Deformed Geometry
The equations solved by the Solid Mechanics interface are formulated in the material frame. The Deformed Geometry functionality in COMSOL Multiphysics allows one to make the material frame differ from the geometry frame, which implies that the geometry of the structure on the material frame can differ from that originally drawn. This is useful for analyzing the behavior of different shapes of an original object, for example as part of shape optimization.
In the COMSOL Multiphysics Reference Manual:
By default, the material does not follow a change in shape. Deformation of the geometric boundaries therefore corresponds to addition or removal of material.
The deformed geometry functionality can be also used to set up an incremental deformation of a structure. This can be achieved by using the Elastic Predeformation node in the Solid Mechanics interface. This can significantly speed up computations is case of large deformations.
Elastic Predeformation
The total displacement field of the solid is represented as
and the corresponding deformation gradient is multiplicatively decomposed as
One can use upd to define the displacement of the material frame with respect to the geometry frame, and take u as an update solution of the equations solved by the Solid Mechanics interface on the material frame. (The corresponding deformation gradient F connects the material and spatial frames.) Note that the virtual work on such a displacement update is done by the total stress, and to get the correct stress, one can use as Fpd the deformation gradient connecting the geometry and material frames, and then set the elastic deformation gradient to
(3-7)
This is used in the stress calculation during the update step. Thus, the transformation from geometry to material frame is assumed to be a result of elastic deformation.
The process can be repeated in a parametric sweep, for example, by gradually ramping up the load, so that the displacement update on each step is small. During each step, the previous value of the total displacement is used in the material frame definition
Alternatively, a time-dependent study can be used. In this situation, the above formula will be applied during each time step to recompute upd before the step, using the stored previous solution, while u will represent a displacement increment computed during the time step. In addition, the density is updated as ρ0/Jpd where
Again, Fpd is the deformation gradient connecting the geometry and material frames, and it will be updated before each time step or parameter sweep value.
The approach can be combined with large strain plasticity. In this case,
which together with Equation 3-7 gives
Note that both Fel and Fpl represent the total deformations of their corresponding types, while Fpd is the total (elastic and plastic) deformation gradient from the previous update.