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

Saurav Sharma; Cosmin Anitescu; Timon Rabczuk

Home/Archive/arXiv

arXiv · 2311.15073

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

Saurav Sharma·Cosmin Anitescu·Timon Rabczuk

View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cs.CE

Keep this discovery

BibTeX RIS

Saurav Sharma, Cosmin Anitescu, Timon Rabczuk. 2023-11-25. A discontinuous Galerkin method based isogeometric analysis framework for flexoelectricity in micro-architected dielectric solids. https://arxiv.org/abs/2311.15073

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Framework for Discharge Time Prediction of Energy Storage Units Based on Coupled Dynamics and Multi-Factor Aging Models

This paper presents a physically interpretable framework for predicting time to empty (TTE) in portable embedded systems. The framework couples usage-driven load-power decomposition, electrical power-voltage-current closure, a semi-empirical aging model, and SOC-temperature dynamics. Smartphone telemetry is mapped to battery current through an interpretable load model and conversion-efficiency correction. Battery capacity loss is modeled by combining Arrhenius temperature dependence, SEI diffusion behavior, and cycle-related power-law degradation. The coupled dynamic model then predicts TTE under different initial SOC values, ambient temperatures, and usage profiles. Chronological hold-out evaluation on a 6.9-h smartphone discharge session yielded a current RMSE of 0.0095 $\pm$ 0.0006 A, a temperature RMSE of 2.93 $\pm$ 0.24$^\circ$C, and a TTE MAPE of 4.81 $\pm$ 0.61%. Evaluation on NASA cell B0005 produced a capacity-loss RMSE of 0.031 Ah. Baseline, ablation, and counterfactual analyses further illustrate the contributions of thermal and aging corrections and the relative influence of load features. The results demonstrate the feasibility and interpretability of the proposed framework, while broader validation across devices and batteries remains necessary.

cs.CE↗

arXiv2026

Node-Shift-Encoding Genetic Algorithm with fuzzy-enhanced reference tour to solve the bi-objective service-oriented TSP

The Travelling Salesman Problem (TSP) remains a key area of research in combinatorial optimization, with applications in logistics, manufacturing, and service delivery. This paper addresses a bi-objective service-oriented TSP in which the clients' ranks in the delivery path matter. Unlike conventional depot-based TSP formulations, the considered problem does not assume a distinguished depot or a fixed tour origin. To address this setting, we adapt the Miller--Tucker--Zemlin (MTZ)-based formulation and derive an original linearization of the resulting model, enabling its solution with off-the-shelf integer linear programming solvers. This adaptation avoids the rigid tour origin imposed by the conventional MTZ formulation, for which fixing the starting node does not affect the tour cost but can affect the objective in a customer-rank-sensitive TSP. To solve this problem, we present a Node-Shift-Encoding (NSE)-based Genetic Algorithm augmented with fuzzy reasoning to update the reference tour throughout the evolutionary process. Experimental evaluation on TSPLIB benchmarks demonstrates that the proposed method achieves improved performance compared with the classical NSE approach.

cs.CE↗

arXiv2026

Geometric organization of olfactory descriptor data in the Poincar\'e disk

Odor quality is commonly represented using high dimensional descriptor profiles, yet their low dimensional organization remains unclear. We investigated whether a two-dimensional hyperbolic embedding can provide an interpretable representation of this structure. We applied hyperbolic metric multidimensional scaling to two complementary datasets: 480 Sagar rating profiles from three participants rating 160 odorants on 15 continuous descriptors, and 4983 GoodScents--Leffingwell molecules annotated with 138 binary descriptors. The embeddings substantially preserved pairwise descriptor distances, supporting subsequent analyses of radial and angular organization. In Sagar, rating profile entropy was strongly and negatively associated with hyperbolic radius, with diffuse profiles closer to the center and concentrated profiles closer to the boundary. This radial organization emerged primarily at the level of the full descriptor profile, rather than any individual descriptor, and remained robust across alternative descriptor representations, participant specific analyses, and averaged ratings. Sweet, musky, fruity, pleasantness showed the strongest directional trends. In GoodScents--Leffingwell, active label entropy, reflecting descriptor multiplicity, increased with radius, whereas orthogonalized descriptor entropy, reflecting spread across orthogonal modes, decreased with radius. Related binary descriptors occupied coherent localized high-density regions. These findings reveal complementary radial and angular organization in the hyperbolic representation of olfactory descriptor data. They support hyperbolic mapping as an interpretable descriptive framework in which radius summarizes global profile properties, while the angular component captures continuous descriptor gradients and categorical organization.

cs.CE↗