Thermodynamically Consistent Linear Electroelastic Formulation and FEM Study of Patch-Actuated Smart Structures: Validation and Interface Stress Evaluation

In this study the electromechanical response of a cantilever composite beam with surface-bonded piezoelectric patches is examined, focusing on interface stresses that may initiate delamination. A thermodynamically consistent electroelastic framework was specialized to the linear piezoelectric law used in finite element software, and a two-dimensional (2D) finite element model was developed and validated under static actuation. The predicted tip displacement was compared against the analytical Euler–Bernoulli solution across all seven mesh levels of the convergence study; findings indicated that the converged ANSYS 17.1 result (h = 5 × 10−5 m) differed from the analytical value by 5.8%, a discrepancy attributed to the plane-strain assumption and the neglect of shear deformation in the Euler–Bernoulli formulation. To resolve the delamination-critical behavior, three-dimensional (3D) models were built using SOLID185/SOLID5 and SOLID186/SOLID226 elements. Interfacial peel σy and shear τxy stresses were evaluated along lengthwise (PATH1) and transverse (PATH2) paths at the patch–core interface, with maximum interface stresses occurring along the transverse PATH2 near the free end, where strong three-dimensional edge effects developed. Both element sets predicted a similar tip displacement, but the SOLID186/SOLID226 elements yielded peak interface stresses approximately 19% higher in peel and 87% higher in shear along the critical transverse PATH2. These findings demonstrate that element choice minimally affects global stiffness but significantly influences local interface stress prediction, providing practical guidance for the selection of appropriate models when assessing the delamination risk in piezoelectric-actuated composite beams.