On a consistent finite-strain plate theory of growth

Wang, Jiong; Steigmann, David J.; Wang, Fan‐Fan; Dai, Hui–Hui

doi:10.1016/j.jmps.2017.10.017

Cited by 36 publications

(42 citation statements)

References 39 publications

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“…Here, n is the unit outward normal to the boundary ∂Ω q and P = J G ∂φ 0 ∂A -p ∂L0 ∂A G −T is recognised as the first Piola Kirchhoff stress tensor. While deriving these equations, we have used the assumption that the rate of deformation of the growth process is very small compared to the elastic deformation (Ben Wang et al, 2018), therefore the growth tensor G is assumed to be constant in time. Auxiliary calculations are presented in Appendix A.…”

Section: Notation Used In This Manuscriptmentioning

confidence: 99%

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Growth induced instabilities in a circular hyperelastic plate

Mehta¹,

Raju²,

Saxena³

2021

Preprint

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In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational approach. The derived plate equations are solved using the compound matrix method for two cases of axisymmetric growth conditions -purely radial, and combined radial and circumferential growth. The effect of growth on the buckling behaviour of the plate (in particular, the critical growth factor and the associated buckling mode shapes) is investigated for different thickness values. These results are applicable to model growth induced deformation in planar soft tissues such as skin.

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Section: Notation Used In This Manuscriptmentioning

confidence: 99%

“…To obtain the 2-D formulation of circular plate, we perform the series expansion of x and p in terms of Z about the bottom surface, Z = 0 following the approach by Wang et al (2018Wang et al ( , 2019b x…”

Section: Specialisation To Two Dimensionsmentioning

confidence: 99%

Growth induced instabilities in a circular hyperelastic plate

Mehta¹,

Raju²,

Saxena³

2021

Preprint

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“…In the current work, we aim to propose a theoretical scheme for shape-programming of thin hyperelastic plates through differential growth. The basis of the current work is a consistent finite-strain plate theory proposed in Wang et al [27]. The plate equation system in this theory is derived from the 3D governing system through a series expansion and truncation approach [28], which incorporates the growth effect and the constraint of elastic incompressibility.…”

Section: Introductionmentioning

confidence: 99%

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

Wang¹,

Li²,

Jin³

2022

Preprint

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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 seriesexpansion and truncation approach. Based on the plate equation system, the problem of shapeprogramming 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.

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“…Growth and swelling of shells: The first general surface formulations using a multiplicative decomposition to couple mechanical deformation and growth seem to be the works by Dervaux et al (2009) and Wang et al (2018) on plates, Rausch and Kuhl (2014) on membranes, Vetter et al (2013Vetter et al ( , 2014 on Kirchhoff-Love shells, and Lychev (2014) on Reissner-Mindlin shells. Similar approaches have also been considered by Papastavrou et al (2013) to model surface growth of bulk materials and Swain and Gupta (2018) to model interface growth.…”

Section: Introductionmentioning

confidence: 99%

The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity

Sauer

Ghaffari

Gupta

2019

International Journal of Solids and Structures

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This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various kinematical quantities, such as area change and curvature, on the elastic and inelastic strains is discussed. This is essential for the development of general constitutive models. In order to fully explore the coupling between elastic and different inelastic deformations, the surface balance laws for mass, momentum, energy and entropy are examined in the context of the multiplicative decomposition. Based on the second law of thermodynamics, the general constitutive relations are then derived. Two cases are considered: Independent inelastic strains, and inelastic strains that are functions of temperature and concentration. The constitutive relations are illustrated by several nonlinear examples on growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells. The formulation is fully expressed in curvilinear coordinates leading to compact and elegant expressions for the kinematics, balance laws and constitutive relations. (183) and consider only inelastic dilatation (â αβ = J in A αβ ) according to Sec. 3.3. Contracting (184) with a αβ and using the relations from Sec. 3.3 thus yields the evolution laẇfor J in . For a generalized viscoelastic solid, see Fig. 2b, evolution law (184) needs to be solved forâ αβ

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On a consistent finite-strain plate theory of growth

Cited by 36 publications

References 39 publications

Growth induced instabilities in a circular hyperelastic plate

Growth induced instabilities in a circular hyperelastic plate

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

The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity

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