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

A discontinuous Galerkin method based isogeometric analysis framework for flexoelectricity in micro-architected dielectric solids