A Hosford-Based Orthotropic Plasticity Model in LS-DYNA

n this contribution, we present a new orthotropic plasticity model available in LS-DYNA. Over the last decades, several orthotropic material models have been proposed in the literature where many of them have been implemented in LS-DYNA. Among these models, the model proposed by Barlat and Lian in 1989 [1], available in LS-DYNA in *MAT_036 [2], is a popular choice, especially in forming simulations. This model allows the user to define up to three R values (Lankford parameters) related to three material directions, namely 0°, 45° and 90° with respect to the rolling direction. Some years ago, the original orthotropic formulation by Barlat and Lian, available under *MAT_036 in LS-DYNA, was extended in such manner that the yield stress can depend on the different material directions. From a user point of view, this meant that up to five flow curves could be defined. Furthermore, up to five R values could also be used where these could be either constant or a function of the plastic strain. In *MAT_036, the extended model is activated by setting the flag HR to 7. However, the extended formulation incorporates the orthotropy in the yield stress as well. The consequence is that these two effects (orthotropy in the effective stress and also in the yield stress) concur against each other. For many materials, especially mild sheet steels, this aspect has often no major influence on the results. However, certain materials do exhibit quite dissimilar R values in the different material directions meanwhile the yield strength is very similar. This is, for instance, the case of many aluminum alloys. In such cases, the extended formulation available through HR=7 in *MAT_036 (or HOSF=0 in *MAT_036E) might lead to concave yield surfaces which, in turn, might lead to numerical instabilities. Therefore, a new option, issued through the flag HOSF, has been implemented in LS-DYNA in *MAT_036E. If HOSF is set to 1, a “Hosford-based” effective stress is used in yield function. This modification tends to alleviate the numerical instabilities observed in the model where the “Barlat-based” effective stress was used whenever the R values were very dissimilar. In a certain sense, the modification can be seen as a new plasticity model because in the new formulation the yield condition is not formulated using any information related to the R values but merely from the flow curves in the different directions. The R values are instead only used in the plastic flow rule. In this paper, we will show the advantages of such formulation as well as the results of the calibration of the material parameters for an aluminum sheet material. The results show that the simulation with the new material model can reproduce the strain fields captured in experiments through DIC very accurately.