A general theoretical scheme for shape-programming of incompressible hyperelastic shells through differential growth

TL;DR

This paper develops a comprehensive theoretical framework for shape-programming of incompressible hyperelastic shells using differential growth, enabling precise control of shell deformation to desired shapes with practical applications in soft device design.

Contribution

It introduces a general theoretical scheme for shape-programming of hyperelastic shells via differential growth, including explicit growth tensor derivation and validation through numerical simulations.

Findings

Explicit growth tensors can produce target shell shapes.

Numerical simulations confirm the accuracy of the shape-programming scheme.

The scheme is applicable to designing soft, intelligent devices.

Abstract

In this paper, we study the problem of shape-programming of incompressible hyperelastic shells through differential growth. The aim of the current work is to determine the growth tensor (or growth functions) that can produce the deformation of a shell to the desired shape. First, a consistent finite-strain shell theory is introduced. The shell equation system is established from the 3D governing system through a series expansion and truncation approach. Based on the shell theory, the problem of shape-programming is studied under the stress-free assumption. For a special case in which the parametric coordinate curves generate a net of curvature lines on the target surface, the sufficient condition to ensure the vanishing of the stress components is analyzed, from which the explicit expression of the growth tensor can be derived. In the general case, we conduct the variable changes and derive the total growth tensor by considering a two-step deformation of the shell. With these obtained results, a general theoretical scheme for shape-programming of thin hyperelastic shells through differential growth is proposed. To demonstrate the feasibility and efficiency of the proposed scheme, several nature-inspired examples are studied. The derived growth tensors in these examples have also been implemented in the numerical simulations to verify their correctness and accuracy. The simulation results show that the target shapes of the shell samples can be recovered completely. The scheme for shape-programming proposed in the current work is helpful in designing and manufacturing intelligent soft devices.