3D FEA with geometric nonlinearities was performed using the commercially available package Abaqus (Dassault Systèmes). The residual stress-induced self-rolling behavior of the 3D-SR-BAs was modeled as a differential thermal expansion–driven shape transformation problem, where hypothetical thermal expansion coefficients were assigned to the constituent layers (35). The temperature was gradually raised to such a level that the resultant thermal stresses were equivalent to the residual stresses. A combination of homogeneous (for regions occupied by only SU-8) and composite (for regions patterned with Pd and Cr) shell sections was used in the computations. The thicknesses and material properties of SU-8, Pd, and Cr layers were summarized in table S1. For meshing, the four-node shell element S4R with reduced integration, hourglass control, and finite membrane strains was used. To replicate the experimental design where one end of our 3D-SR-BA was free to roll along the longitudinal axis while the other was physically anchored to the substrate, we applied an unconstrained boundary condition along the edge at one end, and a fully fixed boundary condition was applied at the opposite end.

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