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# When and where the stress objective rates are used in ABAQUS software?

Hi everyone,

I have a question about the objectivity tensor in ABAQUS software. Below is my question.

The principle of objectivity demands that the constitutive equations involve objective tensors only. Needless to say, because of the arbitrary time dependence, many tensors in the ordinary sense are not objective tensors. To achieve the requirement of objectivity, we introduce the objective stress rates, such as A Truesdell stress rate of the Cauchy stress;B Truesdell stress rate of the Kirchhoff stress;C Green-Naghdi rate of the Cauchy stress;D Green-Naghdi rate of the Kirchhoff stress;E Jaumann rate of the Cauchy stress;F Oldroyd stress rate;

And so on, there may be an infinite variety of objective stress rates as variety of Lie derivative.Then my question is when and where the objective stress rate is used in ABAQUS simulation? Since only Jaumann rate and Green-Naghdi rate of Cauchy stress are used by ABQUS UMAT and VUMAT, is there a possibility of using other stress rates in ABAQUS by user subroutine?

Thank you.

Shunlai

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## Comments

## You can convert between different rate forms

Hi Shunlai,

I think the way abaqus treat stress/strain rate is more or less determined by its corotational local coordinate system. So direct implementation of orther rate forms are not so easy. But if you have a constitutive relation in the form of one type of stress/strain rate, you can easily convert it into the rate form used by Abaqus.

If not so straightforward to convert analytically, you can treat it as following. Expand everything around the current configuration, and neglect all higher order terms in the increment of strain/displacement. By doing that, the constitutive relation is a small-deformation relation, and the rate forms do not really matter, since the rigid-body rotation is already taken care of by abaqus, before passing into UMAT/VUMAT

Hope this helps.

Wei

## Hi Shunlai, ABAQUS

Hi Shunlai,

ABAQUS will use objective stress rate when you activate the large deformation or finite strain option.

It is possible to use other stress rates in ABAQUS, but you should store the stress matrix to the state variable matrix.

Plz avoid updating the stress matrix given by ABAQUS when you use the objective stress rates other thanJauman or Naghdi rate.

Good luck.

Wang

## jaumann rate

Hello,

I have a rate form for a compressible hyperelastic material, i.e., d(2nd_pK)/dt = Tangent_4thorder * d(greenLagrangeStrain)/dt. The problem is under finite strain. In Umat, can I directly set DDSDDE = 'Tangent_4thorder'? When is Jaumann rate calculated?

Thanks,

Zhang

## vumat problem

<p>hii..</p>

<p>im a phd student , and i have question related to updation in shear modulus of a film (which is not constant but a linear function of film thickness E= Eint*(1+(beta*coordinates(z direction)/thickness))).</p>

<p>i have a soft elastic film (2D-shell) and applying a external force by using vdload subroutine to deform the film surface , so my question is that when the film deform ,what will be shear modulus ???(suppose initially position of element /point is =z1 and after deformation it reaches at z2)??</p>

<p>thanks in advance ..</p>

<p> </p>