  Cutting-edge smart materials are transforming the domains of soft robotics,
actuators, and sensors by harnessing diverse non-mechanical stimuli, such as
electric and magnetic fields. Accurately modelling their physical behaviour
necessitates an understanding of the complex interactions between the
structural deformation and the fields in the surrounding medium. For thin shell
structures, this challenge is addressed by developing a shell model that
effectively incorporates the three-dimensional field it is embedded in by
appropriately accounting for the relevant boundary conditions. This study
presents a model for the nonlinear deformation of thin hyperelastic shells,
incorporating Kirchhoff-Love assumptions and a rigorous variational approach.
The shell theory is derived from 3D nonlinear elasticity by dimension reduction
while preserving the boundary conditions at the top and bottom surfaces of the
shell. Consequently, unlike classical shell theories, this approach can
distinguish between pressure loads applied at the top and bottom surfaces, and
delivers a platform to include multi-physics coupling. Numerical examples are
presented to illustrate the theory and provide a physical interpretation of the
novel mechanical variables of the model.
