Return mapping with a line search method for integrating stress of the distortional hardening law with differential softening

• Stress-update algorithms are provided for the anisotropic hardening model. • Comparative study of the N–R and the line search methods is performed. • The numerical instability problem is solved using the newly reformulated algorithm. • The accuracy and the speed of convergence are evaluated. • Significant improvement in the accuracy and the convergent speed is attained. A stress-update algorithm for the recently proposed distortional...