Some solutions for a compressible isotropic elastic material

The analysis of adaptors' deformation and stress is an important prerequisite for the design of the adapters. This paper proposed the mathematical description and analytical method for the sponge cylinder and rubber cylinder under pressure. The analytical formulas on deformation and stress of interference fit between adapters and launchers are deduced. Also, the correctness of the analytical formula is verified by numerical simulation. Furthermore, the effect of precompression and the sponge's thickness ratio on adapter's deformation and stress is studied. The following results can be concluded: the results of numerical simulation are basically consistent with that of analytical formula. After installing the adapter into the launcher, the rubber layer will move inward as a whole, then the sponge layer and the rubber layer are subjected to radial and tangential compressive stress. When the precompression is smaller than 0.0075 or larger than 0.0015, the deformation and stress of adapter are approximately in proportion to precompression. If the precompression keeps constant, the deformation and stress of adapter will have extremum when the thickness ratio of sponge equals to a certain value.

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“…The axisymmetric plane strain problem should satisfy the static equilibrium equation with ignorance of gravity [18].…”

Section: Differential Equation Description Of Sponge Cylindermentioning

confidence: 99%

Study on the Deformation and Stress Analysis of the Sponge/Rubber Adapter

Zhong

Ren

2018

Mathematical Problems in Engineering

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“…We note that (86) is a special Hadamard material, [12]. Recently, in [30], it was shown that a more general solution can be obtained. Starting with the strain-energy function (86) we again have (83 2 ) for the azimuthal displacement.…”

Section: Axial Shearingmentioning

confidence: 99%

Using null strain energy functions in compressible finite elasticity to generate exact solutions

Haughton

2007

Z. angew. Math. Phys.

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In this paper we characterize those strain energy functions in unconstrained nonlinear elasticity that satisfy the equations of equilibrium identically. The idea is to construct a useful, physically reasonable strain-energy function containing one or more components which are null, in such a way that exact solutions may be obtained from the resulting equilibrium equations. We show that the dilatation is a universal null energy while there may be others that depend on the actual problem. To obtain the null energies for a given problem it is often convenient to formulate the variational problem and look at the Euler-Lagrange equations. Specific examples are used to illustrate some of the potential uses of the method in finding exact solutions for physically meaningful constitutive models.

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“…doi:10.1016/j.ijsolstr.2011.01.016 certain classes of compressible elastic materials, such as extended forms of neo-Hookean materials, Mooney-Rivlin materials, harmonic materials, Ogden materials, Varga materials, semilinear materials, etc. ; refer to, e.g., Abeyaratne and Horgan (1984), Aron (1994Aron ( , 2005Aron ( , 2006, Aron and Aizicovici (1997), Aron et al (2006), , Carroll (1988Carroll ( , 1995Carroll ( , 2001Carroll ( , 2005Carroll ( , 2007, , Jiang (1997, 1999), Carroll and Horgan (1990), Chung et al (1986), Gao and Ogden (2009), Haughton (1987, 1993, Hill (2001) Horgan (1989), Horgan and Murphy (2005), Jiang and Beatty (1995), Jiang and Ogden (1998), Jiang and Ogden (2000), Ogden (2002, 2003), Kirkinis et al (2004), Murphy (1992Murphy ( , 2007, Ogden and Isherwood (1978), Rooney and Carroll (2007), Xiao and He (2007), Zhu et al (2010); and many others. Reference is also made to recent review articles by Beatty (1987Beatty ( , 2001 and monographs by Ogden (1984), and Fu and Ogden (2001).…”

Section: Introductionmentioning

confidence: 97%

Hill’s class of compressible elastic materials and finite bending problems: Exact solutions in unified form

Xiao

Yue

2011

International Journal of Solids and Structures

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a b s t r a c t Hill (1978) proposed a natural extension of Hooke's law to finite deformations. With all Seth-Hill finite strains, Hill's natural extension presents a broad class of compressible hyperelastic materials over the whole deformation range. We show that a number of known Hookean type finite hyperelasticity models are included as particular cases in Hill's class and that Bell's and Ericksen's constraints may be derived as natural consequences from Hill's class subjected to internal constraints. Also we present a unified study of finite bending problems for elastic Hill materials. To date exact results are available for certain particular classes of compressible elastic materials, which do not cover Hill's class. Here, with a novel idea of circumventing the strong nonlinearity we show that it is possible to derive exact solutions in unified form for the whole class of elastic Hill materials. Reduced results are also given for cases subjected to internal constraints.

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Some solutions for a compressible isotropic elastic material

Cited by 9 publications

References 41 publications

Study on the Deformation and Stress Analysis of the Sponge/Rubber Adapter

Study on the Deformation and Stress Analysis of the Sponge/Rubber Adapter

Using null strain energy functions in compressible finite elasticity to generate exact solutions

Hill’s class of compressible elastic materials and finite bending problems: Exact solutions in unified form

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