A novel accurate and computationally efficient integration approach to viscoplastic constitutive model

Abstract

A novel, accurate, and computationally efficient integration approach is developed to integrate small strain viscoplastic constitutive equations involving nonlinear coupled first-order ordinary differential equations. The developed integration scheme is achieved by a combination of the implicit backward Euler difference approximation and the implicit asymptotic integration. For the uniaxial loading case, the developed integration scheme produces accurate results irrespective of time steps. For the multiaxial loading case, the accuracy and computational efficiency of the developed integration scheme are better than those of either the implicit backward Euler difference approximation or the implicit asymptotic integration. The simplicity of the developed integration scheme is equivalent to that of the implicit backward Euler difference approximation since it also reduces the solution of integrated constitutive equations to the solution of a single nonlinear equation. The algorithm tangent constitutive matrix derived for the developed integration scheme is consistent with the integration algorithm and preserves the quadratic convergence of the Newton-Raphson method for global iterations.

Extended overstress model and its implicit stress integration algorithm: Formulations, experiments, and simulations

“…The unrealistic deformation only with the elastic deformation behavior is described by the existing overstress model in the impact loading, so that the existing overstress model is inapplicable to the description of the viscoplastic deformation behavior at high strain rate. Equation (21) with Equation ( 22) is extended so as to describe the viscoplastic deformation behavior adequately even at high strain rate by incorporating the term…”

“…15,16 In addition, the numerical methods for viscoplasticity models have been developed in past studies. [17][18][19][20][21] Here, the creep model is insufficient to describe the elastoplastic deformation behavior observed at the quasi-static loading process because it possesses the basically different structure from that of the elastoplasticity model based on the yield surface. In fact, the creep model predicts the viscoplastic deformation for any low stress level since it does not possess the threshold value of stress for the occurrence of viscoplastic deformation.…”

Application of efficient algorithm based on block Newton method to elastoplastic problems with nonlinear kinematic hardening

“…For the purpose of avoiding the increase of computational cost, the approaches to express the equations to be solved by a single scalar formulation have been established (De Angelis and Taylor, 2015; Wali et al ., 2015). These approaches have been extended to a non-associated anisotropic plasticity (Wali et al ., 2016; Bouhamed et al ., 2019) and a viscoplasticity (Kumar and Patel, 2021; De Angelis, 2022). Other approaches to reduce the computational cost of the return mapping algorithm include a state update algorithm (Nodargi and Bisegna, 2016; Nodargi, 2019) and a novel iterative scheme (Magisano and Corrado, 2023) have been proposed.…”

Continuum damage mechanics of cyclic viscoplasticity using asymptotic numerical method

“…Large trial stress state with good convergence for return mapping method was shown by a line search algorithm (Scherzinger, 2017). Combined integration schemes have also been attempted (Kumar and Patel, 2021) with relatively large time increments with limited loss of accuracy. The non-Newtonian methods reviewed here have not been applied for steam turbine or any particular industrial engineering application.…”