New robust and efficient global iterations for large deformation finite element analysis of beams and shells with material nonlinearity

Magisano, Domenico; Corrado, Antonella

doi:10.1016/j.cma.2023.115900

Cited by 13 publications

(1 citation statement)

References 45 publications

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“…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. Another novel approach has been developed to provide better convergence efficiently by using a smoothing Newton method (Jin et al ., 2023).…”

Section: Introductionmentioning

confidence: 99%

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

Yamamoto,

Yamada,

Matsui

2024

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PurposeThe purpose of this study is to present the effectiveness and robustness of a numerical algorithm based on the block Newton method for the nonlinear kinematic hardening rules adopted in modeling ductile materials.Design/methodology/approachElastoplastic problems can be defined as a coupled problem of the equilibrium equation for the overall structure and the yield equations for the stress state at every material point. When applying the Newton method to the coupled residual equations, the displacement field and the internal variables, which represent the plastic deformation, are updated simultaneously.FindingsThe presented numerical scheme leads to an explicit form of the hardening behavior, which includes the evolution of the equivalent plastic strain and the back stress, with the internal variables. The features of the present approach allow the displacement field and the hardening behavior to be updated straightforwardly. Thus, the scheme does not have any local iterative calculations and enables us to simultaneously decrease the residuals in the coupled boundary value problems.Originality/valueA pseudo-stress for the local residual and an algebraically derived consistent tangent are applied to elastic-plastic boundary value problems with nonlinear kinematic hardening. The numerical procedure incorporating the block Newton method ensures a quadratic rate of asymptotic convergence of a computationally efficient solution scheme. The proposed algorithm provides an efficient and robust computation in the elastoplastic analysis of ductile materials. Numerical examples under elaborate loading conditions demonstrate the effectiveness and robustness of the numerical scheme implemented in the finite element analysis.

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