Unveiling the Multiphysics Complexity: An Isogeometric Framework for Inducing Bifurcation and Tracing Post-Buckling Paths in Electroelastic Thin Shells
For researchers simulating soft actuators and sensors, this framework addresses the challenging problem of accurately modeling nonlinear multiphysics coupling and post-buckling in electroelastic shells.
This work presents an isogeometric Kirchhoff-Love shell formulation for simulating bifurcation and post-buckling in electroelastic thin shells under finite deformations. Numerical examples demonstrate accurate capture of large deformations and symmetry-breaking instabilities under coupled electromechanical loading.
Electroelastic shells are widely used in soft actuators, sensors, and energy harvesters owing to their large electrically induced deformations. However, the accurate simulation of their complex nonlinear multiphysics coupling, including bifurcation and post-buckling responses, remains challenging. This work presents an isogeometric Kirchhoff-Love shell formulation for the nonlinear analysis of electroelastic thin structures undergoing finite deformations. The formulation incorporates geometrically nonlinear kinematics, Maxwell-stress-induced electromechanical coupling, material incompressibility, and initial prestretch. Catmull--Clark subdivision surfaces are employed to ensure the C1 continuity required by Kirchhoff--Love shell theory. Consistent tangent operators are derived analytically, and a static condensation procedure is introduced to satisfy the plane-stress constraint. To trace bifurcation and post-buckling equilibrium paths, a staged Newton--Raphson algorithm with arc-length continuation and eigenmode perturbation is adopted. Numerical examples involving spherical membranes, prestretched circular plates, and toroidal membranes demonstrate the capability of the proposed framework to accurately capture large deformations, symmetry-breaking instabilities, and post-buckling responses under coupled electromechanical loading.