Hi all,

I am trying to create a simulation in FEniCS that is a good representation of a conventional tensile testing from zero load to material fracture. I pictured the problem in 3 stages, first to understand variational formulation for linearly elastic material, then that for elasto-plastic material and ultimately that of a realistic ductile metal which includes elastic regime, plastic regime and fracture regime.

My ultimate goal is to run the simulation and have it produce a stress-strain curve from zero stress at zero strain to zero stress at failure strain.

I have been using this numerical tour (https://readthedocs.org/projects/comet-fenics/downloads/pdf/latest/) for a great reference to linear elastic as well as elasto-plastic simulation. Also, I am trying to implement rigid boundary condition to simulate the conditions in a tensile test (Rigid Plate Boundary Condition). However, I am still missing the material softening (failing) part in my stress-strain curve at this point. While I have found several topics on this forum and other sources explaining fracture simulation with phase field in FEniCS, I realized that these examples are all studying the fracture process (fracture initiation + crack development) by itself and I have yet to find examples that implements a variational formulation which represents the material from elastic regime to complete fracture (zero load bearing capability).

I am posting this question here on the forum hoping that someone might have came across similar problems before and can shine some light to where I can find great resources for the variational formulation described above or whether such analysis is feasible in FEniCS

Thanks!

Sincerely,

Toby

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Borden et al. did some work on phase field fracture for ductile materials, which includes plastic yielding before fracture:

I have not tried to implement this in FEniCS, but it looks like the formulation is written up clearly enough for one to do so, and the main difficulties are already covered by the plasticity tutorial you linked above.

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Hi,

FEniCS is a general purpose finite-element solver. What you are asking is really a constitutive material question. Implementing non-linear constitutive material laws is not straightforward from scratch in FEniCS.

For this purpose, we worked to link FEniCS with the constitutive law code generator MFront, the corresponding module is described here along with some documented demos.

What type of constitutive law are you investigating ?

Hi bleyerj,

First of all, thank you for creating the numerical tours, that was very helpful.

I am trying to simulate ductile metal with linear elastic, and plastic deformation as well as damage. The von Mises plasticity with isotropic linear hardening as shown in the example will work for my purpose, but I am trying to implement ultimate tensile stress (UTS) as well as damage into the simulation as well.

I am not sure what constitutive law will be a good representation of the post UTS behavior of the metal but I am imagining something that can show a decrease in load bearing capacity to zero after the stress at Gauss points surpass the UTS, instead of just flagging the simulation to stop. In another word, I am looking for constitutive laws that will represents the material’s behavior from UTS to post fracture.

The reason that I am trying to implement damage into the simulation is for heterogeneous materials. For example, in a plane stress 2D case, if I have a square part/mesh and the left half is weaker than the right. In tensile testing, this sample will have a partial fracture in the left half first but not the right half, then the complete fracture happens when the right half surpass its UTS too. If I don’t have anything that represents the material past UTS, then the simulation would halt itself when the weaker half of the this heterogeneous structure breaks.

Sorry for my lack of systematic solid mechanics knowledge and hope my example illustrates my question.

Well, modelling material behaviour in the post-yielding stage until complete fracture is extremely hard. The softening regime introduces mathematical ill-posedness yielding to mesh dependency. Softening behaviours must therefore be regularized in some sense.

I suggest looking at literature on ductile damage models, phase-field methods, etc.

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