Finite element methods for constrained problems in elasticity

Oden, J. T.; Kikuchi, Noboru

doi:10.1002/nme.1620180507

Cited by 186 publications

(36 citation statements)

References 7 publications

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“…It is commonly called T6/P1. It verifies the discrete LBB condition and yields stable pressure approximations [30]. The hydrostatic pressure is assumed as an internal degree of freedom, which is eliminated by a static condensation at element level.…”

Section: Mechanical Problemsupporting

confidence: 54%

Analysis of a thermoviscoelastic model in large strain

Méo¹,

Boukamel²,

Débordes³

2002

Computers & Structures

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This paper deals with a thermoviscoelastic model and its analysis. The mechanical formulation is based on the generalization to large strain of the Poynting-Thomson rheological model. The heat transfers are governed by the classical heat equation and the Fourier law. We briefly expose the finite element formulation, which takes into account the quasi-incompressibility constraint for the mechanical approach. The influence of several parameters is examined. IntroductionNowadays, elastomers are frequently employed in many sectors such as automobile and aeronautics industries. In their uses, these materials can undergo strong mechanical and thermal loadings. Moreover their mechanical properties highly depend on the temperature and thus the prediction of the behaviour and the assessment of the fatigue strength require a local analysis based on a formulation of thermomechanical models.The behavior of an elastomer can be very different according to:• the temperature, • the degree of crosslinking, • the incorporated particles (carbon black or silicium filled rubbers) • . . . So we can distinguish several approaches in the literature in accordance with the considered phenomenon:• hyperelasticity modeling the static behaviour of the material, • continuum damage mechanics approaching the softening behaviour under deformation, currently call Mullins' effect [28], • nonlinear viscoelasticity for the simulation of the relaxation phenomenon and the eventual dissipation, • thermomechanical coupling to take temperature sensitivity of mechanical characteristics into account and to describe the temperature changes due to the mechanical dissipation.More precisely, for hyperelasticity several stress strain relationships are proposed which are based on the expression of strain energy density in the isotropic, incompressible materials or very nearly so (almost incompressible). Among these behaviour laws, statistical models were carried out with entropic consideration of the molecular chains configurations [38,39], an other way consists in a phenomenological approach deduced from isotropy and incompressibility. These last ones must be adjusted according to experiment [12,26,31,32].Rubber materials, especially carbon black-filled, present a softening effect experimentally observed [13]. This loss of stiffness can be micro-mechanically described by a local separation of the carbon and rubber.* Corresponding

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Section: Mechanical Problemsupporting

confidence: 54%

Analysis of a thermoviscoelastic model in large strain

Méo¹,

Boukamel²,

Débordes³

2002

Computers & Structures

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“…Then, the standard displacement formulation is switched to a mixed one, andĴ J 3 and c are independently interpolated in each element such that both are assumed to be constant in linear displacement elements. For more detailed argument, the reader may refer to Oden and Kikuchi (1982). For steel and polyester cords the employment of hyperelastic material model would not pose any additional difficulty.…”

Section: Materials Models For the Numerical Analysis And Designmentioning

confidence: 99%

Multi-objective optimization of tire carcass contours using a systematic aspiration-level adjustment procedure

Cho

Jeong

Yoo

2002

Computational Mechanics

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While forming a basic tire configuration and supporting most static and dynamic loads of automobiles, tire carcass influences major tire performances according to its contour. Among significant tire performances, we in this study intend to improve the automobile maneuverability and the tire durability by optimizing the sidewall carcass contour. In order to effectively maximize these multi-objectives, we refine the conventional satisficing trade-off methods (STOM) which were proposed originally for the multi-objective structural optimization, by introducing a systematic aspiration-level adjustment procedure. According to the systematic procedure, we perform the sidewall contour optimization that ideally distributes the sidewall carcass tension and minimizes strain-energy density at the belt edge. Since the tire analysis is highly nonlinear problem we employ an incremental analysis scheme, together with the finite-difference sensitivity scheme. Through the numerical experiment, we confirmed that the refined multi-objective optimization technique systematically leads to a final optimum sidewall contour, together with the stable and rapid convergence.

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“…Two approaches are usually used to satisfy the impenetrability condition [11]: one is to impose displacement constraints directly on the formulation and the other is to use gap elements to couple possible areas of contact. To impose displacement constraints directly, points of contact must be identified firstly, and then the constraint conditions can be imposed in several ways, such as penalty method [12], Lagrange multiplier method [13], and constraint function method [14], etc. To impose displacement constraints by using gap elements, various aspects of contact can be modeled by giving the element nonlinear stiffness characteristics that depend on the relative positions of the nodes [15].…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic coupling problems caused by thermal contact resistance: A discontinuous Galerkin finite element approach

Zheng

Liu

2011

Sci. China Phys. Mech. Astron.

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A discontinuous Galerkin (DG) finite element method is presented to solve the thermoelastic coupling problems caused by temperature and pressure dependent thermal contact resistance (TCR). The whole analysis is made up of two parts, thermal and mechanical analysis. In thermal analysis, the DG method is employed to simulate the temperature jump phenomenon, which satisfies the imperfect thermal contact condition in a straightforward manner. In mechanical analysis, the impenetrability condition is fulfilled through a DG approach with penalty functions. The Picard iteration procedure with a relaxation technique is also adopted to accelerate the rate of convergence and avoid numerical instability. Numerical examples show that the present method is an attractive approach for solving thermoelastic coupling problems caused by TCR. The methodology can also be expanded to solve problems with friction finite deformation contact, node-to-segment contact and node-to-surface contact, etc. in a straightforward manner. thermoelastic coupling, thermal contact resistance, discontinuous Galerkin method, penalty method, relaxation technique PACS: 46.25.Hf,

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Finite element methods for constrained problems in elasticity

Cited by 186 publications

References 7 publications

Analysis of a thermoviscoelastic model in large strain

Analysis of a thermoviscoelastic model in large strain

Multi-objective optimization of tire carcass contours using a systematic aspiration-level adjustment procedure

Thermoelastic coupling problems caused by thermal contact resistance: A discontinuous Galerkin finite element approach

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