Hello Xiao,

The legend in the stress-strain curve opens a question I'd like to ask. What is the material? Is it a type of microstructure that can exhibit buckling? I see the measures in the graph are stress and strain, so this means it is normalized at some scale length. Most commonly in structural mechanics, we see buckling associated with a component (plate, column, beam, etc.), so at the material level, it may still behave in a more expected manner of a linear or nonlinear material and the buckling is a function of the design. For example column buckling. We can see the buckling behavior of a column, but at the material level we are not seeing this in the stress-strain curve, it is a function of the geometry. My point is to check if you need to isolate the material response from the geometric response. I'll give another example. A composite honeycomb panel can exhibit facesheet buckling behavior, but this is a function of the design, not the actual materials. Something you might want to just check. I can imagine novel materials that do have a microstructure that does exhibit local buckling. Think of some additive materials with very slender lattice structures that upon compression, those "miniature beams" buckle, then as the space between them is closed up potentially, there is self contact the compression stiffens. It would be good to know what is the material and structure. In a simulation, we may wish to model the "miniature beams" of the lattice in this example, and then we just need a standard material model, as the FEM captures the geometry. But if you are trying to do this at a larger scale and include that geometry effect in the material model, then it can be more effort to get the model to fit that scale of response.

Regards,

Sean