A New Regression Model for the Prediction of the Stress–Strain Relations of Different Materials

Experimental flow stress–strain data under different stress states are often used to calibrate the plastic constitutive model of anisotropic metal materials or identify the appropriate model that is able to reproduce their plastic deformation behavior. Since the experimental stress–strain data are discrete, they need to be mathematically returned to a continuous function to be used to describe an equivalent hardening increment. However, the regression results obtained using existing regression models are not always accurate, especially for stress–strain curves under biaxial stress loading conditions. Therefore, a new regression model is proposed in this paper. The highest-order term in the recommended form of the new model is quadratic, so the functional relationships between stress–strain components can be organized into explicit expressions. All the experimental data of the uniform deformation stage can be substituted into the new model to reasonably reproduce the biaxial experimental stress–strain data. The regression results of experimental data show that the regression accuracy of the new model is greatly improved, and the residual square sum SSE of the regression curves of the new model reduced to less than 50% of the existing three models. The regression results of stress–strain curves show significant differences in describing the yield and plastic flow characteristics of anisotropic metal materials, indicating that accurate regression results are crucial for accurately describing the anisotropic yielding and plastic flow behaviors of anisotropic metal materials.