E EC C CH H HA A AN N NI IIC C CA A AL L L A A AN N NI IS

The constitutive models developed for the behavior simulation of simple isotropic materials are not suitable for the analysis of composite materials due to the strong anisotropy of these latters. There are different reasons and degrees of importance. The composite representation by a single orthotropic material having properties of the whole set has not been satisfactory either. Therefore, the mixing theory will also be presented in this chapter. There exist different formulations for anisotropic materials presenting a non-linear constitutive response (Hill (1971) 1 ), (Bassani (1977) 2 , (Barlat and Lian (1989) 3 , (Barlat et al. (1991) 4 ). These theories are based on threshold functions of discontinuity (yield functions) and anisotropic plastic potentials. Thus, new procedures must be developed to integrate the constitutive equation. The anisotropic formulation presented in this chapter is a generalization of any classic linear or non-linear isotropic formulation such as plasticity, viscoelasticity, damage, etc. This is based on the translation of all the material constitutive parameters, stress and strain states from a real anisotropic space to another fictitious isotropic space. Once they are there, an isotropic constitutive model is used along with other techniques and procedures for the isotropic constitutive equations. The anisotropic formulation presented in this chapter is the generalization of the general properties of the anisotropic formulation.