# Objective stress rate

stress increment
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference.wikipedia
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### Hypoelastic material

hypoelastic
The adjacent figure shows the performance of various objective rates in a simple shear test where the material model is hypoelastic with constant elastic moduli.
As explained below, specific formulations of hypoelastic models typically employ a so-called objective stress rate so that the G function exists only implicitly.

### Continuum mechanics

continuumcontinuous mediacontinuum physics
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. If the stress and strain measures are material quantities then objectivity is automatically satisfied.

### Derivative

differentiationdifferentiablefirst derivative
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference.

### Stress (mechanics)

stressstressestensile stress
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference.

### Frame of reference

reference frameframes of referencereference frames
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference.

### Constitutive equation

constitutive relationconstitutive equationsconstitutive model
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).

### Finite strain theory

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).

### Stress measures

Biot stress tensorKirchhoff stresssecond Piola-Kirchhoff stress
If the stress and strain measures are material quantities then objectivity is automatically satisfied.

### Lie derivative

Lie bracketLie commutatorcommuting vector fields

### Simple shear

shearplane shearshearing
The adjacent figure shows the performance of various objective rates in a simple shear test where the material model is hypoelastic with constant elastic moduli.

### Elastic modulus

modulus of elasticityelastic modulimodulus
The adjacent figure shows the performance of various objective rates in a simple shear test where the material model is hypoelastic with constant elastic moduli.

### Shear stress

shearshearingwall shear stress
The ratio of the shear stress to the displacement is plotted as a function of time.

### Displacement field (mechanics)

displacementdisplacement fielddisplacements
The ratio of the shear stress to the displacement is plotted as a function of time.

### Cauchy stress tensor

stress tensorprincipal stressdeviatoric stress tensor
Under rigid body rotations, the Cauchy stress tensor transforms as

### Covariant transformation

covariancecovariantcovariantly
:Since is a spatial quantity and the transformation follows the rules of tensor transformations, is objective.

### Infinitesimal strain theory

strain tensorstraininfinitesimal strain tensor
For a small enough load step, the material deformation can be characterized by the small (or linearized) strain increment tensor

### Strain-rate tensor

strain rate tensorvelocity gradientdeformation rate tensor
: is the strain rate tensor (also called the velocity strain) and is the material point velocity or displacement rate.

### Walter Noll

Principle of material objectivityMaterial frame-indifferencematerial objectivity
In other words, material constitutive equations should be frame-indifferent (objective).

### Force gauge

NmForce gauge and Force Sensor
Force Gauges usually measure pressure in stress increments and other dependent human factors.