A Modified Arrhenius‐Type Constitutive Model and its Implementation by Means of the Safe Version of Newton–Raphson Method

Arrhenius‐type constitutive models are widely used in thermomechanical processing due to their ease of parameter calibration and ability to track the deformation behavior with various materials. Herein, a modified Arrhenius model is proposed, and the model is implemented in the finite element (FE) simulation to improve the simulation accuracy. The VUMAT Fortran subroutine of the model is established for the commercial nonlinear FE software Abaqus/Explicit based on an implicit time integration scheme and the radial return mapping algorithms. A root‐finding method called the safe version of Newton–Raphson method is applied to calculate the plastic corrector term. The efficiency and accuracy of both analytical and numerical methods are evaluated for calculating the derivatives in this algorithm. The implementation of the user‐defined modified Arrhenius‐type material model is successfully applied to a thermal–mechanical coupling FE model for the hot rolling of heavy steel plate. The goal optimization function is used to calibrate the material parameters for the model. The plastic strain field and temperature field are in accordance with the theoretical derivation and experimental results. It provides valuable references for characterizing and optimizing thermomechanical processing.