Smoothed Classic Yield Function for C2 Continuities in Tensile Cutoff, Compressive Cap, and Deviatoric Sections

In elastoplastic analyses, a yield function needs convexities and C1 continuities, to meet the requirement of return mapping algorithms. However, many classic criteria in geotechnical engineering have shortages: either numerical issues (nonconvexity and gradient discontinuities) or insufficient physical properties (lack of tensile strength and compressive cap). To overcome these deficiencies, a smoothed classic (SC) yield function is proposed after combining the generalized classic yield function, a robust smoothing technique, and investigations on physical meanings. It can reflect general soil properties, including basic shear strength, tensile strength, compressive cap, and the impact of intermediate principal stress. The yield function is convex and C2 continuous; therefore, it avoids many numerical issues in describing general strength behavior. In addition, it can provide a close approximation to the Mohr–Coulomb criterion to avoid discontinuous gradients. Formulas for the gradient, the Hessian, and the calibration procedure are provided.