A physically based method to represent the thermo-mechanical behaviour of elastomers

Lion, Alexander

doi:10.1007/bf01178397

Cited by 170 publications

(79 citation statements)

References 24 publications

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“…Darüber hinaus müssen für die Simulation des viskoelastischen Materialverhaltens typischer gummiähnlicher Materialien große Deformationen und große Abweichungen vom thermodynamischen Gleichgewicht berücksichtigt werden. Von Reese and Govindjee [65] wurde 1998 eine neue Kontinuumsformulierung vorgeschlagen, die im Gegensatz zu vielen anderen Theorien nicht auf kleine Abweichungen vom thermodynamischen Gleichgewicht beschränkt ist, siehe auch Reese und Govindjee [64], Govindjee und Reese [18], Lion [34], [35], Haupt [21], Holzapfel [23] sowie Huber und Tsakmakis [25]. In den letzten Jahren wurde ebenfalls die Identifikation von Materialparametern für visko-elastische konstitutive Gesetze untersucht.…”

Section: Introductionunclassified

“…In 1998 Reese and Govindjee [65] proposed a continuum formulation which is in contrast to many other theories not restricted to viscoelastic response for strain rates near the thermodynamic equilibrium, see also Govindjee and Reese [18], Reese and Govindjee [64], Lion [34], [35], Lundin and Klarbring [39], Haupt [21], Holzapfel [23] and also Huber and Tsakmakis [25]. In this chapter the theory of the viscoelastic material model proposed by Reese and Govindjee [65] is reviewed and the numerical implementation is discussed.…”

Section: Finite Deformation Viscoelasticity In Principal Directionsmentioning

confidence: 99%

“…In 1998 Reese and Govindjee [65] proposed a continuum formulation which is, in contrast to many other theories, not restricted to viscoelastic response for states near the thermodynamic equilibrium (for further elaborations see, e.g. Reese and Govindjee [64], Govindjee and Reese [18], Lion [34], [35], Haupt [21], Holzapfel [23] and Huber and Tsakmakis [25]). In recent years the identification of the material parameters for viscoelastic constitutive laws has additionally been investigated.…”

Section: Introductionmentioning

confidence: 99%

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Generalized parameter identification for finite viscoelasticity

Kleuter

Menzel

Steinmann

2007

Computer Methods in Applied Mechanics and Engineering

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Section: Introductionunclassified

Section: Finite Deformation Viscoelasticity In Principal Directionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized parameter identification for finite viscoelasticity

Kleuter

Menzel

Steinmann

2007

Computer Methods in Applied Mechanics and Engineering

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“…The contribution of the thermoelastic coupling to the dissipation over a stabilized cycle is actually zero [Lion 1997]. The consequence is that it is not necessary to represent thermoelastic effects to estimate the heat build-up temperature.…”

Section: Introductionmentioning

confidence: 99%

Cyclic approximation of the heat equation in finite strains for the heat build-up problem of rubber

Chenadec

Raoult

Stolz

et al. 2009

J. Mech. Mater. Struct.

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It is well-known that rubber exhibits hysteretic mechanical behavior and has a low thermal conductivity. The main consequences are the heat generation and heat build-up phenomena which occur in a rubber component when subjected to repeated deformations. Estimating the heat build-up temperature implies the solution of a coupled thermomechanical problem. Due to the difference between the mechanical and the thermal diffusion characteristic times, a cyclic uncoupled approach is often used to solve the heat build-up problem.In the uncoupled approach, the heat sources are first determined with a mechanical analysis, and the heat equation is then solved on a fixed geometry. At finite strains, the geometry of the body varies with the deformation but the foregoing method does not account for such changes in geometry. The exact solution would require describing the body deformation while solving the thermal problem, but this does not take advantage of the difference between the characteristic times of the thermal diffusion and the mechanical behaviour, respectively, and the exact numerical resolution is therefore unnecessarily time-consuming.The purpose of the current work is to take into account kinematics in the thermal problem when using a cyclic uncoupled approach. The heat problem is written in the reference configuration. That implies that the problem is defined on a fixed domain: the initial configuration of the body. The changes in geometry in the reference heat equation are thus described by mechanical time-dependent variables. The cyclic assumption allows mean variables to be defined, for example the mean temperature. A timeintegration method and an approximation of the heat equation are developed, leading to a simplified formulation with mechanical time-independent terms. This simplified heat problem is based on the mean variables.

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“…In this formulation, however, the evolution equations of the internal variables are linear and, therefore, this theory can be considered as finite linear thermoviscoelasticity. Finite thermoviscoelasticity theories that allow finite perturbations away from thermodynamic equilibrium were presented by [Lion 1996; Keywords: finite thermoviscoelasticity, large deformations, Rubber-like matrix composites, evolving damage, finite strain high-fidelity generalized method of cells. and Govindjee 1998a].…”

Section: Introductionmentioning

confidence: 99%

Finite strain micromechanical modeling of thermoviscoelastic matrix composites

Aboudi

2011

J. Mech. Mater. Struct.

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A finite strain micromechanical analysis is generalized for the modeling of thermoviscoelastic matrix composites. The thermoviscoelastic matrix of the composite is represented by a finite thermoviscoelasticity theory that permits (in contrast to finite linear thermoviscoelasticity theories) large deviations away from thermodynamic equilibrium. As a result, it is possible to subject the composite to large thermomechanical loadings. In addition, the possibility of evolving damage in the matrix is included. The derived micromechanical model is applied to investigate the behavior of a thermoviscoelastic rubber-like matrix reinforced by steel fibers in various circumstances. By subjecting the composite to mechanical loading under isentropic conditions, the micromechanical model is employed for the prediction of thermoelastic inversion point at which the Gough-Joule phenomenon at the rubber-like phase occurs. Results are given that show the effect of damage, elevated temperature and viscoelasticity of the matrix on the global response of the composite including its creep and relaxation behavior.

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A physically based method to represent the thermo-mechanical behaviour of elastomers

Cited by 170 publications

References 24 publications

Generalized parameter identification for finite viscoelasticity

Generalized parameter identification for finite viscoelasticity

Cyclic approximation of the heat equation in finite strains for the heat build-up problem of rubber

Finite strain micromechanical modeling of thermoviscoelastic matrix composites

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