Linear Response in Finite Elasticity

Nader, José Jorge

doi:10.1023/b:elas.0000029956.39597.a5

Cited by 8 publications

(7 citation statements)

References 7 publications

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“…Equation (32) shows that relation between T (1) and T (m) is the same as the relation between H (1) and H (m) . For example, setting m = 2, we have…”

Section: Thermal and Mechanical Tensors Conjugate To A General Class mentioning

confidence: 99%

“…(32,34) to obtain T (m) , H (m) explicitly in terms of T (1) , H (1) and U in tensorial form. Connections between components of T (m) and T (1) , H (m) and H (1) on the Lagrangian principal axis are easier to obtain [11].…”

Section: Thermal and Mechanical Tensors Conjugate To A General Class mentioning

confidence: 99%

“…However, the pioneering work in this context is as early as 1915 by Armanni [29]. This problem is still of interest, for example, we can refer to the recent works of Batra [30,31], Nader [32], Chiskis and Parnes [33], Murphy [34], Darijani et al [25] and Gilchrist et al [35].…”

Section: Constitutive Modelingmentioning

confidence: 99%

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Conjugated kinetic and kinematic measures for constitutive modeling of the thermoelastic continua

Darijani

2014

Continuum Mech. Thermodyn.

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In this paper, the energy-type terms such as the stress power, the rate of the heat transferred to the system and the rate of the specific internal energy are presented in the Lagrangian, Eulerian and twopoint descriptions for thermoelastic continua. In order to solve a problem based on the energy viewpoint, the mechanical, thermal and thermo-mechanical tensors conjugate to the Seth-Hill strains, and a general class of Lagrangian, Eulerian and two-point strain tensors are determined. Also, the energy pairs for thermoelastic continua are simplified for special cases of isentropic and isothermal deformation processes as well as the so-called entropic elastic materials (rubber-like materials and elastomers). At the end, a strain energy density function of the Saint Venant-Kirchhoff type in terms of different strain measures and temperature is considered for modeling the thermo-mechanical behavior of the rubber-like materials and elastomers. It is shown that this constitutive modeling can give results which are in good agreement with the experimental data.

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“…Equation (32) shows that relation between T (1) and T (m) is the same as the relation between H (1) and H (m) . For example, setting m = 2, we have…”

Section: Thermal and Mechanical Tensors Conjugate To A General Class mentioning

confidence: 99%

Section: Thermal and Mechanical Tensors Conjugate To A General Class mentioning

confidence: 99%

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Conjugated kinetic and kinematic measures for constitutive modeling of the thermoelastic continua

Darijani

2014

Continuum Mech. Thermodyn.

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“…We first remark that within the context of Cauchy elasticity, a number of linear stressstrain relations of the form (1.3) for the Cauchy stress have been recently proposed in the literature. Using the principal stress response, the first two of the following were introduced by Batra [1,2] and the third by Nader [6]:…”

Section: Materials Independent Strainmentioning

confidence: 99%

Linear Isotropic Relations in Finite Hyperelasticity: Some General Results

Murphy

2006

J Elasticity

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The form of the classical stress-strain relations of linear elasticity are considered here within the context of nonlinear elasticity. For both Cauchy and symmetric PiolaKirchhoff stresses, conditions are obtained for the associated strain fields so that they are independent of the material constants and compatible with existence of a strain-energy function. These conditions can be integrated in both cases to obtain the most general strain field that satisfies these conditions and the corresponding strain-energy function is obtained. In both cases, a natural choice of form of solution is suggested by the special case of the compatibility conditions being satisfied identically. It will be shown that some strainenergy functions previously introduced in the literature are special cases of the results obtained here. Some recent linear stress-strain relations, proposed in the context of Cauchy elasticity, are examined to see if they are compatible with hyperelasticity.

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“…One focus of attention has been on obtaining non-linear equivalents of the classical stress-strain relation. Although considered as early as 1915 by Armanni [2], this problem is still of interest, as can be seen in the recent work of Batra [3,4], Nader [5], Chiskis and Parvis [6] and Murphy [7].…”

Section: Introductionmentioning

confidence: 99%

Generalisations of the strain-energy function of linear elasticity to model biological soft tissue

Gilchrist

Murphy²,

Rashid

2012

International Journal of Non-Linear Mechanics

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Publication informationInternational Journal of Non-Linear Mechanics, 47 (2): 268-272Publisher Elsevier Item record/more information http://hdl.handle.net/10197/4602 Publisher's statementThis is the author's version of a work that was accepted for publication in International Journal of Non-Linear Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Non-Linear Mechanics (47, 2, (2012) ABSTRACT Strain measures consistent with the classical, infinitesimal form of the strain-energy function are obtained within the context of isotropic, homogeneous, compressible, non-linear elasticity. It will be shown that there are two distinct families of such measures. One family has already been much studied in the literature, the most important member being the strains whose principal values are a function only of the corresponding principal stretches. The second family of strains appears new. The motivation for studying such strains is the intuitive expectation that, for at least moderate deformations, a good fit with experimental data from material characterisation tests will be obtained with the corresponding strain-energy functions. In particular, there is the expectation that such models could prove useful for the modelling of biological soft tissue, whose physiological response is characterised by moderate strains. It will be shown that this is indeed the case for simple tension tests on porcine brain tissue.

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Linear Response in Finite Elasticity

Cited by 8 publications

References 7 publications

Conjugated kinetic and kinematic measures for constitutive modeling of the thermoelastic continua

Conjugated kinetic and kinematic measures for constitutive modeling of the thermoelastic continua

Linear Isotropic Relations in Finite Hyperelasticity: Some General Results

Generalisations of the strain-energy function of linear elasticity to model biological soft tissue

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