Bifurcation in the traction problem for a transversely isotropic material

DOI10.1017/S0305004100070444zbMath0751.73030MaRDI QIDQ3982365

Alexandre Danescu

Publication date: 26 June 1992

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

Mooney-Rivlin materialstored energy functionneo- Hookean materialpure homogeneous deformationstwo-dimensional \(\mathbb{Z}_ 2\)-equivariant bifurcation problem

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Stability of dynamical problems in solid mechanics (74H55) Bifurcations in context of PDEs (35B32)

Related Items (4)

Loss of ellipticity in elasticity with energy limiters ⋮ Remarks on cavity formation in fiber-reinforced incompressible nonlinearly elastic solids ⋮ Instability analysis in pressurized transversely isotropic Saint-Venant-Kirchhoff and neo-Hookean cylindrical thick shells ⋮ Representations for transversely hemitropic and transversely isotropic stress-strain relations

Cites Work

• Symmetry and bifurcation in three-dimensional elasticity
• Singularities and groups in bifurcation theory. Volume I
• Classification and unfoldings of degenerate Hopf bifurcations
• Imperfect bifurcation in the presence of symmetry
• Singularities and groups in bifurcation theory. Volume II
• Smooth functions invariant under the action of a compact Lie group
• Stability of an elastic cube under dead loading: two equal forces
• Periodic and Steady-State Mode Interactions Lead to Tori
• Classification of Z(2)-Equivariant Imperfect Bifurcations with Corank 2
• A singularity theory analysis of a thermal-chainbranching model for the explosion peninsula
• Secondary Bifurcation in Nonlinear Diffusion Reaction Equations
• A theory for imperfect bifurcation via singularity theory

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