Definition of a general implicit orthotropic yield criterion Sergio Oller a, * , Eduardo Car a , Jacob Lubliner b a Departamento de Resistencia de Materiales y Estructuras en la Ingenier  ıa, Universidad Polit ecnica de Catalu~ na, Jordi Girona 1-3, M odulo C1 Campus Norte UPC, Barcelona 08034, Spain b Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, CA 94720, USA Received 20 September 2001; received in revised form 29 October 2002 Abstract The definition of an orthotropic yield criterion presents a serious challenge in the formulation of constitutive models based on such theories as elastoplasticity, viscoplasticity, damage, etc. The need to model the behavior of a real or- thotropic material requires the formulation of orthotropic yield criteria, and these may be difficult to obtain. For metals, orthotropic yield functions have been formulated by Hill [Proc. Roy. Soc. Lon. Ser. A 193 (1948) 281; J. Mech. Phys. Solids 38(3) (1990) 200], Barlat [Int. J. Plasticity 5 (1989) 51; 7 (1991) 693], Chu [NUMISHEET 93 (1993) 199] and Dutko et al. [Comput. Methods Appl. Mech. Engrg. 109 (1993) 73], but in many cases these functions do not describe the true behavior of the metal. The situation is worse when one attempts to represent a nonmetal such as a polymer, ceramic or composite. In this paper, we present a general definition of an explicit orthotropic yield criterion together with a general method for defining implicit orthotropic yield functions. The latter formulation is based on the transformed-tensor method, whose principal advantage lies in the possibility of adjusting an arbitrary isotropic yield criterion to the behavior of an an- isotropic material. As example we choose the adjustment to the Hill, Hoffman [J. Comp. Materials 1 (1967) 200] and Tsai–Wu [J. Comp. Materials 5 (1971) 58] criteria, but these particular cases serve to establish the methodology for achieving the desired function adjustment for any other well-known criterion or experimental set of data obtained from laboratory. Ó 2002 Elsevier Science B.V. All rights reserved. 1. Introduction The work presented in what follows has as its objective the establishment of a tool for formu- lating orthotropic yield functions from isotropic ones with the help of the experimental knowledge of the material and of the transformed-tensor method [3,4,21]. The advantage of this procedure is due to the fact that implicitly convex orthotropic functions are obtained from well-established isotropic ones, such as those of von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, etc. [14,15]. This working strategy * Corresponding author. E-mail addresses: sergio.oller@upc.es (S. Oller), car@cimne.upc.es (E. Car), lubliner@ce.berkeley.edu (J. Lubliner). 0045-7825/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0045-7825(02)00605-9 Comput. Methods Appl. Mech. Engrg. 192 (2003) 895–912 www.elsevier.com/locate/cma