Consistent tangent moduli for multi-yield-surface J2 plasticity model

For problems involving rate constitutive equations, such as rate-independent elasto-plasticity, consistent or algorithmic tangent moduli (operators) play an important role in preserving the asymptotic quadratic rate of convergence of incremental-iterative solution schemes based on Newton's method. Furthermore, consistent (algorithmic) tangent moduli are required in structural response sensitivity analysis based on the direct differentiation method. This paper focuses on the derivation of the consistent tangent moduli for a pressure independent multi-yield-surface J(2) (Von Mises) plasticity model that has been used extensively in nonlinear constitutive modeling of soil materials, but can be used for other materials as well. Application examples are provided to validate the consistent tangent moduli derived herein, and to compare the rate of convergence and computational time of nonlinear incremental-iterative analyses performed using the consistent and continuum tangent moduli, respectively.