2024 Volume 80 Issue 13 Article ID: 23-13129
Complex calculations are often required to accurately predict the complex behavior of geomaterials. It is difficult to evaluate consistent tangent moduli analytically, so that the numerical differentiation, in which the gradient is calculated from the change in stress when a small deformation perturbation is applied, is generally used to evaluate. However, the method using numerical differentiation requires multiple stress calculations, which is large computational cost. In this paper, we formulate the consistent tangent moduli using the Jacobi matrix of the return mapping equation used in the stress integration of elasto-plastic constitutive laws, and compare the calculation speed with that of numerical differentiation. As a result, it was found that the computation time using the analytically derived consistent tangent moduli was 1/5 of that using the numerical differentiation, and the computation speed was greatly improved.
