Jacobian vs. disturbance method for UMATs in ABAQUS: An application to isotropic damage mechanics

Abstract

This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.