Two new hybrid methods in integrating constitutive equations

• We present two innovative hybrid integrations using the Eulers and the exponential schemes.
• We develop the exponential map integrations to account for more sophisticated plasticity models.
• A thorough numerical investigation is used to examine the proposed strategies.
• The newly devised schemes are much more accurate and efficient than their rivals.

It is crucial that more powerful integrations be developed as the plasticity models become more sophisticated. Here, two new robust integrating tactics are suggested based on the Exponential map and Euler's algorithms. The integrations are developed for the Drucker–Prager plasticity with nonlinear mixed hardening. Moreover, two different types of exponential strategies are advanced for the plasticity to be compared to the proposed techniques. Dealing with the apex of the yield surface is generally discussed for the integrations as well. Eventually, the proposed algorithms are thoroughly examined in a broad set of numerical tests comprising accuracy, efficiency, and convergence rate investigations. The results demonstrate the supremacy of the suggested schemes amid the six diverse techniques under discussion.