Weak Form of mixed-formulation for time-domain wave equation ?

Hi,

I want to simulate Asymptotic Homogenization (AH) on a unit cell to see the anisotropy of the unit cell in Abaqus. Has anyone tried to simulate this homogenization method in Abaqus?

I am using following code in python script in abaqus to get the stress data at nodes. How to get it according to global node number so it is easier to plot.

All_points = odb.steps['Step1'].frames[-1].fieldOutputs['S'].getSubset(region=sett,position=ELEMENT_NODAL).values

This gives output according to local node number.

Thank you!

I have small-scale prisms DIC's data and I am wondering about removing the rigid body motion from all the data or just until the peak load(elastic stage).

Hello, i am searching for breast cancer elastography datasets, so that by using machine learning technique, sort out whether the given elastography of breast is benign or malignant.

However i cannot find the place to get enough number of elastography datas...

Would you let me know any?

I sincerely appreiciate it in advances!

I am wondering how Dirichlet boundary conditions in global sparse finite element matrices are actually implemented efficiently. For example lets say that our global finite element matrix was:

K=[5 2 0 -1; 2 4 1 0; 0 1 6 3; -1 0 3 7]

And right-hand side vector b:

b=[b1; b2; b3; b4]

Then to apply a Dirichlet condition on the first node (x1=c) we would zero out the first row, put a 1 at K11, and subtract the first column from the right-hand side. For example our system would become:

K=[1 0 0 0; 0 4 1 0; 0 1 6 3; 0 0 3 7]

Right-hand side:

b=[c; b2-2*c; b3-0*c; b4+1*c]

This is all well and good in theory, but if our K matrix is stored in compressed row format (CRS) then moving the columns to the right-hand side becomes expensive for large systems (with many nodes being dirichlet). An alternative would be to not move the columns corresponding to a Dirichlet condition to the right-hand side, i.e. our system would become:

K=[1 0 0 0; 2 4 1 0; 0 1 6 3; -1 0 3 7]

b=[c; b2;b3;b4]

This however has a major draw back in that the system is no longer symmetric and so we could no longer use preconditioned conjugate gradient (or other symmetric solvers). As far as I know there are a lot of commercial and non-commercial codes using csr format and solving boundary condition problems and

I am assuming that there is probably some standard efficient method used in these commercial or non-commercial codes that solves this problem (obviously I not expecting people to know all the inner workings of every commercial finite element solver, but this problem seems fundamental enough that someone likely has worked on such projects and could provide guidance). I would be grateful if you could help me with detail.

P.S

I am solving the poisson equation with finite element method using simplex triangular element. I stored the non_zero value of global stiffness matrix in compressed row storage format. Also I'm using preconditioned conjugate gradient method parallelized with MPI for solving the system of linear equations. The bottleneck of my work is how to apply the boundary condition in this format.

I am working on the edge and facet finite element method with periodicity conditions, and I need a free, flexible mesh generator to create periodic meshes. Thanks for your help

I generated different 2D microstructures with different fiber volumetric fraction (basically a square representing the matrix and a lot of small rectangles inside, with different measures and random orientations, representing the fibers) I'm attaching an image to be clearer.

To run the simulations using Abaqus I need to define the properties of the two materials, the carbon fibers and the matrix. Regarding the carbon fiber, its properties change in the x direction (main lenght of the fiber) and the y direction. But when I define the material, x and y are referred to the main coordinate system, while I need to refer them to the different directions of the fibers. What can I do? I cannot manually set the axis orientations for each fiber creating new coordinate systems, it would be too timeconsuming considering that I have configurations with 40% of fibers (more than 400). I need to find a way to set the properties according to the main axis of the fibers (rectangles).

To be more specific, I created an RSA alghoritm in Matlab to create the random distribution of fibers. Then, I create the main square (representing the matrix of the composite) in Abaqus and I create the fibers by partion, importing the generated fibers distribution as a sketch.

Thank you all for your attention.

Tilted transverse isotropy (TTI) is sometimes treated as a rotated vertical transverse isotropy (VTI) rock (Figure 1). I have the 6x6 stiffness matrix of a rotated VTI as in the following Figure 2. Then, I would like to rotate or transform into a true coordinate, how could I perform such coordinate transformation to my stiffness matrix?