2005 Volume 45 Issue 4 Pages 61-77
An isotropic hardening elastoplastic model, named subloading tij, has been recently proposed (Nakai and Hinokio, 2004). Three features differentiate subloading tij model from the conventional ones : (a) the use of a modified stress space given by tensor tij; (b) the split of the plastic strain increments in two components and (c) the use of two yield surfaces based on the concept of subloading. These three characteristics greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam-clay model. However, the model formulation and implementation becomes a little more complex. In this paper the basic equations for the evolution of stresses and strains and for the evolution of the internal variables that control the size of the yield surfaces of the model are reformulated in such a way as to resemble those of any conventional elastoplastic model. This facilitates significantly the numerical integration (explicit or implicit) of the corresponding system of differential equations of the model. The present formulation also identifies the physical meaning of each concept and clearly shows where they intervene in the deduction of the elastoplastic constitutive tensors. The model is initially formulated without taking into account the plastic strain increment split, in order to emphasize the effect of adopting the subloading concept. Then the plastic split is considered using a different approach that allows writing the constitutive tensors in a simpler manner. The procedures proposed were successfully tested and all derivatives and algorithms necessary to implement the model are given in the appendices. The authors hope that these procedures make it easier for other researchers to implement and use the model as it is or to use the basic concepts in any other model.
