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# FEAP UMAT - Gauss intergation points: physical/global coordinates

Hi all,

I am writing a umat for FEAP. My UMAT needs the physical/global coordinates of the Gauss Integration point upon which it is being run.

is it possible to get the Physical/Global

coordinates of the Gauss integration point upon which the UMAT

subroutine is being run ?

Reason:

The non-local material

model includes the gradients of some scalar internal variables, and I

don't intend to treat the internal variables as indepent variables

(e.g. displacements) in a User element routine, as it increases the

size of stiffness matrix (K) of the element 5-folds. So the other

possibility is to inform the UMAT about the coordinates of integration

point (and keep those coordinates in a history array) upon which it is

returning the material behavior, so that it can calculate the gradients

on that intergation point.

## You can calculate it

I am not a user of FEAP. However, depending upon you element type and order of integration utilized by FEAP, you can get the intigration piont co-ordinates in isoparametric axes system. You can utilize it for your calculation.

However, I am curious as to why you need global coordiantes for material point calculations. Shouldn't it remain independent of its location in space? And if not, then a question arises: which coordinate system? As far as I know, material models should not be dependent on spacial coordinates (if I am not wrong, a formulation dependent on spacial location will violate associativity).

## Gradient-dependent Constitutive models

Hi,

this plasticity problem is based on a plastic-slip gradient constitutive model. Now comes the limitation of UMAT: it deals with the values of parameters (e.g. plastic slip) at the material point ( intergation point), but it doesn't know how to calculate the gradient of the plastic slip at that material point. So in the first instance, I wrote a UEL, by treating the plastic slip as a field variable whose nodal values are to be calculated (similar to the calculation of nodal values of displacement as its gradient, i.e. strain, is used in the constitutive model), but it got worse as the size of element stiffness matrix became 120x120, (as compared to 24x24 for a normal 3D8N element) due to plastic-slip DOFs.

## I doubt that any code would

I doubt that any code would be able to provide to nodal coordinates in UMAT. In that case, you'll have to work with integration point in normlized coordinates or reformulate your model.

Kumar

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The world started with 0, is progressing with 0, but doesn't want 0.

## Perhaps ABAQUS can ..

Upon my other question, some FEA veterans (Prof. Huang, Prof. Acharya) mentioned that there is a possibility for such computation. Specifically the first comment of Prof. Acharya opens some secrets in UMAT.

Link: http://imechanica.org/node/12935

## Yup, it appears to be a way

Yup, it appears to be a way out. Thanks for sharing this. However, I must

mention that reading writing data takes a good amount of time. So you

can think of storage (static variables)...

Kumar

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The world started with 0, is progressing with 0, but doesn't want 0.