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An Objective time integration scheme Using the Intermediate Configuration in Hyperelasto-Viscoplasticity with Dual Multiplicative Decompositions

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF MECHANICAL ENGINEERING 2025年第3期49卷 1413-1432页

作者： Toluei, Reza Kharazi, Mahsa Sahand Univ Technol Fac Mech Engn Sahand Newtown 513351996 Tabriz Iran

This paper presents a time integration algorithm for hyperelasto-viscoplasticity, formulated in the intermediate configuration and employing a tensor exponential function to ensure plastic incompressibility. For kinematic hardening, an additional intermediate configuration is introduced, following the multiplicative decomposition of the plastic deformation gradient, as established in the viscoplasticity literature. The proposed time integration scheme employs a system of four simultaneous equations to solve for fourteen unknowns, including both tensor- and scalar-valued variables. To reduce computational complexity, symmetric tensor valued variables are employed, thereby minimizing the number of unknowns. Additionally, a consistent tangent modulus tensor based on the intermediate configuration is derived. The efficiency of the framework is then demonstrated through two case studies: simple shear deformation and a finite element analysis. Material responses for the simple shear deformation, considering no hardening, isotropic hardening only, kinematic hardening only, and mixed hardening, are validated by comparison with results from the literature, demonstrating excellent agreement. Under all specified conditions, the modeling of the Bauschinger effect region aligns perfectly with the available results. Even under very large applied shear deformations (up to 10), no shear-stress oscillations are observed when only kinematic hardening is considered. In the finite element case studies, a cantilever beam under large rotation and bending forming processes is analyzed, with results highlighting the robustness and accuracy of the proposed numerical implementation.

关键词： Hyperelasto-viscoplasticity Multiplicative decomposition Intermediate configuration time integration scheme

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Numerical Analysis of an Efficient time integration scheme for Unsteady Conjugate Heat Transfer

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2024年第1期45卷 30-38页

作者： Feodoritova, O. B. Novikova, N. D. Zhukov, V. T. Russian Acad Sci Keldysh Inst Appl Math Moscow 125047 Russia

The computational results of a time integration method for thermal interaction between viscous gas flows and solid domains are presented. The methodology is based on simultaneous integration of the multicomponent gas dynamics equations and the thermal conductivity equation of a solid domain. For three-dimensional spatial discretization of the governing equations, multi-block unstructured grids with definition of grid functions at grid nodes are used. On each time step, the governing system is split into hyperbolic and parabolic subsystems. The numerical method provides an approximation of the fluid-solid interface condition (both normal heat flux and temperature are continuous across the interface). To analyze the accuracy and computational efficiency of the scheme, a model problem of high-speed laminar flow around a heated plate is considered. The numerical results demonstrate good agreement with analytical solution and confirm the effectiveness of the developed methodology.

关键词： conjugate heat transfer fluid-solid thermal interaction unsteady processes multicomponent aerothermodynamics flow time integration scheme

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An accurate time integration scheme for arbitrary rotation motion: application to metal forming simulation

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INTERNATIONAL JOURNAL OF MATERIAL FORMING 2016年第1期9卷 71-84页

作者： Kpodzo, Koffi Fourment, Lionel Lasne, Patrice Montmitonnet, Pierre Mines ParisTech CEMEF Ctr Mat Forming CNRS UMR 7635 CS 10 207 F-06904 Sophia Antipolis France Transvalor 694 Ave Maurice Donat Parc Haute Technol F-06250 Mougins France

Within the frame of implicit velocity based formulations with solid elements, usual time integration schemes often turn out unsatisfactory when the movement has large rotations, especially in metal forming applications such as ring rolling or cross-wedge rolling. These rotations generally require using a much higher order integration scheme with inherent difficulties in implementing such schemes. For pure rotation motions, it is possible to use a low order integration scheme by rewriting the motion equations in the cylindrical frame that is supported by the rotation axis. Accordingly, a first order scheme is sufficient to accurately integrate the movement but it is restricted to specific problems. In the more general case, it is possible to derive parts of the domain where rotations are predominant along with the governing rotation axis from the velocity field gradient. The motion equations are then rewritten in the resulting local cylindrical frame. Performances of this first order scheme are first evaluated and highlighted over simple analytical problems, before being applied to the finite element simulation of the torsion test, and then to more complex metal forming problems involving large rotations. The accuracy and efficiency of this scheme is so numerically demonstrated.

关键词： time integration scheme Large rotations Implicit formulation Velocity formulation Finite elements Metal forming Torsion test Cross-wedge rolling

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The role of time integration in energy conservation in Smoothed Particle Hydrodynamics fluid dynamics simulations

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EUROPEAN JOURNAL OF MECHANICS B-FLUIDS 2023年 97卷 78-92页

作者： Cercos-Pita, Jose Luis -Alonso, Pablo Eleazar Merino Calderon-Sanchez, Javier Duque, Daniel Uppsala Univ Surg Sci Dept Hedenstierna Lab S-75185 Uppsala Sweden Univ Politecn Madrid M2ASAI Res Grp ETS Ingn Navales Madrid 28040 Spain Univ Politecn Madrid CEHINAV Res Grp ETS Ingn Navales Madrid 28040 Spain

The choice of a time integration scheme is a crucial aspect of any transient fluid simulation, and Smoothed-Particle Hydrodynamics (SPH) is no exception. The influence of the time integration scheme on energy balance is here addressed. To do so, explicit expressions allowing to compute the deviations from the energy balance, induced by the time integration scheme, are provided. These expressions, computed a posteriori, are valid for different integration methods. Besides, a new formulation that improves energy conservation by enhancing stability, based on an implicit integration scheme, is proposed. Such formulation is tested with the simulation of a two-dimensional non-viscous impact of two jets, with no artificial dissipation terms. To the best of our knowledge, this is the first stable simulation of a non-dissipative system with a weakly-compressible SPH method. A viscous case, the Taylor-Green vortex, has also been simulated. Results show that an implicit time integration scheme also behaves better in a viscous context.(c) 2022 Elsevier Masson SAS. All rights reserved.

关键词： Stability time integration scheme Energy balance SPH

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Development of Numerical Methodology for Unsteady Fluid-Solid Thermal Interaction in Multicomponent Flow Simulation

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2023年第1期44卷 33-43页

作者： Feodoritova, O. B. Novikova, N. D. Zhukov, V. T. Russian Acad Sci Keldysh Inst Appl Math Moscow 125047 Russia

This paper presents the current state of development of 3D methodology for numerical simulation of unsteady thermal interaction of fluid flow and solid bodies. A fluid is a multicomponent mixture of ideal gases. As heat-conducting solid bodies one can consider aircraft elements, shells of combustion chamber, etc. For fluids, the extended system of the unsteady compressible Navier-Stokes equations supplemented by multicomponent diffusion equations is considered. For solids, unsteady heat conduction equation is written. For fluid-solid interfaces, temperature and normal heat flux are continuous across an interface. The developed technique exploits finite-volume discretization of the governing equations and time integration with splitting over physical processes. The time step calculation is split into hyperbolic and parabolic stages. The hyperbolic stage is implemented with the explicit scheme. The parabolic stage is based on the special explicit-iterative Chebyshev scheme. To simulate the fluid-solid thermal interaction within parabolic stage, the energy equation for both fluid and solid is solved as the unified equation. This provides an approximation of the interface continuity condition and coupling in interfacial heat exchange. The proposed method is generalized for multi-block unstructured grids with parallel calculation of the fluid/solid regions and subsequent processing of the fluid-solid interfaces. To demonstrate the features of our technique, the results of solving a test problem is shown and accuracy of the interface condition are discussed.

关键词： conjugate heat transfer fluid-solid thermal interaction transient processes multicomponent aerothermodynamics flow time integration scheme

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Evolutional behavior of viscoelastic materials: A formulation based on logarithmic approach

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MECHANICS RESEARCH COMMUNICATIONS 2024年 140卷

作者： Firouzi, Nasser Alzaidi, Ahmed S. M. Nezaminia, Hamid Bauhaus Univ Weimar Inst Struct Mech Weimar Germany Taif Univ Coll Sci Dept Math & Stat POB 11099 Taif 21944 Saudi Arabia Univ Kashan Fac Engn Dept Civil Engn Kashan Iran

In this paper, a new formulation for large deformation of visco-elastometic materials is derived. The formulation is based on logarithmic strain, and the internal variable is defined as the viscous part of the logarithmic strain. A derivation of thermodynamically consistent formulation for visco-elastomeric materials is provided. The evolution equation which is related to the deviatoric part of the strain for viscoelastic formulation is solved by the implicit trapezoidal integration rule which leads to a recursive relation.

关键词： Continuum mechanics Viscoelasticity Constitutive equations Evolution equations time integration scheme Computational mechanics

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ENERGY CONSERVING GALERKIN FINITE ELEMENT METHODS FOR THE MAXWELL-KLEIN-GORDON SYSTEM

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2020年第2期58卷 1339-1366页

作者： Ma, Chupeng Cao, Liqun Lin, Yanping Heidelberg Univ Inst Appl Math Neuenheimer Feld 205 D-69120 Heidelberg Germany Heidelberg Univ Interdisciplinary Ctr Sci Comp Neuenheimer Feld 205 D-69120 Heidelberg Germany Chinese Acad Sci Univ Chinese Acad Sci Inst Computat Math & Sci Engn Comp Acad Math & Syst SciLSECNCMIS Beijing 100190 Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we consider the Galerkin finite element methods for the Maxwell- Klein-Gordon system in the Coulomb gauge. We propose a semidiscrete finite element method for the system with the mixed finite element approximation of the vector potential. Energy conservation and error estimates are established for this scheme. A novel energy conserving time integration scheme is presented for solving the semidiscrete system. The existence and uniqueness of solutions to the fully discrete system are proved under some assumptions. Numerical experiments are carried out to support our theoretical analysis.

关键词： Maxwell-Klein-Gordon energy conservation finite element method time integration scheme error estimates

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Highly accurate family of time integration method

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STRUCTURAL ENGINEERING AND MECHANICS 2018年第6期67卷 603-616页

作者： Rezaiee-Pajand, Mohammad Esfehani, S. A. H. Karimi-Rad, Mahdi Ferdowsi Univ Mashhad Dept Civil Engn Mashhad Iran

In this study, the acceleration vector in each time step is assumed to be a mth order time polynomial. By using the initial conditions, satisfying the equation of motion at both ends of the time step and minimizing the square of the residual vector, the m+3 unknown coefficients are determined. The order of accuracy for this approach is m+1, and it has a very low dispersion error. Moreover, the period error of the new technique is almost zero, and it is considerably smaller than the members of the Newmark method. The proposed scheme has an appropriate domain of stability, which is greater than that of the central difference and linear acceleration techniques. The numerical tests highlight the improved performance of the new algorithm over the fourth-order Runge-Kutta, central difference, linear and average acceleration methods.

关键词： high accuracy time integration scheme nonlinear analysis period error stability

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Doppler Passive Fathometry

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2018年第2期144卷 577-583页

作者： Harrison, Chris H. Ctr Maritime Res & Experimentat Viale San Bartolomeo 400 I-19126 La Spezia Italy Univ Southampton Inst Sound & Vibrat Res Southampton SO17 1BJ Hants England

Passive fathometry is a technique whereby broadband ambient ocean noise received on an array of hydrophones is averaged and cross-correlated to produce a sub-bottom profile [Siderius, Harrison, and Porter (2006). J. Acoust. Soc. Am. 120, 1315-1323]. Here this technique is extended to determine the vertical velocity of the array, and compensate for it, without any prior knowledge, i.e., Doppler Passive Fathometry. For Fourier transform lengths beyond a certain limit, the differing Doppler between the direct and bottom reflected paths spoils the correlation match, however it is shown by using some experimental data, where the array was known to suffer from arbitrary but near periodic motion, that compensation is possible, enabling continuing time integration. In the process, the vertical velocity becomes known. Velocity, with peak value similar to +/- 61m/s, is plotted against time and shown to be 90 degrees out of phase with depth, as expected for periodic motion. Since stationary targets have already been detected by noise correlation [Harrison (2008). J. Acoust. Soc. Am. 123, 1834-1837], it is implied that the range of moving targets can also be determined. (C) 2018 Acoustical Society of America.

关键词： HYDROPHONE FOURIER transforms DOPPLER effect time integration scheme PERIODIC motion

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Effective and energy-preserving time discretization for a general nonlinear poromechanical formulation

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COMPUTERS & STRUCTURES 2017年 182卷 313-324页

作者： Burtschell, Bruno Chapelle, Dominique Moireau, Philippe Univ Paris Saclay Inria Paris France Univ Paris Saclay Lab Mecan Solides Ecole Polytech CNRS Paris France

We consider a general nonlinear poromechanical model, formulated based on fundamental thermodynamics principle, suitable for representing the coupling of rapid internal fluid flows with large deformations of the solid, and compatible with a wide class of constitutive behavior. The objective of the present work is to propose for this model a time discretization scheme of the partitioned type, to allow the use of existing time schemes - and possibly separate solvers - for each component of the model, i.e. for the fluid and the solid. To that purpose, we adapt and extend an earlier proposed approach devised for fluid structure interaction in an Arbitrary Lagrangian-Eulerian framework. We then establish an energy estimate for the resulting time scheme, in a form that is consistent with the underlying energy principle in the poromechanical formulation, up to some numerical dissipation effects and some perturbations that we have carefully identified and assessed. In addition, we provide some numerical illustrations of our numerical strategy with test problems that present typical features of large strains and rapid fluid flows, and also a case of singular transition related to total drainage. An example of challenging application envisioned for this model and associated numerical coupling scheme concerns the perfusion of the heart. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： DISCRETIZATION methods THERMODYNAMICS COUPLINGS (Gearing) FLOW (Fluid dynamics) DEFORMATIONS (Mechanics) time integration scheme

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