Stress-Strain Behavior of Elastic Materials

Varga, Olívia; Dill, Ellis H.

doi:10.1115/1.3607660

Cited by 22 publications

(25 citation statements)

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“…There exists a set of three axes subject to max imum strains with respect to strains of linear ele ments in all other directions [62]. The angle between these axes (table XI) and the principal strain axes is shown in table XII.…”

Section: Results Of the Kossel Internal Stress-strain Analysismentioning

confidence: 99%

The Divergent beam (Kossel) x-ray method and its uses in measuring strain contours in an individual grain of Fe-3 weight percent Si transformer sheet

Yakowitz¹

1973

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Section: Results Of the Kossel Internal Stress-strain Analysismentioning

confidence: 99%

The Divergent beam (Kossel) x-ray method and its uses in measuring strain contours in an individual grain of Fe-3 weight percent Si transformer sheet

Yakowitz¹

1973

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“…it turns out that the Ogden law (39) comprises other wellknown finite elasticity models, such as the Varga, neo-Hooke, or Mooney-Rivlin model (Mooney 1940;Rivlin 1948;Varga 1966;Treloar 1975). Since the strain energies (39) describe a porous material, a volumetric response function needs to be defined in order to ensure the compaction point, which is reached when there is no pore space left.…”

Section: Specific Solid Strain Energiesmentioning

confidence: 99%

An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

Ehlers

Karajan

Markert

2008

Biomech Model Mechanobiol

112

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Finite element models for hydrated soft biological tissue are numerous but often exhibit certain essential deficiencies concerning the reproduction of relevant mechanical and electro-chemical responses. As a matter of fact, singlephasic models can never predict the interstitial fluid flow or related effects like osmosis. Quite a few models have more than one constituent, but are often restricted to the small-strain domain, are not capable of capturing the intrinsic viscoelasticity of the solid skeleton, or do not account for a collagen fibre reinforcement. It is the goal of this contribution to overcome these drawbacks and to present a thermodynamically consistent model, which is formulated in a very general way in order to reproduce the behaviour of almost any charged hydrated tissue. Herein, the Theory of Porous Media (TPM) is applied in combination with polyconvex Ogden-type material laws describing the anisotropic and intrinsically viscoelastic behaviour of the solid matrix on the basis of a generalised Maxwell model. Moreover, other features like the deformation-dependent permeability, the possibility to include inhomogeneities like varying fibre alignment and behaviour, or osmotic effects based on the simplifying assumption of Lanir are also included. Finally, the human intervertebral disc is chosen as a representative for complex soft biological tissue behaviour. In this regard, two numerical examples will be presented with focus on the viscoelastic and osmotic capacity of the model.

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“…for some function f (X, Y ), then we require that the following equation 6) holds identically. Now on transforming back to the original variables (x, y, u), using (2.1) and (2.3) we may deduce…”

Section: The Basic Linearizationmentioning

confidence: 99%

“…In three recent papers Hill and Arrigo [3,4] and Arrigo and Hill [5], the present authors have shown that MongeAmpère equations also arise in the context of finite elastic deformations. In particular, it is shown that certain plane strain, plane stress and axially symmetric deformations of the incompressible perfectly elastic Varga material (see Varga [6]) all give rise to MongeAmpère equations of the form (1.1). Three of these may by linearized by a sequence of elementary transformations and the purpose of this brief communication is to show that the same sequence of transformations is also effective when F = u 4 y f (u, u x /u y ), where f denotes an arbitrary function.…”

Section: Introductionmentioning

confidence: 99%

On a Class of Linearizable Monge-Ampère Equations

Arrigo¹,

Hill²

1998

JNMP

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Monge-Ampère equations of the form, u xx u yy − u 2 xy = F (u, u x , u y ) arise in many areas of fluid and solid mechanics. Here it is shown that in the special case F = u 4 y f (u, u x /u y ), where f denotes an arbitrary function, the Monge-Ampère equation can be linearized by using a sequence of Ampère, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this equation due to Khabirov [7].

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Stress-Strain Behavior of Elastic Materials

Cited by 22 publications

References 0 publications

The Divergent beam (Kossel) x-ray method and its uses in measuring strain contours in an individual grain of Fe-3 weight percent Si transformer sheet

The Divergent beam (Kossel) x-ray method and its uses in measuring strain contours in an individual grain of Fe-3 weight percent Si transformer sheet

An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

On a Class of Linearizable Monge-Ampère Equations

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