The elastica and the problem of the pure bending for a non-convex stored energy function

DOI10.1007/BF00043858zbMath0481.73018MaRDI QIDQ1162379

Roger L. Fosdick, Richard D. James

Publication date: 1981

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

zbMATH Keywords

existencehomogeneitymaterial symmetrycomplete characterization of minimal energy deformation fieldsEulerian stateinextensible elastic ribbonkinematic and constitutive propertiesminimization of total potential energyrestriction of frame indifference

Mathematics Subject Classification ID

Related Items (18)

Variational theory for spatial rods ⋮ Nonlinear Elasticity Theory with Discontinuous Internal Variables ⋮ Dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods ⋮ Non-smooth bending and buckling of a strain gradient elastic beam with non-convex stored energy function ⋮ Elasto-plastic localised responses in one-dimensional structural models ⋮ A nonlocal elastica inspired by flexural tensegrity ⋮ Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity ⋮ Régularité de la solution d'un problème variationnel. (Regularity of the solution of a variational problem) ⋮ Stresses and deflections in a pseudo-elastic beam under cyclic loads ⋮ Non-elliptic elastic materials and the modeling of dissipative mechanical behavior: An example ⋮ Axisymmetric Instabilities for Elastic Conical Shells under Compressive End Loadings ⋮ Minimization in incompressible nonlinear elasticity theory ⋮ Théorèmes d'existence en calcul des variations et applications à l'élasticité non linéaire ⋮ On the role of the strong ellipticity condition in nonlinear elasticity ⋮ The equilibrium and post-buckling behavior of an elastic curve governed by a non-convex energy ⋮ Stability of nonlinearly elastic rods ⋮ Large shearing oscillations of incompressible nonlinearly elastic bodies ⋮ On the emergence and propagation of a phase boundary in an elastic bar with a suddenly applied end load

Cites Work

• Co-existent phases in the one-dimensional static theory of elastic bars
• The morphology and stability of material phases
• Equilibrium of bars
• On the dissipation associated with equilibrium shocks in finite elasticity
• Unnamed Item

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