Anisotropic hyperelastic modeling for face-centered cubic and diamond cubic structures

Kim, Wonbae; Chung, Hayoung; Cho, Maenghyo

doi:10.1016/j.cma.2015.03.024

Cited by 9 publications

(4 citation statements)

References 39 publications

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“…The tensile response of graphene sheets using Ogden hyperelastic function was investigated by Saavedra Flores et al [ 40 ]. Kim et al [ 41 ] proposed polynomial-based hyperelastic functions that indicate the mechanical response of FCC and diamond cubic nanostructures. The continuum models were calculated via the application of various types of loadings to the specimens based on the Cauchy-Born hypothesis and fitting the continuum functions to the EAM and Tersoff potentials reference data.…”

Section: Introductionmentioning

confidence: 99%

Mechanical behavior of multilayer graphene reinforced epoxy nano-composites via a hierarchical multi-scale technique

et al. 2021

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Section: Introductionmentioning

confidence: 99%

Mechanical behavior of multilayer graphene reinforced epoxy nano-composites via a hierarchical multi-scale technique

et al. 2021

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“…Therefore, a constitutive equation for hyperelastic polymers is often defined on the basis of parameters derived by differentiating the energy density function of the material because the energy function of a hyperelastic polymer consists of strain terms. Because hyperelastic behavior can vary slightly according to the characteristics of the material, various hyperelastic models, such as the Neo-Hookean, Mooney-Rivlin, and Ogden models, [5][6][7][8][9][10][11] were selected and used to predict the mechanical properties of polymer materials. These hyperelastic models are defined by a fixed energy density function formulation determined by global least-squares data fitting, which does not correctly describe the mechanism underlying the behavior of hyperelastic polymers.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A neural network constitutive model for hyperelasticity based on molecular dynamics simulations

Chung

Cho

2020

Numerical Meth Engineering

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Numerical analysis of the hyperelastic behavior of polymer materials has drawn significant interest from within the field of mechanical engineering. Currently, hyperelastic models based on the energy density function, such as the Neo-Hookean, Mooney-Rivlin, and Ogden models, are used to investigate the hyperelastic responses of materials. Conventionally, constants relating to materials were determined from experimental data by using global least-squares fitting. However, formulating a constitutive equation to capture the complex behavior of hyperelastic materials was difficult owing to the limitations of the analytical model and experimental data. This study addresses these limitations by using a system of neural networks (NNs) to design a data-driven surrogate model without a specific function formula, and employs molecular dynamics (MD) simulations to calculate the massive amount of combined loading data of hyperelastic materials. Thus, MD simulations were used to propose an NN constitutive model for hyperelasticity to derive the constitutive equation to model the complex hyperelastic response. In addition, the probability distributions of the numerical solutions of hyperelasticity are used to characterize the uncertainty of the MD models. These statistical finite element results not only present numerical results with reliability ranges but also scattered distributions of the solution obtained from the MD-based probability distributions.

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“…However, it should be emphasized that hyperelastic models serve a very accurate approach to describe the material behavior of biological tissues as well . In most cases isotropy is assumed, but there exist anisotropic hyperelastic models . Since rubber‐like materials show nearly‐incompressible (in volumetric sense) behavior, most of the hyperelastic models are proposed by assuming incompressible or nearly‐incompressible characteristics.…”

Section: Introductionmentioning

confidence: 99%

Closed‐form stress solutions for incompressible visco‐hyperelastic solids in uniaxial extension

Kossa

2017

Z Angew Math Mech

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This paper is concerned with the theory of incompressible visco-hyperelastic solids. Closed-form stress solutions are derived for five different visco-hyperelastic material models in uniaxial extension. Two loading scenarios are considered: uniaxial extension with constant true strain-rate; uniaxial extension with constant engineering strain-rate. The obtained stress solutions are expressed using only elementary functions, when the applied stretch is linear in the true strain. However, for the constant engineering strain-rate case, all the solutions are expressed using special functions, even for the very simple Hencky's hyperelastic material model. The novel solutions can be used to improve the performance and accuracy of the parameter-fitting procedure of a particular visco-hyperelastic solid. In addition, the closed-form expressions for the stresses may serve reference solution for benchmark problems.

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Anisotropic hyperelastic modeling for face-centered cubic and diamond cubic structures

Cited by 9 publications

References 39 publications

Mechanical behavior of multilayer graphene reinforced epoxy nano-composites via a hierarchical multi-scale technique

Mechanical behavior of multilayer graphene reinforced epoxy nano-composites via a hierarchical multi-scale technique

A neural network constitutive model for hyperelasticity based on molecular dynamics simulations

Closed‐form stress solutions for incompressible visco‐hyperelastic solids in uniaxial extension

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