A deformation theory without ad hoc assumption of an axisymmetric circular cylinder

Zhao, Bin; Zhao, Yushun; Gao, Yang; Zhang, Dechen

doi:10.1007/s00707-010-0359-9

Cited by 10 publications

(11 citation statements)

References 15 publications

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“…Within the framework of the Saint Venant method some simplifying hypotheses of a possible deformed configuration are usually used [2,8,9]. Here we apply the following ones:…”

Section: Boundary Value Problem Of Torsion Of Cylindrical Barmentioning

confidence: 99%

“…However, for small strains, all available models of the nonlinear theory of elasticity can be reduced to the classical quadratic Hooke's potential [8,9]. Therefore, for small angles of twist, Eq.…”

Section: Estimation Of the Axial Force For Hard Device Torsionmentioning

confidence: 99%

“…For a hyperelastic material, the nonnegative scalar potential W exists, such that W (X, I) = 0, where I is the second rank unit tensor, and (X, F) = ∂ W (X, F)/∂F T for all tensors F and almost all points X ∈ Ω. For an isotropic material, the potential is a function of principal invariants of a strain measure, for example the left Cauchy-Green tensor B = F · F T [8,9], the Hencky logarithmic tensor H = ln √ B [10,11] or principal values of the left stretch tensor = B 1/2 . All descriptions are equivalent.…”

Section: Introductionmentioning

confidence: 99%

“…Non-uniform radial deformation effect is not analyzed in the available theories of torsion [7]. Although cross-sectional warpings are considered for prismatic solids, [7][8][9], these effects are not essential for cylinders and cannot be related to the radial deformation.…”

Section: Introductionmentioning

confidence: 99%

“…Let us recall the basic equations of the nonlinear theory of elasticity [8,9]. Consider a solid that occupies a domain Ω ⊂ R 3 in the reference (undeformed) configuration.…”

Section: Introductionmentioning

confidence: 99%

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Power law type Poynting effect and non-homogeneous radial deformation in the boundary-value problem of torsion of a nonlinear elastic cylinder

Brigadnov

2014

Acta Mech

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The boundary value problem of torsion of a solid cylinder is analyzed for a class of hyperelastic materials that exhibit the power law type dependence of the strain energy density on the magnitude of the deformation gradient. The Saint Venant hypotheses are generalized by including the non-homogeneous longitudinal and radial deformations. A nonlinear variational problem with respect to the function of the radial/surface deformation, the function of the longitudinal deformation, the normalized torque and the normalized axial force is formulated. The asymptotic analytical solutions are obtained for the hard device torsion and for large angles of twist. They illustrate the power law type dependencies of the axial force and the reaction torque on the angle of twist with the exponents p and p − 1, respectively. For Treloar (neo-Hookean) materials with p = 2, the classical results can be obtained. The finite element analysis of the hard device torsion is performed by MATLAB. The results indicate that for a homogeneous class of materials and large angles of twist non-homogeneous radial/surface deformation can be observed.

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“…Within the framework of the Saint Venant method some simplifying hypotheses of a possible deformed configuration are usually used [2,8,9]. Here we apply the following ones:…”

Section: Boundary Value Problem Of Torsion Of Cylindrical Barmentioning

confidence: 99%

Section: Estimation Of the Axial Force For Hard Device Torsionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Let us recall the basic equations of the nonlinear theory of elasticity [8,9]. Consider a solid that occupies a domain Ω ⊂ R 3 in the reference (undeformed) configuration.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations