A theoretical scheme for shape-programming of thin hyperelastic plates through differential growth

Wang, Jiong; Li, Zhanfeng; Jin, Zili

doi:10.1177/10812865221089694

Cited by 11 publications

(15 citation statements)

References 36 publications

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“…When solving some concrete problems, the plate equation may be further simplified. For some problems, the plate equation with the asymptotic order O(h) (i.e., only the first two terms of S are substituted in (26)) can already provide accurate predictions on the growth-induced deformations of the hyperelastic plates [42,29]. For some other problems, the magnitudes of the displacement components can be identified in advance, thus the asymptotic analyses may be conducted to simplify the plate equations [24,43].…”

Section: Remarksmentioning

confidence: 99%

“…Dias et al [51], Jones and Mahadevan [52], Acharya [53], Nojoomi [54]). In our previous works [25,28,29], some explicit formulas for shape-programming of single-layered hyperelastic plates through differential growth have been derived. Here, based on the multi-layered plate theory proposed in section 3, we aim to derive some explicit formulas for shape-programming of multi-layered hyperelastic plates.…”

Section: Growth-induced Axisymmetric Deformations Of Bilayer Circular...mentioning

confidence: 99%

“…Thus, it is suitable for modeling the growth-induced deformations in soft material samples. Applications of this plate theory can be found in Wang et al [25], Kadapa et al [26], Mehta et al [27], Li et al [28], Wang et al [29].…”

Section: Introductionmentioning

confidence: 99%

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On a general multi-layered hyperelastic plate theory of growth

Du¹,

Li²,

Chen³

et al. 2022

Preprint

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In this paper, we propose a multi-layered hyperelastic plate theory of growth within the framework of nonlinear elasticity. First, the 3D governing system for a general multi-layered hyperelastic plate is established, which incorporates the growth effect, and the material and geometrical parameters of the different layers. Then, a series expansion-truncation approach is adopted to eliminate the thickness variables in the 3D governing system. An elaborate calculation scheme is applied to derive the iteration relations of the coefficient functions in the series expansions. Through some further manipulations, a 2D vector plate equation system with the associated boundary conditions is established, which only contains the unknowns in the bottom layer of the plate. To show the efficiency of the current plate theory, three typical examples regarding the growth-induced deformations and instabilities of multi-layered plate samples are studied. Some analytical and numerical solutions to the plate equation are obtained, which can provide accurate predictions on the growth behaviors of the plate samples. Furthermore, the problem of 'shape-programming' of multi-layered hyperelastic plates through differential growth is studied. The explicit formulas of shape-programming for some typical multi-layered plates are derived, which involve the fundamental quantities of the 3D target shapes. By using these formulas, the shape evolutions of the plates during the growing processes can be controlled accurately. The results obtained in the current work are helpful for the design of intelligent soft devices with multi-layered plate structures.

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Section: Remarksmentioning

confidence: 99%

Section: Growth-induced Axisymmetric Deformations Of Bilayer Circular...mentioning

confidence: 99%

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On a general multi-layered hyperelastic plate theory of growth

Du¹,

Li²,

Chen³

et al. 2022

Preprint

Self Cite

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“…The power of this method can be seen in the recent paper by Wang et al [1] who illustrated that quite a few existing linear and nonlinear plate theories can be recovered by appropriate specialisations. The first five papers in this special issue [2–6] are all concerned with further extensions/applications/validations of this method. In particular, Wang et al [2], Fu et al [3], and Wang et al [4] study, respectively, the nonlinear deformation of a clamped hyperelastic plate, morphology evolutions of multiple-period post-buckling modes in bilayers, and shape-programming of thin hyperelastic plates through differential growth.…”

mentioning

confidence: 99%

“…The first five papers in this special issue [2–6] are all concerned with further extensions/applications/validations of this method. In particular, Wang et al [2], Fu et al [3], and Wang et al [4] study, respectively, the nonlinear deformation of a clamped hyperelastic plate, morphology evolutions of multiple-period post-buckling modes in bilayers, and shape-programming of thin hyperelastic plates through differential growth. The method has recently been employed to derive a consistent rod theory for a linear elastic anisotropic material with circular cross-section [7].…”

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confidence: 99%

In memory of Prof. Hui-Hui Dai

Chen¹,

Fu²,

Zhong³

2022

Mathematics and Mechanics of Solids

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This special issue of Mathematics and Mechanics of Solids is dedicated to the memory of Professor Hui-Hui Dai who passed away on 5 January 2021 in Hong Kong. Hui-Hui was born on 24 March 1964 in Anhui Province, China. He grew up in Ming Guang, a small town in Jia Shan County, where he attended Ming Guang Primary School and Ming Guang No 1 High School. He was the top scorer in the county in the national university entrance examination at the young age of 16. The years around 1980 were an exciting period in which China had just opened up to the outside world, and universities had an electric atmosphere about science and knowledge after reopening following a 10-year close-down. Hui-Hui must have really enjoyed his studies like his peers. He obtained his BSc from the Department of Mechanics, Zhejiang University, in 1984 and entered Dalian University of Science and Technology in 1984 as an MSc student. Two years into his MSc study, he was awarded a competitive KC Wong Scholarship to study in the United Kingdom. Supervised by Professor Alan Jeffrey in the Department of Engineering Mathematics, University of Newcastle upon Tyne, he obtained his PhD in 1990. After spending just over a year in the University of Western Ontario as a postdoctoral research fellow, he spent another 3 years in the University of Manitoba. He went there as postdoctoral research fellow and was later offered a tenure-tracked position as an Assistant Professor. He moved to the

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Shape-Programming in Hyperelasticity Through Differential Growth

Ortigosa-Martínez,

Martínez-Frutos,

Mora-Corral

et al. 2024

Appl Math Optim

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This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation on a hyperelastic body reaching a given target shape. We consider the two cases of globally compatible growth, where the growth tensor is a deformation gradient over the undeformed domain, and the incompatible one, which discards such hypothesis. We formulate the problem within the framework of optimal control theory in hyperelasticity. The Hausdorff distance is used to quantify dissimilarities between shapes; the complexity of the actuation is incorporated in the cost functional as well. Boundary conditions and external loads are allowed in the state law, thus extending previous works where the stress-free hypothesis turns out to be essential. A rigorous mathematical analysis is then carried out to prove the well-posedness of the problem. The numerical approximation is performed using gradient-based optimisation algorithms. Our main goal in this part is to show the possibility to apply inverse techniques for the numerical approximation of this problem, which allows us to address more generic situations than those covered by analytical approaches. Several numerical experiments for beam-like and shell-type geometries illustrate the performance of the proposed numerical scheme.

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A theoretical scheme for shape-programming of thin hyperelastic plates through differential growth

Cited by 11 publications

References 36 publications

On a general multi-layered hyperelastic plate theory of growth

On a general multi-layered hyperelastic plate theory of growth

In memory of Prof. Hui-Hui Dai

Shape-Programming in Hyperelasticity Through Differential Growth

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