On linear transformations of stress tensors for the description of plastic anisotropy

The derivation of anisotropic yield functions based on the approach of linear transformations of a stress tensor is investigated for general and plane stress states. The number of coefficients available for the description of plastic anisotropy is discussed. A few specific yield functions are given to illustrate the concept. Among these examples, a plane stress formulation is described in more detail, namely, Yld2000-2d [Barlat, F., Brem, J.C., Yoon, J.W., Dick, R.E., Choi, S.H., Chung, K., Lege, D.J., 2000. Constitutive modeling for aluminum sheet forming simulations. In: Khan, A.S, Zhang, H., Yuan, Y. (Eds.), Plastic and Viscoplastic Response of Materials and Metal Forming, Proceedings of the 8th International Symposium on Plasticity and its Current Applications, Whistler, Canada, July 2000. Neat Press, Fulton, MD, pp. 591–593; Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.-H., Chu, E., 2003. Plane stress yield function for aluminum alloy sheets – Part I: theory. Int. J. Plasticity 19, 1297–1319; Yoon, J.W., Barlat, F., Dick, R.E., 2000. Sheet metal forming simulation for aluminum alloy sheets. In: Sheet Metal Forming Simulation: Sing-Tang 65th Anniversary Volume, SAE paper 2000-01-0774, Society of Automotive Engineer, SAE, pp. 67–72]. It is shown that other recently published anisotropic yield functions are, in fact, Yld2000-2d presented in different forms.