The FEA will do what you ask of it, but you have to interpret it properly.
1. Let’s first consider a linear static analysis.
1a. If the stress concentration is finite (i.e. a plate with a hole), the FEA will be able to determine the magnitude of the stress concentration (once convergence is achieved).
1b. If the stress concentration is theoretically infinite (a sharp internal feature or crack), the stress will continue to increase upon mesh refinement (will not converge because the stress is theoretically infinite). This is what a classical solution would predict so the FEM is doing what you should expect it to.
Note: Item 1 is where some people call stress concentrations in FEA “artificial”, but that is not really the case. The FEA actually does what it should, but it’s up to the engineer to address the following items properly. So let’s have a closer look.
2. The next question is how to address the stress concentration. Let’s first consider the static ultimate load case for when the stress concentration is finite. There are two options.
2a. This can be addressed via FEM with a nonlinear analysis (material nonlinearity), but you will also need to know the stress-strain curve of the material *and* have an adequate failure criterion. Note that for composites, a failure criterion to address this scenario does not exist (with the possible exception of a not well-accepted micromechanics criteria). More times than not, we usually go to item 2b.
2b. Rather than using the FEM to solve the problem directly, we can break this into two options (materials that are notch sensitive versus materials that are notch insensitive). If the material is notch insensitive (i.e. ductile), we can ignore the stress concentration (close approximation to the real solution), provided the volume of material in high stress region is relatively small (if there is large volume of material in the region of the stress concentration, this assumption is less valid). We can also use hand calculations and the stress concentration (strain concentration) to get a more accurate result. If the material is notch sensitive (brittle metals, composites, ceramics, etc.), the stress concentration will affect the static ultimate capability and must be considered. For truly brittle materials, this is rather direct (proportionality applies). However, composites are “pseudo-plastic” or “quasi-brittle” and you can’t treat them as either brittle or ductile (at least not in an accurate manner). You will need a different approach for that.
3. Now consider the static ultimate load case for when the stress concentration is theoretically infinite. This is actually a fracture mechanics problem and not a true stress analysis. And you can’t expect a FEA stress analysis to solve a fracture mechanics problem. That said, there are some similarities as discussed in item 2 and some approximations you can make, but be aware of this distinction.
Note: For some problems/industries, there are semi-empirical factors that can be used to correlate the results from the FEA to useful data. But that requires additional testing and is often used when “pure” analytical solutions do not effectively capture the behavior (i.e. test data is used to compensate for analytical shortcomings). Some examples include welds and composite structures.
4. Finally, we should also consider fatigue analysis. If the material is a ductile metal, the stress concentration will affect the fatigue life, so we can’t ignore it this time. If it is finite, you may start with solution to determine the life to develop a crack (i.e. something like Miner’s rule). If it is infinite, you may start directly with LEFM.
Brian
