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- Objective_stress_rate abstract "In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. Many constitutive equations are designed in the form of a relation between a stress-rate and a strain-rate (or the rate of deformation tensor). The mechanical response of a material should not depend on the frame of reference. In other words, material constitutive equations should be frame indifferent (objective). If the stress and strain measures are material quantities then objectivity is automatically satisfied. However, if the quantities are spatial, then the objectivity of the stress-rate is not guaranteed even if the strain-rate is objective.There are numerous objective stress rates in continuum mechanics – all of which can be shown to be special forms of Lie derivatives. Some of the widely used objective stress rates are: the Truesdell rate of the Cauchy stress tensor, the Green–Naghdi rate of the Cauchy stress, and the Jaumann rate of the Cauchy stress.The adjacent figure shows the performance of various objective rates in a pure shear test where the material model is hypoelastic with constant elastic moduli. The ratio of the shear stress to the displacement is plotted as a function of time. The same moduli are used with the three objective stress rates. Clearly there are spurious oscillations observed for the Jaumann stress rate.This is not because one rate is better than another but because it is a misuse of material models to use the same constants with different objective rates. For this reason, a recent trend has been to avoid objective stress rates altogether where possible.".
- Objective_stress_rate thumbnail ObjectiveStressRates.png?width=300.
- Objective_stress_rate wikiPageID "39796969".
- Objective_stress_rate wikiPageLength "33987".
- Objective_stress_rate wikiPageOutDegree "32".
- Objective_stress_rate wikiPageRevisionID "699366546".
- Objective_stress_rate wikiPageWikiLink Category:Continuum_mechanics.
- Objective_stress_rate wikiPageWikiLink Cauchy_stress_tensor.
- Objective_stress_rate wikiPageWikiLink Constitutive_equation.
- Objective_stress_rate wikiPageWikiLink Continuum_mechanics.
- Objective_stress_rate wikiPageWikiLink Covariant_transformation.
- Objective_stress_rate wikiPageWikiLink Derivative.
- Objective_stress_rate wikiPageWikiLink Displacement_field_(mechanics).
- Objective_stress_rate wikiPageWikiLink Elastic_modulus.
- Objective_stress_rate wikiPageWikiLink Finite_strain_theory.
- Objective_stress_rate wikiPageWikiLink Frame_of_reference.
- Objective_stress_rate wikiPageWikiLink Hypoelastic_material.
- Objective_stress_rate wikiPageWikiLink Infinitesimal_strain_theory.
- Objective_stress_rate wikiPageWikiLink Lie_derivative.
- Objective_stress_rate wikiPageWikiLink Objectivity_(frame_invariance).
- Objective_stress_rate wikiPageWikiLink Principle_of_material_objectivity.
- Objective_stress_rate wikiPageWikiLink Pure_shear.
- Objective_stress_rate wikiPageWikiLink Shear_stress.
- Objective_stress_rate wikiPageWikiLink Strain_rate_tensor.
- Objective_stress_rate wikiPageWikiLink Stress_(mechanics).
- Objective_stress_rate wikiPageWikiLink Stress_measures.
- Objective_stress_rate wikiPageWikiLink File:ObjectiveStressRates.png.
- Objective_stress_rate wikiPageWikiLink File:Undeformed_and_deformed_material_element.pdf.
- Objective_stress_rate wikiPageWikiLinkText "Objective stress rate".
- Objective_stress_rate wikiPageUsesTemplate Template:Reflist.
- Objective_stress_rate subject Category:Continuum_mechanics.
- Objective_stress_rate hypernym Derivatives.
- Objective_stress_rate type ChemicalCompound.
- Objective_stress_rate comment "In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. Many constitutive equations are designed in the form of a relation between a stress-rate and a strain-rate (or the rate of deformation tensor). The mechanical response of a material should not depend on the frame of reference. In other words, material constitutive equations should be frame indifferent (objective).".
- Objective_stress_rate label "Objective stress rate".
- Objective_stress_rate sameAs Q17105043.
- Objective_stress_rate sameAs m.0w33pt4.
- Objective_stress_rate sameAs Q17105043.
- Objective_stress_rate wasDerivedFrom Objective_stress_rate?oldid=699366546.
- Objective_stress_rate depiction ObjectiveStressRates.png.
- Objective_stress_rate isPrimaryTopicOf Objective_stress_rate.