Non-elliptic elastic materials and the modelling of elastic-plastic behavior for finite deformation

DOI10.1016/0022-5096(87)90012-3zbMath0608.73044OpenAlexW2000506952MaRDI QIDQ1086015

James K. Knowles, Rohan C. Abeyaratne

Publication date: 1987

Published in: Journal of the Mechanics and Physics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-5096(87)90012-3

zbMATH Keywords

macroscopic responsedissipativeinternal variable formalismnon-elliptic elastic materialsattractor for quasi-static motionsdiscontinuous gradientelastic-perfectly plastic behaviormaximum-dissipationmedium with cavityset of equilibrium statestorque-twist relationstwist problemunobservable equilibrium states

Mathematics Subject Classification ID

Nonlinear elasticity (74B20)

Related Items (16)

On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models ⋮ Nonlinear Elasticity Theory with Discontinuous Internal Variables ⋮ Martensitic phase transitions with surface effects ⋮ Analytical study on the stress-induced phase or variant transformation in slender shape memory alloy samples ⋮ Equilibrium shocks in plane deformations of incompressible elastic materials ⋮ On the mechanical dissipation of solutions to the Riemann problem for impact involving a two-phase elastic material ⋮ On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: Energy and dissipation ⋮ Compact zones of shear transformation in an anisotropic solid ⋮ Non-elliptic elastic materials and the modeling of dissipative mechanical behavior: An example ⋮ Construction of two-phase equilibria in a non-elliptic hyperelastic material ⋮ On the driving traction acting on a surface of strain discontinuity in a continuum ⋮ Kinetic relations and the propagation of phase boundaries in solids ⋮ Phase changes induced by deformation in isothermal elastic crystals ⋮ On the modeling of thermo-mechanical phase transformations in solids ⋮ On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: Reflection and transmission behavior ⋮ Transition to detonation in dynamic phase changes

Cites Work

• Finite deformation by mechanical twinning
• Displacive phase transformations in solids
• On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics
• Discontinuous deformation gradients in plane finite elastostatics of incompressible materials
• The elastic energy-momentum tensor
• On the dissipation associated with equilibrium shocks in finite elasticity
• Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity
• Unnamed Item

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