An anisotropic elastoplastic constitutive model for large strain analysis of ®ber reinforced composite materials E. Car * , S. Oller, E. O~ nate E.T.S. Ingenieros de Caminos, Canales y Puertos, Universidad Polit ecnica de Catalunya, M odulo C1 Campus Norte, 08034 Barcelona, Spain Accepted 26 March 1999 Abstract In this work a generalized anisotropic elastoplastic constitutive model for the large strain analysis of ®ber-reinforced composite materials in the frame of the mixing theory and the ®nite element method is presented. The isotropic equivalent formulation proposed assumes the existence of a ®ctitious isotropic space where a mapped ®ctitious problem is solved. Both real anisotropic and ®ctitious spaces are related by means of linear fourth-order transformation tensors that contain the complete information about the real an- isotropic material. Details of the numerical implementation of the model into a non-linear or large strain ®nite element solution scheme are provided. Application examples showing the performance of the model for analysis of ®ber reinforced composite materials are given. Ó 2000 Elsevier Science S.A. All rights reserved. 1. Introduction The use of composite materials in structures has signi®cantly increased during the past few years. This trend is mainly due to the fact that composite materials have properties which are very dierent from conventional isotropic engineering materials. Composite materials present high strength to weight and high stiness to weight ratio, are corrosion resistant, thermally stable and are well suited for structures in which weight is a fundamental variable in the design process. Structural components requiring high stiness and strength, impact resistance, complex shape and high volume production are suitable candidates to be manufactured using composite materials. This explains why aerospace, automotive and marine industries have taken advantage of the special characteristics of these materials [1,30]. Components manufactured with composite materials are tough and durable, exceeding in many occasions the performance of metal parts. In the redesign process of a structural component using composite materials, simple replacement of the component is not enough. Due to the special characteristics of these materials (high anisotropy and high strength ratio between matrix and ®bers) the redesign of the component is necessary. Furthermore, ana- lytical techniques for components manufactured with composite materials are entirely dierent from conventional methods of analysis used for isotropic materials and require specialist knowledge. The design process of components made up of composite materials is nowadays mostly based on empirical methods. The absence of numerical simulation tools for the non-linear analysis of the behavior of composite ma- terials is observed in the literature. www.elsevier.com/locate/cma Comput. Methods Appl. Mech. Engrg. 185 (2000) 245±277 * Corresponding author. E-mail address: car@cimne.upc.es (E. Car). 0045-7825/00/$ - see front matter Ó 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 4 5 - 7 8 2 5 ( 9 9 ) 0 0 2 6 2 - 5