A novel iterative method based on fixed stress rates for hydromechanical problems with nonlinear constitutive relationships

Abstract This paper focuses on the development of alternative coupling strategies for hydromechanical applications considering highly nonlinear constitutive models to represent the behavior of porous media. We present a novel consistent iterative coupling formulation based on fixed stress rates to define the coupling terms between mass balance and equilibrium equations. We show that controlling stress rates allows the application of an adaptive iterative coupling scheme with single or multi-rate solutions. The proposed methodology has been implemented in a framework that manages sequential simulations, exchanges of information between models, and checks the convergence of the iterative process. We present several numerical tests in which we evaluate the stability, accuracy, and performance of the proposed coupling technique. From the results, we confirm that the rate form of the fixed stress split guarantees solution stability and yields results as accurate as those obtained through fully implicit solutions, even for highly nonlinear constitutive behavior.

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