Theoretical scheme on shape-programming of thin hyperelastic plates through differential growth

TL;DR

This paper presents a theoretical framework for programming the shape of thin hyperelastic plates via differential growth, enabling the design of complex 3D shapes from flat plates for soft device manufacturing.

Contribution

A novel theoretical scheme linking growth functions to target shapes of hyperelastic plates using a derived finite-strain plate equation system.

Findings

Explicit relations between growth functions and target shapes.

Numerical simulations confirm the scheme's effectiveness.

Applicable for designing intelligent soft devices.

Abstract

In this paper, a theoretical scheme is proposed for shape-programming of thin hyperelastic plates through differential growth. First, starting from the 3D governing system of a hyperelastic (neo-Hookean) plate, a consistent finite-strain plate equation system is formulated through a series-expansion and truncation approach. Based on the plate equation system, the problem of shape-programming is studied under the stress-free assumption. By equating the stress components in the plate equations to be zero, the explicit relations between growth functions and geometrical quantities of the target shape of the plate are derived. Then, a theoretical scheme of shape-programming is proposed, which can be used to identify the growth fields corresponding to arbitrary 3D shapes of the plate. To demonstrate the efficiency of the scheme, some typical examples are studied. The predicted growth functions in these examples are adopted in the numerical simulations, from which the target shapes of the plate can be recovered completely. The scheme of shape-programming proposed in the current work is applicable for manufacture of intelligent soft devices.