Stable splitting scheme for general form of associated plasticity including different scales of space and time

Kassiotis, Christophe; Ibrahimbegović, Adnan; Matthies, Hermann G.; Brank, Boštjan

doi:10.1016/j.cma.2009.09.011

Cited by 3 publications

(5 citation statements)

References 44 publications

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“…We note in passing that the same kind of results can be used for other coupled problems where the time integration schemes of the sub-problems are different, such as thermomechanics [43] or with different time scales for mechanics and thermal component as well as a generalized nonlinear operator split for problems with internal variables [44]. However, the proof given herein is entirely original, as the dual quantities are exchanged in each iteration.…”

Section: Error Propagation Stability and Convergence Of Dfmt-bgs Algmentioning

confidence: 76%

“…v · e x = 1 − cos 2π t T char (44) where T char = 5 s. For such harmonic function, the solution of the fluid flow within the fluid-structure interaction problem exhibits an oscillating behavior that is reached after a short transition period. The maximum value of the Reynolds number in the cavity reaches Re = 200, and thus the flow can be considered as laminar.…”

Section: Lid-driven Cavity Flow With Flexible Bottommentioning

confidence: 98%

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Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

et al. 2010

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In this work we consider the fluid-structure interaction in fully nonlinear setting, where different space discretization can be used. The model problem considers finite elements for structure and finite volume for fluid. The computations for such interaction problem are performed by implicit schemes, and the partitioned algorithm separating fluid from structural iterations. The formal proof is given to find the condition for convergence of this iterative procedure in the fully nonlinear setting. Several validation examples are shown to confirm the proposed convergence criteria of partitioned algorithm. The proposed strategy provides a very suitable basics for code-coupling implementation as discussed in Part II.

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Section: Error Propagation Stability and Convergence Of Dfmt-bgs Algmentioning

confidence: 76%

Section: Lid-driven Cavity Flow With Flexible Bottommentioning

confidence: 98%

Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

et al. 2010

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“…First option condenses the complete set of nonlinear algebraic equations into a single nonlinear scalar equation for each yield surface, which can be done if the matrix that relates the stress resultants and the strains has constant entries, see e.g. [47], [28]. Second option solves the complete set of nonlinear algebraic equations related to the update of internal variables.…”

Section: Introductionmentioning

confidence: 99%

“…Second option solves the complete set of nonlinear algebraic equations related to the update of internal variables. We mention that the second option was elaborated in [28] for a general form of associated plasticity. The two derived procedures differ from one another by how the active set of yield surfaces is chosen.…”

Section: Introductionmentioning

confidence: 99%

Stress resultant plasticity for shells revisited

Dujc

Brank

2012

Computer Methods in Applied Mechanics and Engineering

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In this work, we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the Ilyushin-Shapiro two-surface yield function with isotropic and kinematic hardening. The main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity. Four different algorithms are derived and compared. Three of them yield practically identical final results, yet they differ considerably in computational efficiency and implementation complexity, since they solve different sets of equations and they use different procedures that choose active yield surfaces. One algorithm does not provide acceptable accuracy. It turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently. Several numerical examples are presented to illustrate the Ilyushin-Shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms.

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“…Methods for computing these problems were developed using an explicit step-by-step integration scheme, which is numerically unstable and requires very small steps. In [10], a systematic approach to the numerical computation of plastic flow processes and construction of a numerical scheme of the Newton iteration process was developed. In [2,13], the implicit numerically stable scheme of intermediate points is used for the solution of problems of force elastoplastic deformation.…”

mentioning

confidence: 99%

Numerical analysis of processes of thermoplastic deformation of axisymmetric bodies with regard for unloading

Mukha¹,

Nespliak

2012

J Math Sci

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We investigate the thermoelastoplastic state of an isotropic homogeneous medium under the action of temperature loads. A mathematical model of plastic flow is considered. We propose a method for constructing an unconditionally stable numerical scheme of the finite-element method for the solution of such problems. The process of propagation of the primary and secondary unloading zones in a body is shown. The time distribution of the intensity of plastic strain at a corner point of the body is presented. Results obtained without regard for the dependence of the yield strength on temperature and with regard for it are investigated.A number of works, a review of which is presented in [1, 6-8, 9, 12], are devoted to the investigation of thermoplastic deformation in bodies of revolution. A series of works [3,5,11,12] is devoted to the use of the finite-element method and Newton-Raphson-Kantorovich methods for the solution of spatial problems on studying the thermoelastoplastic stress-strain state [3,5,11,12]. Methods for computing these problems were developed using an explicit step-by-step integration scheme, which is numerically unstable and requires very small steps. In [10], a systematic approach to the numerical computation of plastic flow processes and construction of a numerical scheme of the Newton iteration process was developed. In [2,13], the implicit numerically stable scheme of intermediate points is used for the solution of problems of force elastoplastic deformation. In the proposed work, this scheme is used to improve the accuracy and efficiency of determination of thermoplastic strains.The aim of this work is also to investigate the character of unloading in an axisymmetric thick-walled body of revolution for different dependences of the limit of elasticity on temperature. For this purpose, the nonstationary problem of heat conduction [4] is solved by the Newton-Kantorovich method. On the basis of obtained temperature fields, the problem of thermoplastic deformation is reduced to a sequence of nonlinear boundaryvalue problems each of which is linearized by the Newton method. The solution of the linearized problem is performed on the basis of schemes of the finite-element method. Finite elements are constructed relative to a some basic surface. This makes it possible to solve easily the problem of identification of spatial finite elements. On the basis of the described method, the problem of investigation of the propagation of plastic and unloading zones in an axisymmetric thick-walled body of revolution is solved. The obtained results indicate the reliability and efficiency of the proposed method. Statement of the Problem and Main RelationsConsider the deformation process of a solid isotropic body located in a volume V bounded by a surface S and subjected to force and thermal loads that do not lead to loss of its stability. Let us use a mathematical

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Stable splitting scheme for general form of associated plasticity including different scales of space and time

Cited by 3 publications

References 44 publications

Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

Stress resultant plasticity for shells revisited

Numerical analysis of processes of thermoplastic deformation of axisymmetric bodies with regard for unloading

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