Analysis of rolling force energy for thick plates based on linear yield criterion with accurate description of velocity field

For addressing the challenge of integrating the nonlinear Mises specific plasticity power, this manuscript derives the formulation of the specific plastic power based on the Double Mean approximation criterion (DM criterion). This derivation establishes the necessary conditions for integrating the internal deformation power of a thick plate. Meanwhile, a sinusoidal velocity field that satisfies the kinematically admissible conditions is formulated, and the finite element method is employed to simulate the flow behavior of the deformed metal, thereby validating the reliability of the velocity field. Based on this, the internal deformation power is determined through energy analysis of the constructed velocity field using the DM criterion, Tresca criterion, and TSS criterion. The root vector decomposition method is utilized to derive the friction power and shear power, while various criteria are employed in obtaining the analytical solutions for the rolling force using the energy method. Comparison with the existing Sims model and experimental data demonstrates that the rolling force models in accordance with the DM criterion and Tresca criterion both have errors less than 15%, and their predictive accuracy surpasses that of the Sims model. However, the TSS criterion has a prediction error greater than 25% and performs poorly. Among them, the average relative error of the rolling force and rolling torque on the basis of the DM criterion is 7.15%, and the Tresca criterion can offset the high bias brought by the upper bound method, with an average relative error of only 3.64% for rolling force and rolling torque.