An embedding-aware continuum thin shell formulation

TL;DR

This paper develops a nonlinear hyperelastic shell model that incorporates three-dimensional field effects and boundary conditions, enabling accurate simulation of smart material behaviors in thin structures.

Contribution

It introduces a continuum shell formulation derived from 3D elasticity that accounts for multi-physics coupling and distinguishes between different pressure loadings.

Findings

The model accurately captures complex deformation behaviors.

Numerical examples validate the theoretical approach.

The formulation allows for multi-physics interactions in thin shells.

Abstract

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.