Definition of a general implicit orthotropic yield criterion

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 orthotropic 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 anisotropic 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.