Fig 2. Analytical and computational models.
(A) Cartoon of post with analytical model parameters defined. The lower segment (blue) of the post is made of PDMS, and the top (gray) is the Ni shell. The black center line represents the deflection of the beam from the relaxed upright position (parameterized by w(s)). Note that since the Ni segment does not bend, w(s) for the Ni shell for all time points is entirely determined by the position and angle of the PDMS segment at its top end. The applied magnetic field applies a moment to the Ni segment (Mmag). (B) The analytical model focuses on the PDMS portion of the ASAP and incorporates the magnetic and drag forces experienced by the Ni segment as shear force and moment boundary conditions at the top end of the PDMS segment (Sdrag, Mmag and Mdrag). There is an applied moment from the magnetic field, and there are shear and moment drag terms generated by the motion of the Ni portion that are entirely determined by the time dependent position and angle of the top end of the PDMS portion. (C) Rendering from COMSOL showing the mesh and geometry of the finite element model. The model has no slip boundary conditions on the top and bottom, blue; while the left and right sides can have either no-slip or slip boundary conditions, red. The entire post, both the elastic lower portion and the stiffer upper shell, are explicitly modeled. The surfaces perpendicular to the plane of the post motion, orange, have zero pressure boundary condition. Box Dimension: 50 um x 50 um x 100 um.