Study Neo-Hookean and Yeoh Hyper-Elastic Models in Dielectric Elastomer-Based Micro-Beam Resonators

Barforooshi, Saeed Danaee; Mohammadi, Ardeshir Karami

doi:10.1590/1679-78252432

Cited by 23 publications

(4 citation statements)

References 25 publications

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“…Also, the fourth-order Runge–Kutta method is used to accurately validate the results of the Lindstedt–Poincare method with respect to material and geometric properties. To evaluate the error between the numerical method and the analytical approach and the closeness of two methods, integral absolute error has been used (Barforooshi and Mohammadi, 2016). In this method, the error integral between the analytical and numerical method in time is calculated, and the results are presented in terms of percentages as shown in Table 6.…”

Section: Resultsmentioning

confidence: 99%

A perturbation analysis in nonlinear free vibration of a microbeam reinforced by shape memory alloy layer based on the modified couple stress theory

Ghaffari

Mohammadi

2020

Journal of Vibration and Control

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Numerous applications have been found in various microelectromechanical systems for shape memory alloys. This study analyzes the nonlinear free vibrations of a sandwiched microbeam, consisting of a shape memory alloy core and two elastic layers on either side. The behavior of the shape memory layer is modeled with the one-dimensional Brinson model. The equation of motion is derived from Hamilton’s principle and the modified couple stress theory for the Euler–Bernoulli beam and then truncated into a reduced-order model through Galerkin’s technique. An approximate analytical solution is obtained using the Lindstedt–Poincare method for different temperatures. The effects of temperature, material length scale parameter, aspect ratio, and maximum vibration amplitude on nonlinear normalized frequency have been investigated. The results have been compared with those of some previous studies and can provide a better understanding of the design of sandwiched microbeams, which have a shape memory alloy layer.

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Section: Resultsmentioning

confidence: 99%

A perturbation analysis in nonlinear free vibration of a microbeam reinforced by shape memory alloy layer based on the modified couple stress theory

Ghaffari

Mohammadi

2020

Journal of Vibration and Control

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“…Skin grafts have been observed to have less stress compared to skin at high strain [55] Hyperelastic constitutive material models (e.g., Fung, Yeoh, Humphrey) can be used to characterize the non-linear mechanical behavior of synthetic skin grafts. In this study Yeoh, Mooney-Rivlin, and the neo-Hookean hyperelastic curve fit model were used to calculate the constant coefficients (𝑐 , 𝑐 , and 𝑐 ) [56,57,58,59]. Non-linear hyperelastic curves work on the strain energy density function (Ѱ), which is based on the materia type.…”

Section: Materials Characterizationmentioning

confidence: 99%

Development and Characterization of Novel Anisotropic Skin Graft Simulants

Gupta

Singla

Chanda

2023

Dermato

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Split-thickness skin grafting is a well-known procedure for the treatment of small- and medium-sized burns. However, its effectiveness has been reported to be limited in the case of large and severe burns due to much lower real expansion offered by the grafts than the claimed expansion by graft mesh manufacturers. Recent computational studies have indicated that the collagen fiber orientation within the skin layers have a significant effect on the skin graft expansion. In this study, biofidelic anisotropic synthetic skin with one and two layers and all possible fiber orientations were developed, and incision patterns used in traditional graft meshing techniques were projected to fabricate novel synthetic skin grafts with a theoretical meshing ratio of 3:1. A biaxial tensile testing device was designed to simulate skin graft stretching in clinical settings, and a wide range of synthetic skin graft variants were mechanically tested. The measured quantities included induced nonlinear stress–strain, void area, and meshing ratio. In addition, the stress–strain responses were characterized using nonlinear hyperelastic models. The key observations include the generation of higher induced stresses in two-layer grafts. In the one-layer graft models, a 15° fiber orientation produced the highest expansion at a minimal stress value of 0.21 MPa. In the two-layer graft models, the 45°–15° fiber orientation generated the maximum expansion with minimum stress. A range of such findings were analyzed to determine the graft orientations that may allow enhanced expansion without generating much stress. This information would be indispensable not only for understanding the expansion potential of skin grafts, but also for further research and the development of skin grafts with enhanced expansion for severe burn injury treatment.

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“…They used the finite element model to check the accuracy of the reduced order model. Danaee Barforooshi and Karami Mohammadi (2016) considered a hyperelastic microbeam with geometric and material nonlinearity. Geometric nonlinearity was introduced by von Kármán and Yeoh, and neo-Hookean models were used for the material nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of a hyper-elastic microbeam using a new “augmented Biderman model”

Mohammadi¹,

Barforooshi²

2019

Journal of Theoretical and Applied Mechanics

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A new augmented Biderman model inspired by the modified couple stress theory has been introduced to investigate the size effect in addition to nonlinear material effects. Then, this model is used to investigate free vibration of a hyper-elastic microbeam. Classical Biderman strain energy does not include the effect of small size in hyper-elastic materials. In order to consider the effect of small size, terms inspired by the modified couple stress theory are added to the classical Biderman strain energy function. In order to provide the possibility of calculating these terms, a relation between the material constants in the hyper-elastic Biderman model and the linear elastic constants is obtained. The equations of motion of the microbeam is obtained based on the extended Hamilton principle, and then is solved using Galerkin discretization and perturbation methods. The effect of thickness to length scale ratio on the normalized frequency is studied for different modes. It is shown that when thickness gets larger in comparison with the length scale parameter, the normalized frequency tends to classical Biderman results. The results obtained are validated by results of the Runge-Kutta numerical method and indicate an excellent agreement. Mode shapes of the microbeam based on the classical and the augmented models are depicted, where the augmented model anticipates stiffer behavior for hyperelastic microbeams.

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Study Neo-Hookean and Yeoh Hyper-Elastic Models in Dielectric Elastomer-Based Micro-Beam Resonators

Cited by 23 publications

References 25 publications

A perturbation analysis in nonlinear free vibration of a microbeam reinforced by shape memory alloy layer based on the modified couple stress theory

A perturbation analysis in nonlinear free vibration of a microbeam reinforced by shape memory alloy layer based on the modified couple stress theory

Development and Characterization of Novel Anisotropic Skin Graft Simulants

Free vibration of a hyper-elastic microbeam using a new “augmented Biderman model”

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