The integrability criterion in finite elastoplasticity and its constitutive implications

DOI10.1007/s00707-006-0362-3zbMath1107.74008OpenAlexW2020261630MaRDI QIDQ871594

Albert Thomas Marie Meyers, Heng Xiao, Otto Timme Bruhns

Publication date: 20 March 2007

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00707-006-0362-3

zbMATH Keywords

logarithmic rateHencky strainEulerian rate equation

Mathematics Subject Classification ID

Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) (74C15) Theory of constitutive functions in solid mechanics (74A20)

Related Items (6)

On the non-oscillation criterion for multiplicative anisotropic plasticity at large simple shear deformation ⋮ Multiplicative representation of the deformation gradient tensor in geometrically nonlinear multilevel constitutive models ⋮ On evolution equations for elastic deformation and the notion of hyperelasticity ⋮ Finite elastoplastic \(J_{2}\)-flow models with strain recovery effects ⋮ Coupling effects of finite rotation and strain-induced anisotropy on monotonic and cyclic failure of metals ⋮ Thermodynamic laws and consistent Eulerian formulation of finite elastoplasticity with thermal effects

Cites Work

• A study on rate-type constitutive equations and the existence of a free energy function
• A critical review of the state of finite plasticity
• On objective corotational rates and their defining spin tensors
• Strain rates and material spins
• Hypo-elasticity model based upon the logarithmic stress rate
• Logarithmic strain, logarithmic spin and logarithmic rate
• Existence and uniqueness of the exactly integrable hypoelastic equation \(\overset\circ\tau^*=\lambda(\text{tr }D)I+2\mu \)D and its significance to finite inelasticity
• A weakened form of Ilyushin's postulate and the structure of self-consistent Eulerian finite elastoplasticity
• Coordinate-independent representation of spins in continuum mechanics
• Self-consistent Eulerian rate type elasto-plasticity models based upon the logarithmic stress rate.
• Objective stress rates, path-dependence properties and non-integrability problems
• Elastoplasticity beyond small deformations
• The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate
• The Simplest Rate Theory of Pure Elasticity

This page was built for publication: The integrability criterion in finite elastoplasticity and its constitutive implications