Energy estimates in one-dimensional rate-type viscoplasticity

DOI10.1016/0022-247X(88)90211-9zbMath0637.73039MaRDI QIDQ1098683

B. George

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

equilibriuminitial-boundary value problemsindependentrate-independent plasticityEnergy estimatesparticle velocitydependent on the plastic workL(sup 2) estimates for stressL(sup p) estimates for strainpositive definite free energy functionsviscoplastic models

Mathematics Subject Classification ID

Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) (74C10) Plastic materials, materials of stress-rate and internal-variable type (74C99) Dynamical problems in solid mechanics (74Hxx)

Related Items (10)

Unnamed Item ⋮ A nonlocal rate-type viscoplastic approach to patterning of deformation ⋮ Some remarks on the behaviour of the solution in dynamic processes for rate-type models ⋮ Convex and non-convex energy in three-dimensional rate-type semilinear viscoelasticity ⋮ Some stability-instability problems in phase transitions modelled by piecewise linear elastic or viscoelastic constitutive equations ⋮ Energy estimates in three-dimensional rate-type semilinear viscoelasticity with non-convex free energy ⋮ Numerical aspects in modelling phase transitions by rate-type constitutive equations ⋮ On the thermodynamics of rate-type fluids and phase transitions. II: Phase transitions ⋮ A thermodynamic approach to rate-type models of elastic-plastic materials ⋮ Unnamed Item

Cites Work

• Some energetic properties of smooth solutions in rate-type viscoelasticity
• The energy in one-dimensional rate-type semilinear viscoelasticity
• On rate-type constitutive equations and the energy of viscoelastic and viscoplastic materials
• Quasilinear rate-type constitutive equations and finite time of relaxation hypothesis
• Some exact solutions for wave propagation in viscoelastic, viscoplastic and electrical transmission lines
• Plastic wave propagation in a bar of material exhibiting a strain rate effect
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