What are the re-calculate elastic constants in the code?

[akihoo]

Dear Erlap,

Thank you for sharing the code.

In CPFEM, the elastic constants are necessary parameters for simulation, such as C11, C12, and C44 for cubic crystal, or C11, C12, C44, C13, and C33 for hcp. But in the usermaterials.f, you did a re-calculate elastic constants, for example: e1 = (C11**2 + C11*C12 - 2.*C12**2)/(C11 + C12), v12 = C12/(C11 + C12), g12 = C44. Moreover, in hcp material, no single C** is given; only e1, e3, and g12 are found.

What are those re-calculate elastic constants meaning in the code? Why the C** is not needed in the hcp material?

The next question is, if I want to define some fully elastic materials, i.e., α and β pure Titanium, should I only define the C11~C44 regardless of the so-called re-calculate elastic constants, and turn off all the additional models such as the slip and Harding model.

At last, how can I calculate the elastic strain energy through the UMAT?

Thanks for your kind help,
Best,
Feiyu

[EralpDemir]

Hi Feiyu,
Those are very good points.

1. We needed the isotropic shear modulus and Poisson's ratio for backstress calculations and we did this only for cubic materials. It needs to be modified hexagonal materials as you suggested, for example by assuming random distribution of orientations.

2. Yes, it is possible to do elastic simulations, simply turn off slip law by setting slipmodel=0 and hardeningmodel=0 as well.

3. UMAT should have strain energy as output. Since all the strains will be elastic in your case, you may look at the total strain energy.

Hope this helps,
Eralp