This study examines a new approach to facilitate the convergence of upcoming user-subroutines UMAT when the secant material matrix is applied rather than the conventional tangent (also known as Jacobian) material matrix. This algorithm makes use of the viscous regularization technique to stabilize the numerical solution of softening material models. The Newton–Raphson algorithm predictor-corrector of ABAQUS then applies this type of viscous regularization to a UMAT using only the secant matrix. When the time step is smaller than the viscosity parameter, this type of regularization may be unsuitable for a predictor-corrector with the secant matrix because its implicit convergence is incorrect, transforming the algorithm into an undesirable explicit version that may cause convergence problems. A novel 3D orthotropic damage model with residual stresses is proposed for this study, and it is analyzed using a new algorithm. The method’s convergence is tested using the proposed implicit-to-explicit secant matrix as well as the traditional implicit and explicit secant matrices. Furthermore, all numerical models are compared to experimental data. It was concluded that both the new 3D orthotropic damage model and the new proposed time step algorithm were stable and robust.