The code I used for this simulation was adapted from this paper by Hirshikesh, S. Natarajan, R. K. Annabattula, E. Martinez-Paneda. I also found this post to be helpful to reproduce the results given in the paper.
But now, I wanted to see the crack movement along with the displacement between the nodes of mesh elements where they are separated by crack as shown in the first image I attached above.
I hope to know how this can be done using FEniCS. Any inputs on this would be appreciated.
Thank You
Hi! So here are some thoughts on this problem:
The first simulation you showed clearly changes the mesh by both refiniement/remeshing techniques and by changing the connectivity of the nodes and the overall geometry of the mesh. Therefore the crack is represented by the shape of the mesh. In your simulation, following the approach from the paper you attached, the crack is approximated by a phase field function. So the aim of the model from the paper is to represent the crack just by a function and alter the mechanical properties in the crack according to that function, so that the elements in the crack region would behave as if there are no elements. My point is that if you want to model the crack as geometric property of the mesh you would also have to rethink the equations proposed in the paper. A crack propagation simulation is not the same as a phase field model for cracking.
Now to your actual question:
One possiblity would be to directly modifiy the mesh. You could run a simulation and stop it if a critical stress is reached in the cracktip and then delete overstressed elements from the dolfinx mesh object. You can use the cell_tags propertiy to find those elements by index. A more sophisticated way to introduce the discontinuity in the cracktip would be to use discontinuous Galerkin (“DG”) elements of degree 1 or higher for the displacement field. As the vertex values of neighbouring DG1 elements can be discontinuous the elements don’t have to “touch” each other and can move apart. But this would also require some additional trickery since you would want this porperty only in the crack and you would have to define when the seperations happen and what happens if the crack is closed again and so on. But don’t just use DG1 functions for your model - this will not work!
Hi @wolfla, Thanks for your insightful take on this problem. Sorry for the late reply.
I wanted to ask that what constitutive relations I must use ? in addition to the good old linear elastic relations such as -
I would like to know where I can find those equations which does include the fracture modelling, their strong forms and weak (or variational) forms which would let me proceed with this problem. For now I am concerned with elastic behaviour + fracture (generally brittle material property), in the future I wish to introduce plasticity as well.
Any inputs on the same would be highly appreciable.
Thank You.
