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determining the local area change
Posted 12.03.2021, 04:13 GMT-5 Structural & Acoustics Version 5.5 5 Replies
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Hello, we would like to determine the local area change of a deformed membrane (e.g. a spherical balloon which is blown up from r1 to r2 = 2r1 would have an area change of (2r1/r1)^2 = 4 on each point of the surface. An arbitrary object could exhibit different local area changes throughout the surface). "Include geometric nonlinearity" is activated.
Generally, the area change can be calculated out of the deformation gradient F using Nanson's formula. This involves an inversion and transposition of F, however the expression field only allows the entry of single components of F, e.g. FdxX, which would make the insertion of the whole formula quite hard. Is there any other way of inserting a matrix operation as expression without using individual components?
Or is there already another method implemented for determining the local area change? I was looking at the ratio of meshvol_spatial/meshvol, as it seems that evaluating meshvol_spatial on a surface yields the mesh area. Could anyone confirm if that's a valid approach?
Thanks a lot!
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You can use the variable mbrn.J_area which is available in the Membrane interface.
-------------------Henrik Sönnerlind
COMSOL
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alright great, thanks for pointing this one out! What would be the approach for a geometry where the Membrane interface is not applicable? Do you know by any chance how mbrn.J_area compares to my suggestion of evaluating meshvol_spatial/meshvol?
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Yes, meshvol_spatial/meshvol will work, as long as the problem is not axisymmetric. In that case, the circumferential extension is not taken into account, but you could use the expression
meshvol_spatial/meshvol*r/R
-------------------Henrik Sönnerlind
COMSOL
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awesome, thanks for confirming! Yep, I encountered mentioned deviation for axisymmetric problems, thanks for pointing that out. One last question: So meshvol_spatial evaluated on a surface yields the area of the mesh-element on the surface whereas spatial.J_mesh or solid.J takes the whole volume of the mesh-element (which is however selected by bordering the surface) into account, correct?
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Correct!
-------------------Henrik Sönnerlind
COMSOL