Volume changes associated with the deformation of rubber-like solids

Ogden, Ray W.

doi:10.1016/0022-5096(76)90007-7

Cited by 110 publications

(56 citation statements)

References 18 publications

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“…(26), resulting from the entropy change associated with the volume change, is however problematic from a mechanics consideration [37,39]. To account for the volume change in rubber elasticity, many other forms of the free energy function have been suggested [37,[39][40][41][42]. In the present study, following Hong et al [27], we take the elastic free energy function as …”

Section: A Free Energy Function For Hydrogelmentioning

confidence: 99%

A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

Kang

Huang

2010

Journal of Applied Mechanics

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A hydrogel consists of a cross-linked polymer network and solvent molecules. Depending on its chemical and mechanical environment, the polymer network may undergo enormous volume change. The present work develops a general formulation based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions along with proper boundary conditions. A specific material model is employed in a finite element implementation, for which the nonlinear constitutive behavior is derived from a free energy function, with explicit formula for the true stress and tangent modulus at the current state of deformation and chemical potential. Such implementation enables numerical simulations of hydrogels swelling under various constraints. Several examples are presented, with both homogeneous and inhomogeneous swelling deformation. In particular, the effect of geometric constraint is emphasized for inhomogeneous swelling of surface-attached hydrogel lines of rectangular cross-sections, which depends on the width-to-height aspect ratio of the line. The present numerical simulations show that, beyond a critical aspect ratio, crease-like surface instability occurs upon swelling.

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Section: A Free Energy Function For Hydrogelmentioning

confidence: 99%

A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

Kang

Huang

2010

Journal of Applied Mechanics

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“…Liu (6) showed the constitutive equation which contains isotropic tangent modulus based on the strain invariants under the isotropic assumption; Ogden (3) showed the constitutive equation based on the stretch ratio. Ishikawa and Kotera (7) showed the explicit anisotropic constitutive equation including tangent modulus based on the strain invariants.…”

Section: Constitutive Equation For Fiber Reinforced Hyperelastic Matementioning

confidence: 99%

“…To put it another way, we can say that a hyperelastic body is a material in which a strain energy function is existent and from which an elastic body stress will be obtained by differentiating that strain energy function with respect to the strain. To get that strain energy function, models such as the Mooney-Rivlin model (2) , which is based on the strain invariants, and the Ogden model (3) , which is based on the stretch ratio, are often used. Other models, such as the Gent model (4) and the Arruda-Boyce model (5) , which are the form that focuses on molecular structures, also offer an advantage in that deriving a model from uniaxial tests is easy, and they are used a lot lately.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation for Fibre Reinforced Rubber

Ishikawa

Tokuda

Kotera

2008

JCST

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On the basis of hyperelastic material behavior various forms of the strain energy density function, depending either on the invariants of the right Cauchy-Green deformation tensor or on the principal stretches, have been proposed under the isotropy assumption. If a material behaves transversely isotropic behavior with respect to the reference configuration, then the strain energy function can depend on five principal invariants. Five principal invariants are ordinary three invariants and additional fourth and fifth invariants. In the area of automotive belt designing technique, the most material of belt is composed of fiber reinforced hyperelastic. In this paper, we propose the polynomial strain energy function and determinate its material constants for the fiber reinforced material.

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“…For future reference we note that i tr(do) = ho" {8 fV0/8a0) ~ p0 , (1)(2)(3)(4)(5)(6)(7)(8) where the dot denotes the scalar product and tr denotes the trace. Thus tr(d0) = 5-d0 = do • 5-2.…”

Section: Introductionmentioning

confidence: 99%

“…(1.2) and the equilibrium equations can be put as div s = 0 (1. 3) when there are no body forces, div denoting the divergence operator relative to X.…”

Section: Introductionmentioning

confidence: 99%

Nearly isochoric elastic deformations: volume changes in plane strain

Ogden¹

1979

Quart. Appl. Math.

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Abstract.Plane deformations of nearly incompressible elastic solids are examined with a view to calculating the volume changes accompanying an arbitrary (plane) deformation. The dilatation is shown to be determined from a knowledge of the deformation appropriate to the corresponding incompressible material under the same boundary conditions. This work parallels that given in a previous paper for three-dimensional deformations and relies on the decomposition of the deformation gradient into its dilatational and isochoric parts.It is emphasized that the manner in which the response function of an incompressible material is transmitted into that of a nearly incompressible material is of critical importance in the calculation of the dilatation. This is illustrated for a specific boundary-value problem and for isotropic materials. In particular, it is shown that when the incompressible neo-Hookean solid is considered in the compressible context mutually contradictory results may be obtained. These results are assessed in the light of experimental evidence available for rubberlike solids.

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Volume changes associated with the deformation of rubber-like solids

Cited by 110 publications

References 18 publications

A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

Numerical Simulation for Fibre Reinforced Rubber

Nearly isochoric elastic deformations: volume changes in plane strain

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