A finite element approach for large strains of nearly incompressible rubber-like materials

Cescotto, Serge; Fonder, G.

doi:10.1016/0020-7683(79)90073-8

Cited by 54 publications

(13 citation statements)

References 29 publications

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“…Since rubber is highly extensible, and large strains are observed experimentally [23,24], small-strain elasticity theory using moduli E and G (the shear modulus) is not suitable for describing the response of tires to large strains, whereas the mechanical energy W stored in a unit volume as the result of the deformation provides a useful means of measuring these responses. In tire applications, rubber compounds are often assumed to be isotropic, and cord/rubber composites are assumed to be elastic.…”

Section: Constitutive Model For Tire Materialsmentioning

confidence: 99%

Thermomechanical analysis of an aircraft tire in cornering using coupled ale and lagrangian formulations

Kondé¹,

Rosu

Lebon

et al. 2013

Open Engineering

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Abstract:The thermomechanical behavior of an aircraft tire is predicted, using experimental devices, a model based on finite element software and an appropriate method of expressing the heat generated by skid in terms of the local friction coefficient, depending on the temperature. In the thermomechanical model, a steady state mechanical analysis is combined with a transient thermal problem. This combined approach is based on three main computing steps: the deformation step, the dissipation step and the thermal step. The deformation step calculates the stress and the velocity fields, which are used as inputs in the dissipation step to calculate the heat generated due to friction. The internal dissipation is assumed to be negligible. Finally, the thermal step yields new thermal maps based on the heat flux computed in the dissipation step. The coupling is established by updating the friction coefficient in the first two steps.

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Section: Constitutive Model For Tire Materialsmentioning

confidence: 99%

Thermomechanical analysis of an aircraft tire in cornering using coupled ale and lagrangian formulations

Kondé¹,

Rosu

Lebon

et al. 2013

Open Engineering

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“…The constitutive relation obtained and used in [9][10][11] has the form are the invariants introduced in [12]. Furthermore,…”

Section: Elastic Potential W Of a Slightly Compressible Materialmentioning

confidence: 99%

Constitutive Relations for Finite Elastic-Inelastic Strains

Rogovoi

2005

J Appl Mech Tech Phys

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The evolutionary constitutive elastic-inelastic relation with its compatible objective derivative is derived in general form using the kinematics of superposition of small elastic and inelastic strains on finite elastic-inelastic strains. The equation is rendered concrete using the elastic law for a slightly compressible material.Key words: elastic-inelastic behavior, finite strains, slight compressibility, evolutionary constitutive equations.1. Preliminary Information. Using three configurations: an initial configuration ae 0 , a current configuration ae, and an intermediate configuration ae * close to the current configuration and employing the kinematics of superposition of small strains (position gradients) on finite strains, Novokshanov and Rogovoi [1] derived constitutive equations for finite elastic strains of a simple material relative to the intermediate configuration.According to the Celerier-Richter theorem or the Noll reduction theorem, the constitutive equation for a simple material that satisfies the objectivity principle is written as (see [2])( 1.1) where T is the true stress tensor; R and U are the orthogonal tensor and the symmetric positive definite pure-strain tensor in the polar decomposition of the position gradient F = R · U ;g 1 (U ) is the material response to pure strain. Relation (1.1) can be written in several equivalent forms [1], in particular,where J = I 3 (F ) is the third basic invariant F , which defines the relative volume change; andg 6 is the material response function. In [1], the functiong 6 is linked tog 1 by the relationg 1 = J −1 U ·g 6 · U . For the intermediate configuration ae * close to the current configuration, the constitutive equation (1.2) is written asHere T * is the stress reached in the configuration ae * (the initial stress for this configuration), h = ( ae * ∇ u) t is the gradient (relative to the configuration ae * u) of the vector of small displacements that transform the intermediate configuration to the current configuration, e = (h + h t )/2 is the small-strain tensor relative to the configuration ae * , d = (h − h t )/2 is the small-rotation tensor,L IV 6 is the fourth-rank tensor (generally, anisotropic) which defines the elastic response of the material to small strains relative to the intermediate configuration.The approximate relation (1.3) can be made exact by dividing by the increment in the time of transition from the intermediate to the current configuration and passing to the limit, i.e., by letting the intermediate configuration to the current configuration. As a result, we have the evolutionary equation T Tr =L IV 6 ··ė (1.4)with the Truesdell objective derivative.

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“…where γ 1 , γ 2 , γ 11 , γ 22 and γ 12 are obtained by transforming Γ 1 , Γ 2 , Γ 11 , Γ 22 and Γ 12 to the current configuration:…”

Section: Constitutive Equations For Hyperelastic Materialsmentioning

confidence: 99%

“…The constant c and the function H(J) are chosen such that the stresses vanish in the initial, undeformed configuration. An alternative method to obtain a stress-free initial configuration is to substitute I 1 and I 2 in(5) 11 :…”

Section: Constitutive Equations For Hyperelastic Materialsmentioning

confidence: 99%

3D finite element analysis of rubber‐like materials at finite strains

Liu

Hofstetter

Mang

1994

Engineering Computations

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The paper starts with a review of constitutive equations for rubber‐like materials, formulated in the invariants of the right Cauchy—Green deformation tensor. A general framework for the derivation of the stress tensor and the tangent moduli for invariant‐based models, for both the reference and the current configuration, is presented. The free energy of incompressible rubber‐like materials is extended to a compressible formulation by adding the volumetric part of the free energy. In order to overcome numerical problems encountered with displacement‐based finite element formulations for nearly incompressible materials, three‐dimensional finite elements, based on a penalty‐type formulation, are proposed. They are characterized by applying reduced integration to the volumetric parts of the tangent stiffness matrix and the pressure‐related parts of the internal force vector only. Moreover, hybrid finite elements are proposed. They are based on a three‐field variational principle, characterized by treating the displacements, the dilatation and the hydrostatic pressure as independent variables. Subsequently, this formulation is reduced to a generalized displacement formulation. In the numerical study these formulations are evaluated. The results obtained are compared with numerical results available in the literature. In addition, the proposed formulations are applied to 3D finite element analysis of an automobile tyre. The computed results are compared with experimental data.

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A finite element approach for large strains of nearly incompressible rubber-like materials

Cited by 54 publications

References 29 publications

Thermomechanical analysis of an aircraft tire in cornering using coupled ale and lagrangian formulations

Thermomechanical analysis of an aircraft tire in cornering using coupled ale and lagrangian formulations

Constitutive Relations for Finite Elastic-Inelastic Strains

3D finite element analysis of rubber‐like materials at finite strains

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