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A general theoretical scheme for shape-programming of incompressible hyperelastic shells through differential growth
International Journal of Solids and Structures, Volume: 265-266, Start page: 112128
Accepted Manuscript under embargo until: 24th January 2024
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...
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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 toverify their correctness and accuracy. The simulation results show that thetarg et 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.
Hyperelastic shell, Differential growth, Shape-programming, Theoretical scheme, Numerical simulations
Faculty of Science and Engineering
This work is supported by the National Natural Science Foundation of China (Project No.: 11872184). Z.L. is supported by the China Scholarship Council (CSC) Grant #202106150121. M.H. and Z. L. are indebted to the funding through an Engineering and Physical Sciences Research Council (EPSRC), United Kingdom Impact Acceleration Award (EP/R511614/1).