esys-escript

Use Escript to simulate a Cosserat material

Asked by ceguo

Hi everyone,

I notice that in one of your publication Muhlhaus et al, 2010 (The influence of non-coaxiality on shear banding in viscous-plastic materials) that you simulated a Cosserat continuum using escript. I'm very interested to do this, maybe starting from a 2d simulation. In this case we have one more variable phi (rotation) in addition with displacements (dx,dy). I also notice that you suppressed dy, so you still have only 2 variables in your study. I'm wondering is escript capable to handle a fully implemented cosserat mechanics problem in 2d (or even in 3d)?

I've tried a simple implementation myself using Cosserat linear elasticity (but seems failed). Since we have one more variable phi_z, I used 3d domain to simulate the 2d case. After I formulated the equilibrium equations (got three equations), I set corresponding coefficients to the general PDE (besides A, I have to set B and D). But escript failed to solve the PDE with error message: "Paso_SparseMatrix_invMain: non-regular main diagonal block"

Any suggestions are appreciated.

Ning

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Aurelie Papon (a-papon) said : 		#1

Hi!

Two suggestions:

- In Escript the number of variables and the number of equations are disconnected. In others words, you do not need to consider a 3D domain to solve your 2D case.

- Use DirectSolver instead of PasoSolver. By doing so, the solver will check the regularity of the whole matrix and
not the regularity of each block (separately).

Aurélie

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Lutz Gross (l-gross) said : 		#2

Would like to add that in the per we actually didn't solve for the full cosserat model but for (omega_c, v_{1,2}).
PS: I guess what Aurélie means is that in escript the number of equations and the number of spatial dimensions are not linked. So you can solve a 2D Cosserat model on a 2D domain.

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Lutz Gross (l-gross) said : 		#3

Would like to add that in the per we actually didn't solve for the full cosserat model but for (omega_c, v_{1,2}).
PS: I guess what Aurélie means is that in escript the number of equations and the number of spatial dimensions are not linked. So you can solve a 2D Cosserat model on a 2D domain.

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ceguo (hhh-guo) said : 		#4

Hi Aurélie,

- Since I have 3 unknowns (u_x, u_y, phi_z) and 3 momentum equations, if I use 2d domain, I will encounter "slice index out of range" error.
- Actually I already used DirectSolver by setting "mypde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)". But I still get "Paso_SparseMatrix_invMain: non-regular main diagonal block".

Maybe I should solve the problem by solving two coupled PDEs (one for stress equilibrium and one for moment equilibrium) instead of condensing them into one.

Ning

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Lutz Gross (l-gross) said : 		#5

"- Since I have 3 unknowns (u_x, u_y, phi_z) and 3 momentum equations, if I use 2d domain, I will encounter "slice index out of range" error."
Can you clarify where this error occurs?

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ceguo (hhh-guo) said : 		#6

I am solving a unknown vector u which has three components corresponding to u_x, u_y and phi_z respectively. So the coefficients of the general PDE A_ijkL, B_ijk, C_ijk and D_ij all have their subscripts running from 0 to 2. But in dim=2 case, it is not allowed and causes this error. I'm trying to separate the unknown variables to see if I can handle it. Thanks.

Ning

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Lutz Gross (l-gross) said : 		#7

If you solve a system of 3 equations on a 2D domain A_ijkl has the shape (3,2,3,2):

domain=Rectangle(...)
mypde=LinearPDE(domain, numEquations=3, numSolution=3)
print mypde.getShapeOfCoefficient("A")

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ceguo (hhh-guo) said : 		#8

Great!
After taking your advice, I got the code run. I'm trying to benchmark the results.
Thanks!

Ning