Stimuli-responsive shell theory

Shell structures are used widely in nature and human-made systems due to their ability to efficiently carry load using a relatively light structure, where the shell is a curved surface with small, but finite thickness compared to the other dimensions. The geometric characteristic of thin shells, i.e. slenderness, makes the shells able to rapidly change shape via elastic instabilities. Despite the traditional view of instabilities as deleterious and undesirable events for structural stability, nature has successfully harnessed these instabilities to morph the shape of soft thin shell systems for several purposes such as movement, development, and morphogenesis, which can result from non-mechanical stimuli, e.g. heating, swelling, and biological growth, in the absence of external, mechanical loadings. Through the shape-morphing process, lilies bloom during spring, and Venus flytraps catch prey. Additionally, this process has been applied to design soft robotics actuators and adaptive metamaterials. Therefore, this thesis aims to understand the deformation and the instabilities induced by non-mechanical stimuli for soft thin shells and to present a novel stimuli-responsive shell theory. First of all, two-field partial differential equations are derived for deformation problems under non-mechanical stimuli, based on the linear momentum balance for the mechanical field and the non-mechanical quantity balance for the non-mechanical field. For the mechanical field, the Kirchhoff-Love shell kinematics are utilized to describe the behavior of soft thin surfaces. In addition, the concept of the multiplicative decomposition of deformation gradient is applied to calculate the internal stress state induced by non-mechanical stimuli, and the projection method is employed in the stress constitution to consider the general multi-layer surface as an exact 2D shell. Moreover, the effect of mass addition from biological growth is dealt with on the stress constitution. For the non-mechanical field, the internal diffusion flux is ...