  Flexoelectricity - the generation of electric field in response to a strain
gradient - is a universal electromechanical coupling, dominant only at small
scales due to its requirement of high strain gradients. This phenomenon is
governed by a set of coupled fourth-order partial differential equations
(PDEs), which require $C^1$ continuity of the basis in finite element methods
for the numerical solution. While Isogeometric analysis (IGA) has been proven
to meet this continuity requirement due to its higher-order B-spline basis
functions, it is limited to simple geometries that can be discretized with a
single IGA patch. For the domains, e.g., architected materials, requiring more
than one patch for discretization IGA faces the challenge of $C^0$ continuity
across the patch boundaries. Here we present a discontinuous Galerkin
method-based isogeometric analysis framework, capable of solving fourth-order
PDEs of flexoelectricity in the domain of truss-based architected materials. An
interior penalty-based stabilization is implemented to ensure the stability of
the solution. The present formulation is advantageous over the analogous finite
element methods since it only requires the computation of interior boundary
contributions on the boundaries of patches. As each strut can be modeled with
only two trapezoid patches, the number of $C^0$ continuous boundaries is
largely reduced. Further, we consider four unique unit cells to construct the
truss lattices and analyze their flexoelectric response. The truss lattices
show a higher magnitude of flexoelectricity compared to the solid beam, as well
as retain this superior electromechanical response with the increasing size of
the structure. These results indicate the potential of architected materials to
scale up the flexoelectricity to larger scales, towards achieving universal
electromechanical response in meso/macro scale dielectric materials.
