Hi everone,

I have written a UMAT to simulate metal-foams with the constitutive model

of Deshpande & Fleck.

#### Constitutive Model & Implementation

It has an oval like yield criterion in the J2/I1 plane. (I1 meaning the first

Invariant of sigma, J2 meaning the second Invariant of the deviatoric part of

sigma)

This yield criterion is used to calculate the new stresses with the help of the

Closest-Point-Projection Algorithm (CPP).

All of the aforementioned works fine.

#### Calculation of Jacobian-Matrix

To calculate DDSDDE I use kind of a forward differential approach because

its the only DDSDDE that let ABAQUS/Standard converge.

I start from sigma_n1(stress at the end of the increment) and use 6 different

pertubations to calculate each row of DDSDDE.

With the use of

(1) deltaEpsilon = (a,0,0,0,0,0)

for the Iteration of the pertubated stress, I calculate sigma_n1* (the

perturbated stress) with my Implementatino of the CPP-Algorithm

Then I use the forward differential scheme,

(2) df(x) / dx = ( f(x+h) - f(x) ) / h

to calculate the Jacobian-matrix.

In this case I calculate the first row,

(3) DDSDDE(1,i) = ( sigma_n1*(i) - sigma_n1(i) ) / epsilon(i)

(epsilon(i) is always a)

#### Verifying/testing the UMAT

My testing refers to a simple compression test with a cube:

I tested the UMAT using a cube with a single-element mesh and it worked

fine.

It works for given stresses or strains.

All the ouput (sigma/eps curves...) is and the wallclock time it takes is ok.

Then I created a multiple-element mesh cube and tried to analyse it.

The Analysis smoothly runs through the purely elastic region, enters the

elastoplastic region and continues quite a while. Then it suddenly stops at a

Point and ABAQUS tells me the equilibrium conditions do not converge any more.

The strain and strains ABAQUS stops increase with lesser elements.

It works completely for 2x2x2 elements, but not for 3x3x3 and more.

I have tried to mess around with DDSDDE and calculate it explicitely but it

did not work out. The only one that worked is the aforementioned.

I would be very thankful if anybody has an idea on how to find and fix this problem.

Greetings, ixfem

(I have to excuse for my poor english, but its not my first language.)