A comparison of some simple constitutive relations for slightly compressible rubber-like materials

Levinson, M.; Burgess, Ian

doi:10.1016/0020-7403(71)90042-7

Cited by 106 publications

(31 citation statements)

References 10 publications

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“…which has been proposed by Levinson and Burgess [3] and has been named &&polynomial compressible material'' by the authors. In equation (8), is the shear modulus of the material for vanishingly small strains, f is a material constant whose value lies between zero and unity, and is expressed as…”

Section: Formulationmentioning

confidence: 98%

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Stability and Breathing Motions of Pressurized Compressible Hyperelastic Spherical Shells

Akyüz

Ertepinar

2001

Journal of Sound and Vibration

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Section: Formulationmentioning

confidence: 98%

“…The material of the body is assumed to be a polynomial material [3] which is homogeneous, isotropic, compressible, hyperelastic and reduces to Blatz}Ko material when some material constants are specialized. The shell is "rst subjected to a "nite, uniform, radial extension.…”

Section: Introductionmentioning

confidence: 99%

Stability and Breathing Motions of Pressurized Compressible Hyperelastic Spherical Shells

Akyüz

Ertepinar

2001

Journal of Sound and Vibration

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“…Several examples of specific volumetric functions G(J) have been presented over the years (see, for instance, Başar and Weichert [21]). Among these, we recall the particularly simple choice of Levinson and Burgess [22], leading to a model called 'simplified Blatz-Ko' in [19], that is…”

Section: Compressible Neo-hookean Materialsmentioning

confidence: 99%

Large-amplitude love waves

Ferreira¹,

Boulanger²,

Destrade³

2008

The Quarterly Journal of Mechanics and Applied Mathematics

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In the context of the finite elasticity theory we consider a model for compressible solids called "compressible neo-Hookean material". We show how finite-amplitude inhomogeneous plane wave solutions and finite-amplitude unattenuated solutions can combine to form a finiteamplitude Love wave. We take a layer of finite thickness overlying a solid half-space, both made of different pre-stressed compressible neoHookean materials. We derive an exact solution of the equations of motion and boundary conditions, and also obtain results for the energy density and the energy flux of the waves. Finally, we investigate the special case when the interface between the layer and the substrate is in a principal plane of the pre-stain. A numerical example is given.

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“…Their elastic properties are described by the Levinson--Burgess potential [3] Eo [ For the model of an isotropic and compressible material of high-polymeric reinforcing fibers under large deformations, we used the elastic potential of Blatz and Ko [4] ~f -4 (1 + vf) uf (1.4)…”

mentioning

confidence: 99%

Analysis of elastomeric composites based on fiber-reinforced systems. 2. Unidirectional composites

Akhundov¹

1999

Mech Compos Mater

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Based on the calculation method [1], the deformation (elastic) properties of unidirectional elastomeric composites are analyzed in the region of nonlinear deformation (under large deformations). The method is based on the structural macroscopic theory for composite media [2], which takes into account the changes in the metrics of the matrix and fibers in a deformable medium of composite materials. The composites considered have poorly compressible (rubberlike) and compressible matrices with a tetragonal (square) stacking of fibers. The cross sections of the fibers in the initial (nondeformed) state of the composites are assumed to be round. The transverse tension and longitudinal shear of the composites are studied at different compressibility of the elastomeric material of the matrix. Results of the micro-and macromechanical analysis of the composites are given. The behavior of composites with low-and high-modulus fibers in tension and shear is examined in relation to the orientation of fibers with respect to the field of loading macroscopic stress. The quantities used are designated as in [1], except for those describing the reinforcing fibers and matrix. Since the composites considered have only one reinforcing system, the quantities referring to fibers are marked by an "f~ instead of "1, ~ while those characterizing the matrix are marked by an "m ~ instead of "M. ~ Coordinate indices of components of the vector and tensor quantities relative to the Cartesian coordinates are enclosed in parentheses as being physical components.

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A comparison of some simple constitutive relations for slightly compressible rubber-like materials

Cited by 106 publications

References 10 publications

Stability and Breathing Motions of Pressurized Compressible Hyperelastic Spherical Shells

Stability and Breathing Motions of Pressurized Compressible Hyperelastic Spherical Shells

Large-amplitude love waves

Analysis of elastomeric composites based on fiber-reinforced systems. 2. Unidirectional composites

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