  In this work, we construct an effective continuum model for architected
sheets that are composed of bulky tiles connected by slender elastic joints.
Due to their mesostructure, these sheets feature quasi-mechanisms -- low-energy
local kinematic modes that are strongly favored over other deformations. In
sheets with non-uniform mesostructure, kinematic incompatibilities arise
between neighboring regions, causing out-of-plane buckling. The effective
continuum model is based on a geometric analysis of the sheets' unit cells and
their energetically favorable modes of deformation. Its major feature is the
construction of a strain energy that penalizes deviations from these preferred
modes of deformation. The effect of non-periodicity is entirely described
through the use of spatially varying geometric parameters in the model. Our
simulations capture the out-of-plane buckling that occurs in non-periodic
specimens and show good agreement with experiments. While we only consider one
class of quasi-mechanisms, our modeling approach could be applied to a diverse
set of shape-morphing systems that are of interest to the mechanics community.
