Electric–Mechanical coupling analysis of two-dimensional piezoelectric heterogeneous materials in flexible electric devices with extended multiscale isogeometric analysis

Piezoelectric heterogeneous materials are widely used in flexible electronic device design, enhancing sensitivity to external stimuli like pressure and acceleration. Despite their usefulness, analyzing these inherently periodic structures poses significant computational challenges. In response, this paper presents a multiscale isogeometric analysis approach tailored for simulating piezoelectric materials. We introduce an electric–mechanical coupling model using isogeometric analysis (IGA) for two-dimensional piezoelectric membrane structures, assuming the plane stress hypothesis. Our proposed algorithm enables precise calculation of both displacement and electric potential solutions, demonstrating superior convergence properties compared to traditional finite element methods. Furthermore, we extend this approach to multiscale isogeometric analysis for computing numerical solutions in porous structures and heterogeneous composite piezoelectric materials under tensile and bending conditions. Through rigorous numerical testing, we evaluate the proposed extended multiscale isogeometric analysis method, showcasing its efficacy in achieving a balance between computational efficiency and simulation accuracy. This IGA-based electro-mechanical coupling model and numerical algorithm pave the way for more streamlined and precise simulations of piezoelectric materials within the context of flexible electronic devices.