Supporting Information: Spatiotemporally programmable metasurfaces via viscoelastic shell snapping

Supplementary Text 1: Material modeling and characterization We used the following incompressible neo-Hookean material model to define the instantaneous constitutive behavior of the shells, = tr − 3, (S1) where W is the strain energy density function, µ is the shear modulus, F is the deformation gradient tensor. To describe the viscoelastic behavior of the shells, Prony series were used and the shear modulus µ can be expressed as = 1 − ∑ 1 − ⁄ , (S2) where µ0 is the instantaneous shear modulus, n is the number of the series terms, is the dimensionless relaxation modulus, t is the time, and τi is the relaxation time constant. Here we characterize the viscoelastic properties of the silicone rubber (Dragon SkinTM30) and urethane rubber (VytaFlexTM 20). We modeled their viscou