Modeling and simulation of thermally actuated bilayer plates

Bartels, Sören; Bonito, Andrea; Muliana, Anastasia; Nochetto, Ricardo H.

doi:10.1016/j.jcp.2017.10.044

Cited by 27 publications

(44 citation statements)

References 35 publications

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“…It can be seen that the final configuration of the cube in our simulation is almost the same as the one in Bartels et al [28]. This proves the validity of the new proposed deformation model.…”

Section: Numerical Experimentssupporting

confidence: 80%

“…Figure 10(b) shows the deformation process of the cube when the temperature change is 758C. Figure 10(c) shows the deformation process of a cube with the same parameters as in Bartels et al [28].…”

Section: Numerical Experimentsmentioning

confidence: 91%

“…The convergence is proved and the performance is explored via several numerical experiments. To model and simulate the bending deformation of thermally actuated polymeric bilayer structures, Bartels et al [28] modified the conventional method by adding the coefficients of thermal expansion of polymers into the mathematic model. The accuracy of this model is adequate and this model can be extended to generalized bilayer structures whose shape is not limited to rectangle.…”

Section: Introductionmentioning

confidence: 99%

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Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

Liu

Duan

et al. 2019

Mathematics and Mechanics of Solids

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This paper addresses the problem of deformation modeling and simulation of 4D printed polymeric bilayer structures considering the thickness ratio. Through an equivalent transformation, the folding deformation model is transformed into two simpler deformation models, stretching and bending, which greatly reduces the complexity of the modeling problem. The stretching deformation model is developed by Hooke’s law, and based on the final strain of the stretching deformation, which is determined by the thickness ratio, a new hyperelastic energy density function considering the thickness ratio is defined to calculate the energy of the bilayer structure during the bending deformation. According to the new energy density function, the bending deformation model considering the thickness ratio is developed by minimizing the energy of the bilayer structure during the bending deformation. Numerical simulations show encouraging results obtained by the proposed model.

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Section: Numerical Experimentssupporting

confidence: 80%

Section: Numerical Experimentsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

Liu

Duan

et al. 2019

Mathematics and Mechanics of Solids

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“…Convergent finite element discretizations and iterative strategies for the numerical solution of the bilayer plate bending problem have been devised in the articles [14,13] extending the ideas described in the Sections 3.2 and 4.2. The iterative scheme of [14] is unconditionally stable but requires a subiteration, i.e., the solution of a nonlinear system of equations in every time step, which limits its practical applicability, while the scheme used in [13] is explicit and efficient but can only be expected to be conditionally stable. We devise here a new semi-implicit scheme with improved stability properties.…”

Section: Applications Modifications and Extensionsmentioning

confidence: 99%

Finite element simulation of nonlinear bending models for thin elastic rods and plates

Bartels

2020

Geometric Partial Differential Equations - Part I

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Nonlinear bending phenomena of thin elastic structures arise in various modern and classical applications. Characterizing low energy states of elastic rods has been investigated by Bernoulli in 1738 and related models are used to determine configurations of DNA strands. The bending of a piece of paper has been described mathematically by Kirchhoff in 1850 and extensions of his model arise in nanotechnological applications such as the development of externally operated microtools. A rigorous mathematical framework that identifies these models as dimensionally reduced limits from three-dimensional hyperelasticity has only recently been established. It provides a solid basis for developing and analyzing numerical approximation schemes. The fourth order character of bending problems and a pointwise isometry constraint for large deformations require appropriate discretization techniques which are discussed in this article. Methods developed for the approximation of harmonic maps are adapted to discretize the isometry constraint and gradient flows are used to decrease the bending energy. For the case of elastic rods, torsion effects and a self-avoidance potential that guarantees injectivity of deformations are incorporated. The devised and rigorously analyzed numerical methods are illustrated by means of experiments related to the relaxation of elastic knots, the formation of singularities in a Möbius strip, and the simulation of actuated bilayer plates.

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“…Swelling regions, which govern the folding shapes, are modeled by changing the length of the bond in the active networks (swelled regions). Finite element method has been used to simulate large deformation shape reconfigurable in multilayered 2D planar surfaces activated with various stimuli (e.g., Mailen et al, 2015;Tajeddini and Muliana, 2017;Bartels et al, 2018). Bartels et al (2018) also discussed the occurrence of corner folding (termed as dog ears) of planar surfaces instead of folding into desired cylindrical shapes, which is attributed to a slow diffusivity process.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of Thin Layered Composites Under Non-mechanical Stimuli

2020

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This study presents a non-linear deformation analysis of a thin composite plate undergoing shape reconfigurations triggered by electric field inputs. The composite plate consists of electro-active and inactive (substrate) layers. Prescribing electric field inputs to the electro-active layer induces large curvatures in the composites, while the in-plane stretch is relatively small. This has a consequence that only shapes with zero (or nearly zero) Gaussian curvature can be attained by prescribing the electric field, which leads to snap-through shape reconfigurations in order to achieve developable surfaces. When the substrate is made of an elastic layer, the shape returns to its original planar configuration upon removal of the electric field. In order to fully or partially retain the reconfigured shape upon removing the electric field input, a substrate layer made of a shape memory polymer is considered. Shape reconfigurations and retentions of the composites having elastic substrate and shape memory substrate are simulated.

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Modeling and simulation of thermally actuated bilayer plates

Cited by 27 publications

References 35 publications

Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

Finite element simulation of nonlinear bending models for thin elastic rods and plates

Modeling and Simulation of Thin Layered Composites Under Non-mechanical Stimuli

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