Void formation and growth in a class of compressible solids

Lei, Hin Chi; Chang, Hao‐Wei

doi:10.1007/bf00042789

Cited by 8 publications

(9 citation statements)

References 29 publications

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“…It is easy to obtain the numerical solutions of 2 for different values of the load parameter Q = q/p from (6). For a neo-Hookean cube, Rivlin tn'n3 presented similar formula.…”

Section: Deformation and Stress Of Rectangular Plate Without Voidmentioning

confidence: 90%

Growth of voids in a hyperelastic rectangular plate

Chang-jun

Ren

2005

J. of Shanghai Univ.

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The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an tmiaxi~l extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an central circular-cylinder void becomes an elliptic-cylinder void, but an ~ non-centeral circular-cylinder void becomes an ellitfdc-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concemrafion was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyze.

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“…It is easy to obtain the numerical solutions of 2 for different values of the load parameter Q = q/p from (6). For a neo-Hookean cube, Rivlin tn'n3 presented similar formula.…”

Section: Deformation and Stress Of Rectangular Plate Without Voidmentioning

confidence: 90%

Growth of voids in a hyperelastic rectangular plate

Chang-jun

Ren

2005

J. of Shanghai Univ.

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“…Spherically symmetric deformations of hollow and solid spheres in the conventional isotropic compressible theory involving a strain energy density W (I 1 , I 2 , I 3 ) have been the object of much previous study with respect to inflation and cavitation. In addition to the work summarized by Horgan and Polignone [1], later work includes Lei and Chang [14], Murphy and Biwa [15], Shang and Cheng [16], Pericak-Spector et al [17], and Murphy [18]. In general, closed form integration techniques are easily obtained only for special forms of the stored energy density W (I 1 , I 2 , I 3 ).…”

Section: Spherical Geometry Formulationmentioning

confidence: 98%

On the cavitation of a swollen compressible sphere in finite elasticity

Pence

Tsai

2005

International Journal of Non-Linear Mechanics

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“…For the prescribed dead load p 0 > 0, if c ≥ 0 is a solution of (24), then τ rr (0+) can be obtained by (23). For any prescribed dead load p 0 > 0, c = 0 is a solution of (24) and τ rr (0+) is given by (23), so r(R) = R and p(R) = −p 0 are the trivial solutions of the spherical symmetric deformation for an incompressible hyper-elastic sphere.…”

Section: Cavitated Bifurcation For Incompressible Hyper-elastic Spherementioning

confidence: 99%

“…Kakavas [21] studied the influence of cavitation on the stress-strain fields of the compressible Blatz-Ko material in the case of finite deformations. Further references are [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Study on cavitated bifurcation problems for spheres composed of hyper-elastic materials

2005

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In this paper, spherical cavitated bifurcation problems are examined for incompressible hyper-elastic materials and compressible hyper-elastic materials, respectively. For incompressible hyper-elastic materials, a cavitated bifurcation equation that describes cavity formation and growth for a solid sphere, composed of a class of transversely isotropic incompressible hyper-elastic materials, is obtained. Some qualitative properties of the solutions of the cavitated bifurcation equation are discussed in the different regions of the plane partitioned by material parameters indicating the degree of radial anisotropy in detail. It is shown that the cavitated bifurcation equation is equivalent, by use of singularity theory, to a class of normal forms with single-sided constraint conditions at the critical point. Stability and catastrophe of the solutions of the cavitated bifurcation equation are discussed by using the minimal potential-energy principle. For compressible hyper-elastic materials, a group of parameter-type solutions for the cavitated deformation for a solid sphere, composed of a class of isotropic compressible hyper-elastic materials, is obtained. Stability of the solutions is also discussed.

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Void formation and growth in a class of compressible solids

Cited by 8 publications

References 29 publications

Growth of voids in a hyperelastic rectangular plate

Growth of voids in a hyperelastic rectangular plate

On the cavitation of a swollen compressible sphere in finite elasticity

Study on cavitated bifurcation problems for spheres composed of hyper-elastic materials

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