Functionally graded piezoelectric materials: modeling, thermal-electro-mechanical behavior and control strategies-A comprehensive Review

Abstract Functionally graded materials (FGMs) and their piezoelectric extensions (FGPMs) represent a significant advancement in structural materials, offering continuous variation in properties through the thickness that reduces stress concentration, enhances thermal resistance, and prevents delamination. When piezoelectric layers are integrated into FGMs, multifunctional systems with structural robustness and active sensing/actuation capabilities are obtained. This paper provides a critical review of two decades of research on FG and FGPM plates and shells, with emphasis on modeling, simulation, and active control. The review covers classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT), exact three-dimensional and state-space solutions, alongside numerical strategies including refined finite elements, smoothed FEM, and meshfree methods. Scale-dependent approaches such as nonlocal elasticity and modified couple-stress theory are discussed for micro- and nano-scale systems. The influence of thermal environments, nonlinear effects, actuator placement, and feedback control strategies is analyzed. Comparative tables summarize modeling assumptions, costs, and application domains. Finally, gaps such as limited experimental validation, lack of robust Multiphysics control, and the need for open benchmark datasets are highlighted. This review serves as a comprehensive resource and roadmap for advancing FGPM research toward aerospace, mechanical, and MEMS/NEMS applications.