scholarly journals On the convergence to equilibria of a sequence defined by an implicit scheme

2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Thierry Horsin ◽  
◽  
Mohamed Ali Jendoubi ◽  
◽  
Keyword(s):  
Implicit Scheme ◽  
Convergence To Equilibria

An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids

2021 ◽  
Vol 36 (3) ◽  
pp. 165-176
Author(s):  
Kirill Nikitin ◽  
Yuri Vassilevski ◽  
Ruslan Yanbarisov
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Fluid Flows ◽  
Numerical Results ◽  
Implicit Scheme ◽  
New Approach

Abstract This work presents a new approach to modelling of free surface non-Newtonian (viscoplastic or viscoelastic) fluid flows on dynamically adapted octree grids. The numerical model is based on the implicit formulation and the staggered location of governing variables. We verify our model by comparing simulations with experimental and numerical results known from the literature.

scholarly journals Fully Implicit Stress Update Algorithm for Distortion−Based Anisotropic Hardening with Cross−Loading Effect: Comparative Algorithmic Study and Application to Large−Size Forming Problem

2021 ◽  
Vol 11 (12) ◽  
pp. 5509
Author(s):  
Hongjin Choi ◽  
Seonghwan Choi ◽  
Soo-Chang Kang ◽  
Myoung-Gyu Lee
Keyword(s):  
Predictive Accuracy ◽  
Large Strain ◽  
Implicit Scheme ◽  
Loading Path ◽  
Plastic State ◽  
Loading Conditions ◽  
Integration Algorithm ◽  
Implicit Algorithm ◽  
Fully Implicit ◽  
Large Size

A fully implicit stress integration algorithm is developed for the distortional hardening model, namely the e−HAH model, capable of simulating cross−hardening/softening under orthogonal loading path changes. The implicit algorithm solves a complete set of residuals as nonlinear functions of stress, a microstructure deviator, and plastic state variables of the constitutive model, and provides a consistent tangent modulus. The number of residuals is set to be 20 or 14 for the continuum or shell elements, respectively. Comprehensive comparison programs are presented regarding the predictive accuracy and stability with different numerical algorithms, strain increments, material properties, and loading conditions. The flow stress and r−value evolutions under reverse/cross−loading conditions prove that the algorithm is robust and accurate, even with large strain increments. By contrast, the cutting−plane method and partially implicit Euler backward method, which are characterized by a reduced number of residuals, result in unstable responses under abrupt loading path changes. Finally, the algorithm is implemented into the finite element modeling of large−size, S−rail forming and the springback for two automotive steel sheets, which is often solved by a hybrid dynamic explicit–implicit scheme. The fully implicit algorithm performs well for the whole simulation with the solely static implicit scheme.

scholarly journals LayerPCM: An implicit scheme for dielectric screening from layered substrates

2021 ◽  
Vol 154 (22) ◽  
pp. 224114
Author(s):  
Jannis Krumland ◽  
Gabriel Gil ◽  
Stefano Corni ◽  
Caterina Cocchi
Keyword(s):  
Implicit Scheme ◽  
Dielectric Screening

An Implicit Scheme for Shallow Water Flow with Wet Dry Interface

2018 ◽  
Vol 45 (1) ◽  
pp. 61-68 ◽  
Author(s):  
Hriday Mani Kalita ◽  
Arup Kumar Sarma
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Implicit Scheme ◽  
Shallow Water Flow

scholarly journals A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

2021 ◽  
Author(s):  
Chennakesava Kadapa
Keyword(s):  
Wave Propagation ◽  
Wave Speed ◽  
Critical Time ◽  
Incompressible Material ◽  
Implicit Scheme ◽  
Bulk Wave ◽  
Lumped Mass ◽  
Time Step ◽  
Material Models ◽  
Shear Wave Speed

AbstractThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

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