Conjugate stresses of the Seth–Hill strain tensors

Farahani, K.; Naghdabadi, R.

doi:10.1016/s0020-7683(99)00209-7

Cited by 26 publications

(16 citation statements)

References 4 publications

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“…The corotational rate of the Eulerian (or spatial) Hencky strain h associated with the so-called logarithmic spin Ω log is identical to the Eulerian stretching D, and h is the only strain enjoying this property [18]. According to (10), this means:…”

Section: Preliminariesmentioning

confidence: 99%

“…Connections between components of T (m) and T (1) , H (m) and H (1) on the Lagrangian principal axis are easier to obtain [11]. In the following, conjugacy relations are extracted based on Hill's principal axis method [10,11].…”

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

confidence: 99%

“…The most of the work prior to 1991 dealt with stresses conjugate to Lagrangian strain measures. For example, the works by Hill [2,3], Guo and Dubey [4], Hoger [5], Wang and Duan [6], Xiao [7], Dui and Ren [8], Dui et al [9] and Farahani and Naghdabadi [10,11] can be mentioned, which provide expressions for the conjugate stresses to Lagrangian strain measures either in the component or in basis-free form. Also, on the subject of work-conjugacy, strain measures and associated stresses, two introductory reviews are worthy of mention.…”

Section: Introductionmentioning

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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Section: Preliminariesmentioning

confidence: 99%

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

confidence: 99%

Section: Introductionmentioning

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 the spirit of Seth-Hill strain family [20], we propose a new strain measure that takes into account the exponential increase of stress with Green strain to absorb the nonlinearity and thus result in a simpler stress-strain relation. In the circumferential (θ) and axial (z) directions, we define the new strains as: (6) where n is a material constant characterizing the strain nonlinearity with respect to Green strain E θθ and E zz (for n=0, Eq.…”

Section: A Generalized Strain Measurementioning

confidence: 99%

“…(10) is measured at a scale different from the conventional definition. In fact, conjugate stress measures [20,23] are usually sought for specific strains to keep the energy measure universal. In the present case, a meaningful stress measure is more important than a consistent energy scale.…”

Section: Nominal Strain Energymentioning

confidence: 99%

A bilinear stress–strain relationship for arteries

Zhang

Kassab

2007

Biomaterials

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A comprehensive understanding of the mechanical properties of blood vessels is essential for vascular physiology, pathophysiology and tissue engineering. A well known approach to study the elasticity of blood vessels is to postulate a strain energy function such as the exponential or polynomial forms. It is typically difficult to fit experimental data to derive material parameters for blood vessels, however, due to the highly-nonlinear nature of the stress-strain relation. In this work, we generalize the strain definition to absorb the elastic nonlinearity and then propose a 2D bilinear stress-strain relation between Kirchhoff stress and the new strain measure. The model is found to represent the Fung's exponential model very well. The novel linearized constitutive relation simplifies the determination of material constants by reducing the nonlinearity and provides a clearer physical interpretation of the model parameters. The limitations of the constitutive model and its implications for vascular mechanics are discussed.

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Constitutive Models of Coronary Vasculature

Kassab

2019

Coronary Circulation

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Conjugate stresses of the Seth–Hill strain tensors

Cited by 26 publications

References 4 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

A bilinear stress–strain relationship for arteries

Constitutive Models of Coronary Vasculature

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