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Material coordinate in the General Form PDE
Posted Aug 16, 2023, 1:54 p.m. EDT General, Structural Mechanics, Modeling Workflow 4 Replies
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I'm aware that in Comsol, x, y, z coordinates are utilized for Spatial coordinates, while X, Y, Z are used for Material coordinates. The transformation for Spatial and Material aspects is managed by the Solid Mechanics Interface when the solid undergoes deformation.
My query pertains to employing General Form PDE to manage mechanical deformation. How can I effectively apply the solved u, v, w to modify the values of Spatial coordinates x, y, z for unrelated non-mechanical simulations? Any advice will be appreciated.
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Here is one possible approach:
In the General Form PDE interface, set the frame to Material.
Then, you add Moving Mesh with Prescribed Deformation to the domain, and enter (u,v,w) as the deformation vector.
-------------------Henrik Sönnerlind
COMSOL
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Here is one possible approach:
In the General Form PDE interface, set the frame to Material.
Then, you add Moving Mesh with Prescribed Deformation to the domain, and enter (u,v,w) as the deformation vector.
I appreciate your insightful answer. I have an additional inquiry. I'm curious about the scenario where a Solid Mechanics Interface coupled with General Form PDE for a time-dependent analysis, i.e. both two studies are added into the same component and the dependent variables of these two physics are coupld in some ways. In each computational step, the Solid Mechanics interface calculates the deformed structure as well as the deformation gradient that links the material and spatial frames. My question is, as these calculations progress, does the spatial frame x, y, z for the General Form PDE also undergo iterative updates according to the spatial frame of Solid Mechanics? Furthermore, are these evolving spatial coordinates employed for calculating spatial derivatives within the General Form PDE? I hope COMSOL can automatically handle it.
Something I would like to add is for the coupling between Solid Mechanics and Electrostatics interface, in the Equation View of Charge Conservation, we can see a clear definition of electric fields as follows:
From material frame,
es.EX = -VX
es.EY = -VY
es.EZ = -VZ
Transform to spatial frame,
es.Ex = spatial.invF11 es.EX+spatial.invF12 es.EY+spatial.invF13 es.EZ
es.Ey = spatial.invF21 es.EX+spatial.invF22 es.EY+spatial.invF23 es.EZ
es.Ez = spatial.invF31 es.EX+spatial.invF32 es.EY+spatial.invF33 es.EZ
I'm curious if, in the Discretization method of the General Form PDE, the selection of the Spatial frame implies an implicit transformation from material to spatial frame?
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If you use Spatial Frame in the General Form PDE, then the equations are interpreted in the current spatial frame, as given by the deformations from Solid Mechanics.
What you see in the equations for electrostatics is a slightly different case: Equations formulated on material frame, with results variables converted to spatial frame. Note that there is a setting in Charge Conservation (Solid/Nonsolid) which determines whether the equations are formulated on material or spatial frame.
-------------------Henrik Sönnerlind
COMSOL
Please login with a confirmed email address before reporting spam
If you use Spatial Frame in the General Form PDE, then the equations are interpreted in the current spatial frame, as given by the deformations from Solid Mechanics.
What you see in the equations for electrostatics is a slightly different case: Equations formulated on material frame, with results variables converted to spatial frame. Note that there is a setting in Charge Conservation (Solid/Nonsolid) which determines whether the equations are formulated on material or spatial frame.
Thank you for the detailed explanation! Your insights about the different frame choices and their implications in these fields are really helpful. I appreciate your response.