Discontinuous deformation gradients in the finite twisting of an incompressible elastic tube

DOI10.1007/BF00042481zbMath0511.73035MaRDI QIDQ1839089

Rohan C. Abeyaratne

Publication date: 1981

Published in: Journal of Elasticity (Search for Journal in Brave)

zbMATH Keywords

weak formulationelastic tubeelastostatic shocksloss of ellipticitydiscontinuous deformation gradientscomposed of materialdissipativity and stability of solutionsfinite twistingisotropic, incompressible, elastic materialslack of uniqueness of solutionsno classical solutionno smooth solutionoccurrence of elastostatic fields

Mathematics Subject Classification ID

Related Items (23)

Deformation induced loss of ellipticity in an anisotropic circular cylindrical tube ⋮ Nonlinear Elasticity Theory with Discontinuous Internal Variables ⋮ Existence and uniqueness results for minimization problems with nonconvex functionals ⋮ Analysis of strain localization in strain-softening hyperelastic materials, using assumed stress hybrid elements ⋮ Discontinuous deformation gradients away from the tip of a crack in anti- plane shear ⋮ Emergence and disappearance of load induced fiber kinking surfaces in transversely isotropic hyperelastic materials ⋮ Hyperelastic internal balance by multiplicative decomposition of the deformation gradient ⋮ On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: Energy and dissipation ⋮ Dynamic growth of martensitic plates in an elastic material ⋮ Non-smooth solutions in the azimuthal shear of an anisotropic nonlinearly elastic material ⋮ Non-elliptic elastic materials and the modeling of dissipative mechanical behavior: An example ⋮ Numerical simulation of equilibrium shocks in maximally dissipative elastic systems. I: The one-dimensional case ⋮ Construction of two-phase equilibria in a non-elliptic hyperelastic material ⋮ Azimuthal Shear of a Transversely Isotropic Elastic Solid ⋮ Kinetic relations and the propagation of phase boundaries in solids ⋮ Minimization in incompressible nonlinear elasticity theory ⋮ Helical shear of an elastic, circular tube with a non-convex stored energy ⋮ The equilibrium and post-buckling behavior of an elastic curve governed by a non-convex energy ⋮ An admissibility condition for equilibrium shocks in finite elasticity ⋮ Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium ⋮ On the emergence and propagation of a phase boundary in an elastic bar with a suddenly applied end load ⋮ On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: Reflection and transmission behavior ⋮ On martensitic phase nucleation with surface effects

Cites Work

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• On the ellipticity of the equations of nonlinear elastostatics for a special material
• Equilibrium of bars
• On the failure of ellipticity of the equations for finite elastostatic plane strain
• The elastic instability of a director rod
• On the dissipation associated with equilibrium shocks in finite elasticity
• Finite-deformation analysis of the elastostatic field near the tip of a crack: Reconsideration and higher-order results
• COMBINED AXIAL AND TORSIONAL SHEAR OF A TUBE OF INCOMPRESSIBLE ISOTROPIC ELASTIC MATERIAL
• Large elastic deformations of isotropic materials VI. Further results in the theory of torsion, shear and flexure

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