objective stress rate

I am using Johnson-Cook material model to simulate foam response, but am confused about which stress rate definition the material model uses. The manual mentions that Abaqus/Explicit uses Green-Naghdi stress rate for viscoelastic materials, but the Johnson-Cook model definition shows viscoplastic behavior, while the elasticity limi depends on the strain rate. Thus I am confuesd if Abaqus/Explicit uses Jaumann or Green-Naghdi stress rate for Johnson-Cook material model. Can someone please guide me,

I am using Johnson-Cook material model to simulate foam response, but am confused about which stress rate definition the material model uses. The manual mentions that Abaqus/Explicit uses Green-Naghdi stress rate for viscoelastic materials, but the Johnson-Cook model definition shows viscoplastic behavior, while the elasticity limi depends on the strain rate. Thus I am confuesd if Abaqus/Explicit uses Jaumann or Green-Naghdi stress rate for Johnson-Cook material model. Can someone please guide me,

Check out my new article on a source of confusion in material and spatial versions of constitutive equations at http://www.parresianz.com/mechanics/incremental-objectivity/

-- Biswajit

Hi,

I want to derive the rate form of the consitutive relation for hypoelastic material:

Jaumann stress rate=L:D

where L is a fourth order modulus tensor and D is the rate of deformation. 

Most papers that I have seen begin with this expression. But I would like to know how to arrive at this equation.

Any suggestion?

Thanks

Brunda