Defining the problem

[lokitkhemka]

I am trying to create a plane-strain problem with quad-elements and monotonic loading. I have nodes that are fixed and nodes that allow only vertical displacements. How can I define the element-type, for the following element line, for example:

element 224 374 375 438 437

where 224 is the element id and 374, 375, 438 and 437 are the node ids. Is the element type CP4?

Also, how can I define the fixed and roller nodes (nodes that have only vertical displacements)?

I was going through triaxial_compression_of_sand example, but I don't understand the table given in the file monotonic

0 0
1 1
10 6

How can I create an equivalent table for increase of load factor from 0.0 to 1.0 from time 0 to 100, for example?

Thank you in advance for any help you can provide.

[TLCFEM]

1. For CP4, you do element CP4 224 374 375 438 437 material_tag, leave the thickness as 1 is okay, plane strain is controlled by the material used.
2. Use PlaneStrain to wrap any 3D material into a plane strain one that can be used with membrane elements.
3. Define boundary conditions using fix and fix2, fixing both DoF 1 and DoF 2 to have a fixed node, fixing only DoF 1 to allow vertical displacement (if DoF 1 is horizontal axis).
4. A Tabular amplitude shall contain a table with two columns which defines the curve.

Check those pages and see which part still cannot be understood.

[lokitkhemka]

Hi,

I have few questions regarding the Drucker Prager criterion as implemented in suanpan

In the cookbook the yield surface is defined as $\sqrt{J_2} + \eta p - \xi c $, where $\xi$ and $\eta$ are the parameters. The flow surface is defined $\sqrt{J_2} + \bar{\eta} p $. So, in the input file, if I set eta_y and eta_f, will I have the associative flow rule?

Also, comparing the yield equation with the equation in the wikipedia link: $\sqrt{J_2} - A - B I_1$, where $A = \frac{6 c \cos \phi}{\sqrt{3} (3 - \sin \phi)}$ and $B = \frac{2 \cos \phi}{\sqrt{3} (3 - \sin \phi)}$. I can use this equation to compute both $\xi$ and $\eta$ in the form of $\phi$ and $c$ (usually $c$ and $\phi$ are the parameters available to me). Is this approach appropriate? I don't know much about constitutive models, so that is why I am asking to you. However, both the equations need a reference pressure (or hydrostatic pressure) and I see a no way to define it in suanPan (link to the suanpan doc page. I am trying to define Drucker Prager material with no hardening and associative flow rule.

Thank you so much.

[TLCFEM]

1. Yes, the associative plasticity is achieved by setting $\eta_y=\eta_f$.
2. There are many different ways to compute $\eta$, the wiki page is correct, furthermore, see this page.
3. The hydrostatic pressure, $p$ ($I_1$ in wiki page), is computed and updated with the changes of stress, so it is not a model parameter. You most likely need to pick a proper friction angle $\phi$ and an initial cohesion $c$.
4. The same model is also documented in this book, if you have access to, you can check it out.

In general you always want to assign some hardening, say for example 1%, for numerical stability.
A pure plastic response yields zero stiffness, causing convergence issues.