On the generalized nonlinear mechanics of compressible, incompressible, isotropic, and anisotropic hyperelastic membranes

Firouzi, Nasser; Żur, Krzysztof Kamil

doi:10.1016/j.ijsolstr.2022.112088

Cited by 9 publications

(3 citation statements)

References 46 publications

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“…In this subsection, we establish the weak formulation of the model by incorporating the boundaries (2) and (3).…”

Section: Weak Formulationmentioning

confidence: 99%

“…Secondly, we obtain the weak formulation of the boundary value problem for the model (1) in conjunction with boundary conditions (3). Multiplying both sides of the equation by the test function v(x) ∈ H 1 0 (I) ∩ H 2 (I) and integrating over the interval I and using the integration by parts formula, we obtain…”

Section: Weak Formulationmentioning

confidence: 99%

“…These equations are widely utilized for modeling the bending response of beams and plates under various loading conditions. Additionally, fourth-order equations play a significant role in representing the behavior of thin membranes subjected to different loading conditions [2,3]. The utilization of one-dimensional fourth-order equations is crucial for accurately modeling the behavior of diverse physical systems, particularly those involving thin structures [4].…”

Section: Introductionmentioning

confidence: 99%

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Hermite Finite Element Method for One-Dimensional Fourth-Order Boundary Value Problems

Wu,

Qiu

2024

Mathematics

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One-dimensional fourth-order boundary value problems (BVPs) play a critical role in engineering applications, particularly in the analysis of beams. Current numerical investigations primarily concentrate on homogeneous boundary conditions. In addition to its high precision advantages, the Hermite finite element method (HFEM) is capable of directly computing both the function value and its derivatives. In this paper, both the cubic and quintic HFEM are employed to address two prevalent non-homogeneous fourth-order BVPs. Furthermore, a priori error estimations are established for both BVPs, demonstrating the optimal error convergence order in H2 semi-norm and L2 norm. Finally, a numerical simulation is presented to validate the theoretical results.

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“…In this subsection, we establish the weak formulation of the model by incorporating the boundaries (2) and (3).…”

Section: Weak Formulationmentioning

confidence: 99%

Section: Weak Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hermite Finite Element Method for One-Dimensional Fourth-Order Boundary Value Problems

Wu,

Qiu

2024

Mathematics

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Distributed load identification for hyperelastic plates using gradient-based and machine learning methods

Khosrowpour,

Hematiyan

2024

Acta Mech

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Hyperelastic constitutive model parameters identification using optical-based techniques and hybrid optimisation

Mollaee,

Budgett,

Taberner

et al. 2023

Int J Mech Mater Des

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In this paper we propose a new optical-based technique to identify the constitutive relation coefficients of the hyperelastic material using a hybrid optimisation approach. This technique can be used in place of traditional mechanical testing of elastomers for applications that involve inhomogeneous deformation. The purpose of the proposed method is to identify the incompressible hyperelastic material constitutive relation coefficients using a single experiment under different loading cases. The method comprises sample surface 3D reconstruction and uses finite element simulations to replicate the experiments, and uses a hybrid optimisation technique to minimise the error between actual 3D deformations and FE simulation results. The proposed hybrid technique predicts the hyperelastic constitutive relation coefficients more accurately than other optimisation methods. This study introduces a novel approach by employing a subpixel image registration algorithm for 3D reconstruction. The method requires a single experiment with diverse loading cases to accurately determine the coefficients of hyperelastic constitutive relations. The setup is portable and can be accommodated in a small suitcase. For this purpose, an apparatus was constructed comprising a stereoscopic system with eight cameras and a six-degree-of-freedom force-torque sensor to measure the induced forces and torques during the experiments. We identified the constitutive relation coefficients of Ogden N1, Ogden N3, Yeoh, and Arruda-Boyce relations which are commonly used models for silicone materials, using a traditional uniaxial test, optical uniaxial test (experiments performed using a constructed optical system), and inhomogeneous deformations tests. The study demonstrated that the coefficients obtained from inhomogeneous deformation tests provided the most accurate FE predictions. It was also shown that hyperelastic constitutive relation coefficients obtained from traditional uniaxial tests are insufficient to describe the material behaviour when the material undergoes inhomogeneous deformations.

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On the generalized nonlinear mechanics of compressible, incompressible, isotropic, and anisotropic hyperelastic membranes

Cited by 9 publications

References 46 publications

Hermite Finite Element Method for One-Dimensional Fourth-Order Boundary Value Problems

Hermite Finite Element Method for One-Dimensional Fourth-Order Boundary Value Problems

Distributed load identification for hyperelastic plates using gradient-based and machine learning methods

Hyperelastic constitutive model parameters identification using optical-based techniques and hybrid optimisation

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