain damage model for fibrous soft tissue. Continuum damage mechanics is used to describe the softening behaviour of soft tissues under large deformation. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. We considered the internal variables associated to damage to correspond to separated contributions of the matrix and fibres. In order to show clearly the performance of the constitutive model, we present 3D simulations of the behaviour of the human medial collateral ligament and of a coronary artery. Results show that the model is able to capture the typical stress–strain behaviour observed in fibrous soft tissues and seems to confirm the soundness of the proposed formulation. Copyright 2006 John Wiley & Sons, Ltd. Received 2 March 2006; Revised 1 June 2006; Accepted 2 June 2006 KEY WORDS: continuum damage; anisotropic hyperelastic material; fibred materials; soft tissues 1. INTRODUCTION Biological soft tissues are subjected to large deformations with negligible volume changes and show an anisotropic mechanical response due to their internal structure. The extra-cellular matrix is composed of a network of collagen fibrils and elastin fibres embedded in a viscous and isotropic ground substance. Their mechanical stiffness and ultimate tensile strength have been shown to depend on the length of collagen fibrils; longer fibrils permit a greater number of inter-fibrillar connections, resulting in a more efficient force transmission. Experimental evidence shows that tissues subjected to axial tensile stresses [1, 2] have a typical non-linear response, with an initial ∗ Correspondence to: M. Doblar´ e, Mechanical Engineering Department, University of Zaragoza, Agust´ ın de Betancourt Building, Mar´ ıa 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, FIS2005- 05020-C03-03 Copyright 2006 John Wiley & Sons, Ltd.