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

Li, Zhanfeng; Wang, Jiong; Hossain, Mokarram; Kadapa, Chennakesava

Authors

Zhanfeng Li

Jiong Wang

Mokarram Hossain



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 one of the possible growth tensors (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 typical 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.

Citation

Li, Z., Wang, J., Hossain, M., & Kadapa, C. (2023). A general theoretical scheme for shape-programming of incompressible hyperelastic shells through differential growth. International Journal of Solids and Structures, 255-256, Article 112128. https://doi.org/10.1016/j.ijsolstr.2023.112128

Journal Article Type Article
Acceptance Date Jan 20, 2023
Online Publication Date Jan 24, 2023
Publication Date 2023-03
Deposit Date Feb 15, 2023
Journal International Journal of Solids and Structures
Print ISSN 0020-7683
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 255-256
Article Number 112128
DOI https://doi.org/10.1016/j.ijsolstr.2023.112128
Keywords Hyperelastic shell, Differential growth, Shape-programming, Theoretical scheme, Numerical simulations