A general theoretical scheme for shape-programming of incompressible hyperelastic shells through differential growth. (15th March 2023)

• Record Type: Journal Article
• Authors: Li, Zhanfeng; Wang, Jiong; Hossain, Mokarram; Kadapa, Chennakesava
• Is Part Of: International journal of solids and structures. Volume 265/266(2023)
• Publication Date: 2023-03-15
• Subjects: Hyperelastic shell -- Differential growth -- Shape-programming -- Theoretical scheme -- Numerical simulations; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2023.112128
• Languages: English
• ISSNs: 0020-7683

Abstract

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. Graphical abstract: Highlights: A consistent finite-strain shell theory with the growth effect is established. Shape-programming of shell samples through differential growth is investigated. The explicit growth functions corresponding to any target surfaces are derived. A theoretical scheme for shape-programming of hyperelastic shells is proposed. Some typical examples are studied to demonstrate the efficiency of the scheme.