Semi-implicit integration algorithm for non-coaxial model based on vertex theory and its application

A semi-implicit integration algorithm is presented for the non-coaxial model based on the yield vertex theory. In the stress updating considering the non-coaxial terms, the plastic flow direction is expressed explicitly. The Gram-Schmidt orthogonalization process aiming to formulate the non-coaxial flow is conducted under the given stress condition. According to the orthogonality among tensors, the stress updating equation is further simplified, and the Newton-Raphson iteration is established based on the simplified equation. With this algorithm programmed into the user subroutines, Vumat, the constitutive model is implemented into the finite element analysis based on ABAQUS. Through the explicit procedure, the simple shear tests and trapdoor problems are simulated with different non-coaxial model parameters. The results are compared to those of the coaxial model. The calculated results show that the proposed algorithm is converged and robust, and is be suitable for the numerical analysis.