Hyperelastic materials behavior modeling using consistent strain energy density functions

Darijani, H.; Naghdabadi, R.

doi:10.1007/s00707-009-0239-3

Cited by 70 publications

(27 citation statements)

References 25 publications

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“…Physically, this criterion describing a process of yielding energy by material when it is deformed towards equilibrium and storing energy when the material is deformed away from equilibrium. Restrictions on the form of the strain energy function that occurs from the Drucker stability criterion are discussed in detail by [17,82,109].…”

Section: Effective Constitutive Model and Optimisation Of Materials Pamentioning

confidence: 99%

“…[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/23/15 3:08 PM are used to fit the experimental data of the first PiolaKirchhoff stress T against the stretch ratio λ and find the model for the strain energy, which can best represent the mechanical behaviour of the measured samples and obtain the material parameters for that model.…”

Section: Uniaxial Test For Incompressible Hyperelastic Materialsmentioning

confidence: 99%

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Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Wex

Arndt

Stoll

et al. 2015

Biomedical Engineering / Biomedizinische Technik

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Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function--a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

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Section: Effective Constitutive Model and Optimisation Of Materials Pamentioning

confidence: 99%

Section: Uniaxial Test For Incompressible Hyperelastic Materialsmentioning

confidence: 99%

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Wex

Arndt

Stoll

et al. 2015

Biomedical Engineering / Biomedizinische Technik

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“…Several strain energy density expressions have been suggested for rubber. Darijani and Naghdabadi used the phenomenological approach due to its relative simplicity and consistency within a continuum framework, to obtain the suitable forms for strain energy density function. They showed that a strain energy function for incompressible materials could be expressed as follows

W = w (λ_{1}) + w (λ_{2}) + w (λ_{3})

where

w (λ_{i})

is the sum of the series as

w (λ_{i}) = \sum_{k = 1}^{\infty} A_{k} (λ_{i}^{m_{k}} - 1) + \sum_{k = 1}^{\infty} B_{k} (λ_{i}^{- n_{k}} - 1)

where

m_{k}, n_{k}

take real positive values and the coefficients

A_{k}

and

B_{k}

are the material parameters.…”

Section: Fundamentalsmentioning

confidence: 99%

“…In simple tension/compression, we know that

σ_{1} = σ, λ_{1} = λ

, and

σ_{2} = σ_{3} = 0

. For isotropy of the material,

λ_{2}, λ_{3} = λ^{- 0.5}

and the stress‐deformation relations are combined to give

σ = λ \frac{d \overset{true\sim}{W}}{d λ}, \overset{true\sim}{W} = \int_{1}^{λ} \frac{σ}{λ} d λ

where

\overset{true\sim}{W} true(λ true) = W true(λ, λ^{- 0.5}, λ^{- 0.5} true)

.…”

Section: Fundamentalsmentioning

confidence: 99%

“…The determination of material parameters and the evaluating effectiveness of these models is based on the correlation between the values of the strain energy density (rather than the stresses) cast from the theory and the test data . The test data involve a state of pure homogeneous deformation that includes simple tension/compression, pure shear, and equi‐biaxial tension tests.…”

Section: Fundamentalsmentioning

confidence: 99%

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New polynomial strain energy function; application to rubbery circular cylinders under finite extension and torsion

Bahreman

Darijani

2014

J of Applied Polymer Sci

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In this article, a strain energy density function is proposed in terms of the principal invariants of the left Cauchy‐Green strain tensor for Rubber‐like materials. This model due to its mathematical structure lies in the category of polynomial hyperelastic models. To compare the performance of the proposed model with the Rivlin set, some test data of rubber‐like materials with pure homogeneous deformations are used. It is shown that the proposed model has better agreement with the test data compared to the selected model. As an application of the proposed model, it is used to obtain a closed form solution for analysis of rubbery solid circular cylinders with S‐shaped and semi J‐shaped mechanical behavior under the torsion superimposed on the axial extension. Moreover, the results predicted from the proposed model are compared to classic models to investigate the results accuracy for simplification done. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41718.

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Computer‐Aided Engineering of Stretchable Hollow Fibers to Enable Wearable Microfluidics

Hossain

Khan

2023

Adv Materials Technologies

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Melt‐extruded hollow thermoplastic fibers are a new class of materials for advanced applications, i.e., robotic clothes, stretchable touch and twist sensors, and programmable knitted textiles. Under large mechanical deformation (strain), such materials exhibit hyperelasticity. However, fundamental knowledge of strain‐energy density harnessing integrated computational materials engineering (ICME) has remained untapped for hollow fibers. Due to this key knowledge gap, most emerging applications demand iterative and costly approaches to producing and studying hollow fibers. Herein, a data‐driven pathway harnessing the ICME is introduced to study, predict, and optimize the hyperelastic behavior of hollow fibers. MCalibration software is used to calibrate the material properties of the fibers utilizing the Three‐Network Model (TNM) and emulated experimental stress–strain behavior in a finite‐element‐based multiphysics environment (COMSOL) with 99.99% confidence. The feasibility of predicting strain‐energy density is shown to modulate shape and geometries for new understandings without running cost‐incurring melt extrusions or experiments. Furthermore, the strain‐energy density is leveraged as a tool to attach fibers on fabrics that otherwise need iterations. As a proof‐of‐concept, fibers to fabrics are attached for wearable microfluidic demonstrations. This ICME approach can be extended to design the next generation of pre‐programmed, undiscovered functional devices fabricated from hyperelastic hollow fibers.

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Hyperelastic materials behavior modeling using consistent strain energy density functions

Cited by 70 publications

References 25 publications

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

New polynomial strain energy function; application to rubbery circular cylinders under finite extension and torsion

Computer‐Aided Engineering of Stretchable Hollow Fibers to Enable Wearable Microfluidics

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