Hello guys :grinning_face_with_smiling_eyes: ! So i wanna calculate the components of a 2D stiffness tensor and i already have all the values of the stress (sigma11,sigma22,sigma12) and strains (epsilon11,epsilon22,epsilon12). How can i do that ? [stifnesss]

@CHAIkah : After thinking about this problem some more, I have realized I should make one minor correction to my answer(s). The 2D strain vector is generally formulated as \varepsilon = \begin{bmatrix} \varepsilon_{11} \\ \varepsilon_{22} \\ \gamma_{12} \end{bmatrix} = \begin{bmatrix} \varepsilon_…

Any ideas about how can we solve that ? :cold_sweat:

Hi @CHAIkah , It would help if you provide a little more detail about your problem. For example: Are you trying to solve a homogenization problem? (i.e. to find the effective stiffness tensor) What format do you have the stresses and strains in? For example, do you know the strains pointwise throu…

Hey @conpierce8 ! Yes it’s a homogenization problem so I’m trying to extract the effective stiffness tensor. It’s a 2D square divided into 10 phases each phase contains a different material under compression on the top and bottom boundaries. I didn’t specify in the code if it’s plane strain/stres…

Hi @CHAIkah , I’ll be able to help you more effectively if you provide a code example. In the meantime, note the following: You need to study three different load cases (uniaxial strain in x, uniaxial strain in y, and shear strain) to get the full 2D stiffness tensor. (This is the approach taken i…

Hi @CHAIkah , Since this isn’t a working code, I can’t provide a full solution. But, you should be able to use sigma_fs = TensorFunctionSpace(mesh, "Real", 0) sigma_test = TestFunction(sigma_fs) sigma_avg = assemble(sum(inner(sigma(w, i), sigma_test)*dx(i) for i in range(nphases))) / area to compu…

[image] conpierce8: You need to study three different load cases (uniaxial strain in x xx , uniaxial strain in y yy , and shear strain) you mean i need to study three different load cases (uniaxial strain in x , uniaxial strain in y , and shear strain and each time i’ll get a column of the te…

That’s correct. The “effective stiffness” tensor C^{eff} is defined by the relation \left< \sigma \right> = C^{eff} \left< \varepsilon \right> where \left<\cdot\right> denotes the volume average. When you apply an affine boundary condition, the volume average of the strain \left< \varepsilon \rig…

i understand now. Thank you it works ! but @conpierce8 this is what i got and i don’t understand why isn’t symmetrical. -1.572410583195420555e-03 2.216522418232252676e+03 1.108260422906548456e+03 4.414543445680684272e+03 -6.237213042085443552e-04 2.207271410980084511e+03 -6.237146402310145103e-…

@CHAIkah can you share your complete code? I suspect there may be an error with your boundary conditions, since the third column is a linear combination of the first two columns (within discretization error).

Hi @CHAIkah , Your affine Dirichlet boundary conditions should be applied on all boundaries. In order to directly extract the stiffness tensor components from the average stress, you need to apply a unit strain. Otherwise you will need to divide the stress by the strain to find the stiffness tensor…

Extract stiffness tensor C

CHAIkah July 8, 2021, 1:04pm 8

you mean i need to study three different load cases (uniaxial strain in x , uniaxial strain in y , and shear strain and each time i’ll get a column of the tensor ?

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Extract stiffness tensor C

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