A new staggered algorithm for thermomechanical coupled problems

This study presents a new staggered coupled strategy to deal with thermomechanical problems. The proposed strategy is based on the isothermal split methodology, i.e. the mechanical problem is solved at constant temperature and the thermal problem is solved for a fixed configuration. Nevertheless, the procedure for this strategy is divided into two phases within each increment: the prediction and the correction phases, while the interchange of information is performed on both. This allows taking advantage of automatic time-step control techniques, previously implemented for the mechanical problem, which is the main feature that distinguishes it from the classical strategies. The aim of the proposed strategy is to reduce the computational cost without compromising the accuracy of the results. The new coupling strategy is validated using three numerical examples, comparing its accuracy and performance with the ones obtained with the classical (commonly employed) strategies for solving thermomechanical problems. Moreover, the influence of the time-step size on the accuracy is analysed. The results indicate that the proposed strategy presents accuracy close to the one obtained with the implicit coupling algorithm, while the computational cost is only slightly higher than the one required by the explicit strategy. (C) 2017 Elsevier Ltd. All rights reserved.The authors gratefully acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT) under projects P2020-PTDC/EMS-TEC/0702/2014 (POCI-01-0145-FEDER-016779) and P2020-PTDC/EMS-TEC/6400/2014 (POCI-01-0145-FEDER-016876) by UE/FEDER through the program COMPETE 2020. The second author is also grateful to the FCT for the Postdoctoral grant SFRH/BPD/101334/2014.info:eu-repo/semantics/publishedVersio

Partitioned solution strategies for electro-thermo-mechanical problems applied to the field-assisted sintering technology

Dedicated to engineers and scientists in the field of coupled problems and computational ­mechanics, this thesis addresses partitioned solution strategies for electro-thermo-mechanically coupled problems applied to the field-assisted sintering technology (FAST). By simultaneously applying uniaxial pressure and an electric current to generate high heating rates, the FAST process offers short production cycles for sintering materials. To approach the process conditions at high temperatures in a realistic and holistic way radiative heat transfer is numerically treated as an additional field. Finally, a fully coupled four-field problem is composed where for the electric, thermal and mechanical fields the finite element method is applied while solving the radiation field using computational fluid dynamic (CFD) solvers. The numerical results are ­compared to experiments. Moreover, an in-depth study of coupling algorithms is carried out to improve the convergence of the partitioned solution...</p

Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains

AbstractThis paper introduces a fully implicit partitioned coupling scheme for problems of thermoelasticity at finite strains utilizing the p-version of the finite element method. The mechanical and the thermal fields are partitioned into symmetric subproblems where algorithmic decoupling has been obtained by means of an isothermal operator-split. Numerical relaxation methods have been implemented to accelerate the convergence of the algorithm. Such methods are well-known from coupled fluid–structure interaction problems leading to highly efficient algorithms. Having studied the influence of three different strategies: polynomial prediction methods, numerical relaxation with constant relaxation coefficients, its dynamic variant with a residual based relaxation coefficient and a variant of a reduced order model — quasi-Newton method, we present several numerical simulations of quasi-static problems investigating the performance of accelerated coupling schemes

Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains

This paper introduces a fully implicit partitioned coupling scheme for problems of thermoelasticity at finite strains utilizing the -version of the finite element method. The mechanical and the thermal fields are partitioned into symmetric subproblems where algorithmic decoupling has been obtained by means of an isothermal operator-split. Numerical relaxation methods have been implemented to accelerate the convergence of the algorithm. Such methods are well-known from coupled fluid-structure interaction problems leading to highly efficient algorithms. Having studied the influence of three different strategies: polynomial prediction methods, numerical relaxation with constant relaxation coefficients, its dynamic variant with a residual based relaxation coefficient and a variant of a reduced order model - quasi-Newton method, we present several numerical simulations of quasi-static problems investigating the performance of accelerated coupling schemes

Partitioned coupling strategies for multi-physically coupled radiative heat transfer problems

This article aims to propose new aspects concerning a partitioned solution strategy for multi-physically coupled fields including the physics of thermal radiation. Particularly, we focus on the partitioned treatment of electro-thermo-mechanical problems with an additional fourth thermal radiation field. One of the main goals is to take advantage of the flexibility of the partitioned approach to enable combinations of different simulation software and solvers. Within the frame of this article, we limit ourselves to the case of nonlinear thermoelasticity at finite strains, using temperature-dependent material parameters. For the thermal radiation field, diffuse radiating surfaces and gray participating media are assumed. Moreover, we present a robust and fast partitioned coupling strategy for the fourth field problem. Stability and efficiency of the implicit coupling algorithm are improved drawing on several methods to stabilize and to accelerate the convergence. To conclude and to review the effectiveness and the advantages of the additional thermal radiation field several numerical examples are considered to study the proposed algorithm. In particular we focus on an industrial application, namely the electro-thermo-mechanical modeling of the field-assisted sintering technology

Monolithic and partitioned coupling schemes for thermo-viscoplasticity

In this article we investigate a fully, thermo-mechanically coupled viscoplasticity model in view of various numerical aspects. First, we develop the entire system of differential-algebraic equations resulting from the spatially discretized principle of virtual displacements, the principle of virtual temperatures, and the evolution equations of the internal variables provided by the constitutive model. In the time-integration step this system is solved both using a fully monolithic approach based on a Backward-Euler scheme in combination with the Multilevel-Newton algorithm as well as a partitioned approach solving the fully coupled system. The latter is treated by means of a combination of a Backward-Euler method and an accelerated Gauss-Seidel/Multilevel-Newton scheme to solve the resulting system of algebraic equations within each time-integration step. Additionally, we consider a specific treatment of the interpolation between different meshes within the partitioned approach. This is shown for p-version finite elements based on hierarchical shape functions. Finally, it turns out that the specific constitutive model of small-strain thermo-viscoplasticity, which is based on the decomposition into kinematic hardening and energy storing strains, yields a problem-adapted stress algorithm. This allows to reduce the stress algorithm on Gauss-point level to the solution of one scalar equation. Numerical examples serve to elucidate the behavior and properties of the proposed methods

Fast Solvers for Unsteady Thermal Fluid Structure Interaction

We consider time-dependent thermal fluid structure interaction. The respective models are the compressible Navier–Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet–Neumann method and a fixed point iteration is employed. As a reference solver, a previously developed efficient time-adaptive higher-order time integration scheme is used. To improve on this, we work on reducing the number of fixed point coupling iterations. Using the idea of extrapolation based on data given from the time integration by deriving such methods for SDIRK2, it is possible to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic. This leads to schemes that can use less than two iterations per time step. Furthermore, widely used vector extrapolation methods for convergence acceleration of the fixed point iteration are tested, namely Aitken relaxation, minimal polynomial extrapolation and reduced rank extrapolation. These have no beneficial effects