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- Objective_stress_rates 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_rates wikiPageID "39796969".
- Objective_stress_rates wikiPageLength "33866".
- Objective_stress_rates wikiPageOutDegree "31".
- Objective_stress_rates wikiPageRevisionID "675778187".
- Objective_stress_rates wikiPageWikiLink Category:Continuum_mechanics.
- Objective_stress_rates wikiPageWikiLink Cauchy_stress_tensor.
- Objective_stress_rates wikiPageWikiLink Constitutive_equation.
- Objective_stress_rates wikiPageWikiLink Continuum_mechanics.
- Objective_stress_rates wikiPageWikiLink Covariant_transformation.
- Objective_stress_rates wikiPageWikiLink Derivative.
- Objective_stress_rates wikiPageWikiLink Displacement_field_(mechanics).
- Objective_stress_rates wikiPageWikiLink Elastic_moduli.
- Objective_stress_rates wikiPageWikiLink Elastic_modulus.
- Objective_stress_rates wikiPageWikiLink Finite_strain_theory.
- Objective_stress_rates wikiPageWikiLink Frame_of_reference.
- Objective_stress_rates wikiPageWikiLink Hypoelastic_material.
- Objective_stress_rates wikiPageWikiLink Infinitesimal_strain_theory.
- Objective_stress_rates wikiPageWikiLink Lie_derivative.
- Objective_stress_rates wikiPageWikiLink Objectivity_(frame_invariance).
- Objective_stress_rates wikiPageWikiLink Principle_of_material_objectivity.
- Objective_stress_rates wikiPageWikiLink Pure_shear.
- Objective_stress_rates wikiPageWikiLink Shear_stress.
- Objective_stress_rates wikiPageWikiLink Strain_rate_tensor.
- Objective_stress_rates wikiPageWikiLink Stress_(mechanics).
- Objective_stress_rates wikiPageWikiLink Stress_(physics).
- Objective_stress_rates wikiPageWikiLink Stress_measures.
- Objective_stress_rates wikiPageWikiLink File:Undeformed_and_deformed_material_element.pdf.
- Objective_stress_rates wikiPageWikiLinkText "Objective stress rates".
- Objective_stress_rates wikiPageWikiLinkText "objective stress rate".
- Objective_stress_rates hasPhotoCollection Objective_stress_rates.
- Objective_stress_rates wikiPageUsesTemplate Template:Reflist.
- Objective_stress_rates subject Category:Continuum_mechanics.
- Objective_stress_rates hypernym Derivatives.
- Objective_stress_rates type ChemicalCompound.
- Objective_stress_rates 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_rates label "Objective stress rates".
- Objective_stress_rates sameAs m.0w33pt4.
- Objective_stress_rates sameAs Q17105043.
- Objective_stress_rates sameAs Q17105043.
- Objective_stress_rates wasDerivedFrom Objective_stress_rates?oldid=675778187.
- Objective_stress_rates isPrimaryTopicOf Objective_stress_rates.