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Periodic Conditions and defining strain on beam models
Posted Nov 12, 2021, 2:58 p.m. EST Structural & Acoustics, Parameters, Variables, & Functions, Structural Mechanics Version 5.6 1 Reply
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Hello, I've been working with the domain module "Cell Periodicity" on 3D structural mechanics for a while to obtain the Elastic Matrix and Compliance Matrix of different microstructures defining a RVE geometry. Recently I've been told to research the mechanical proberties of trabecular bone tissue, since it's a random structure I have to define a big and complex RVE so it becomes impossible to use Cell Periodicity since the mesh would have too many elements.
Our alternative is to use beam elements instead of solid 3D elements of structural mechanics, but Comsol doesn't have neither the Cell Perodicity, nor the Periodic Boundary Conditions that I use to define the 6 load cases to obtain the Elastic Matrix.
We are trying to reproduce the Periodic Boundary Condition by adding extra beams that are not part of the original geometry and they have a high cross section area and inertia moment, so when we define a coefficient of thermal expansionof 1 on those beams and we define a temerature of 294.15K they produce an unitary themal expansion that depends on how we orientate those "extra/imaginary beams" on our microstructure, so we use them to bind our points like in the Periodic Condition module and we orientate those beams and expand them depending on the load case we're trying to reproduce.
The thing is, this alternative becomes very unstable if we want to combine all those beams in a single model, by adding beams to make the load case 2 the load case 1 doesn' converge or gives a singular matrix, and to make the load cases 4 5 and 6 (the shear cases) I'd have to find a way to make the thermal expansion on x direction depend on the y coordinate and viceversa (load case of shear xy).
I'd like to know if there's a simpler way to bind edges to make a periodic condition and still use beam elements.
I'll add some images of my work (using cell periodicity and trying to reproduce the same RVE and load case with beams).
Best Regards.
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Just to let people know, I found an alternative way to do periodic conditions by defining integration coupling variables and variables that use those integrals on displacement.
Basically, all I had to do was define integrals at each point of my beams, and define variables that are either for the "source src" point or for the "destionation dst" point. For example, if I want to stretch at x direction, I define a variable at point x=0 Pu1, and then at the point at the opposite end of the x direction x=long I define displacement Pu2=Pu1+strain (that way, I make the periodic condition since the displacement is relative to the source point, and I added a strain to make the corresponding load case since I need to obtain the homogeneized elastic Matrix by stretching on each of the 6 load cases).
I hope this makes any sense for people wondering how to make a periodic condition in Comsol other than 3D models.
Best Regards.