A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials

Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibers embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modeled by incorporating the strains experienced by the fibers. From histological studies on soft tissues it is evident that for a wide range of tissues the fibers have an oblique mean orientation about the physiological loading directions. Thus, we require a mathematical framework of tensors defined in nonorthogonal basis to capture the direction-dependent response of fibers under high induced loads. In this work, we propose a novel approach to determine the fiber strains with the aid of the contravariant tensors defined in an oblique coordinate system. To determine the fiber strains, we introduce a fourth-order contravariant fiber orientation transformation tensor. The approach helps us successfully in determining the fiber strains, for a family of symmetrically and asymmetrically oriented fibers, with the aid of a single anisotropic invariant. The proposed model was fitted with the experimental data from literature to determine the corresponding material parameters.

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“…The Eulerian or spatial elasticity tensor C ijkl can be arrived from literature [43], [46] using the Piola push forward of C ijkl as…”

Section: Derivation Of the Elasticity Tensormentioning

confidence: 99%

The Use of Contravariant Tensors to Model Anisotropic Soft Tissues

Basak

Rajagopal

Basappa

et al. 2021

Int. J. Appl. Mechanics

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“…Decoupled implementations, however, are not straightforward due to the complicated procedures in deriving stress and elasticity tensors. The decoupled stress and elasticity tensors for some models have been derived by Nicholson [11], Weiss, Maker, and Govindjee [12], Itskov [13], Suchocki [14], and Cheng and Zhang [15].…”

Section: Nomenclature Bmentioning

confidence: 99%

“…For the general CSE functional, the eight parameters ∆ 1 , ∆ 2 , · · · , ∆ 8 , using (15) and (16), are more specifically given by…”

Section: Elasticity Tensors In Reference and Current Configurationsmentioning

confidence: 99%

Modeling and Implementing Compressible Isotropic Finite Deformation without the Isochoric–Volumetric Split

Zhao¹,

Study²

2020

JAAM

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Constitutive models and finite element implementations of compressible finite deformation are straightforwardly formulated by the general isotropic continuum stored energy (CSE) functional without the isochoric-volumetric split. Coupled stress and elasticity tensors in reference and current configurations are derived. Modeling and predicting capabilities of the general CSE functional are exhibited through multiaxial experimental tests of compressible NR and SBR rubbers. Characterization of kinematic relation, rather than pressure-volume relation, is emphasized in experimental tests of compressibility. The isochoric-volumetric split does not hold based on either theoretical analyses or experimental validations.

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“…An interesting particularity of this model is that the Yeoh model is a polynomial of the first variant, I 1 in which I 2 and I 3 are ignored 16 . For hyperelastic materials subjected to uniaxial tension, the principal stretches are expressed as λ 1 = λ and λ 2 = λ 3 , whereas the incompressibility condition implies λ 1 λ 2 λ 3 = 1 17 and together with the principal stretches expression, it yields λ 2 = λ 3 =

λ^{\frac{- 1}{2}}

.…”

Section: Deriving Constitutive Model Equationmentioning

confidence: 99%

Anticipating local flaps closed‐form solution on 3D face models using finite element method

Kwan

Najhan

Yau

et al. 2020

Numer Methods Biomed Eng

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A realistic three‐dimensional (3D) computational model of skin flap closures using Asian‐like head templates from two different genders, male and female, has been developed. The current study aimed to understand the biomechanics of the local flap designs along with the effect of wound closures on the respective genders. Two Asian head templates from opposite genders were obtained to use as base models. A third‐order Yeoh hyperelastic model was adapted to characterize as skin material properties. A single layer composed of combined epidermis and dermis was considered, and the models were thickened according to respective anatomical positions. Each model gender was excised with a fixed defect size which was consequently covered by three different local flap designs, namely advancement, rotation, and rhomboid flaps. Post‐operative simulation presented various scenarios of skin flap closures. Rotation and rhomboid flaps demonstrated maximal tension at the apex of the flap for both genders as well as advancement flap in the female face model. However, advancement flap closure in the male face model was presented otherwise. Yet, the deformation patterns and the peak tension of the discussed flaps were consistent with conventional local flap surgery. Moreover, male face models generated higher stresses compared to the female face models with a 70.34% mean difference. Overall, the skin flap operations were executed manually, and the designed surgery model met the objectives successfully while acknowledging the study limitations. Novelty File 3D head templates were considered to address the gap as 3D face models were uncommonly employed in understanding the biomechanics of the local flaps realistically. Most of the existing studies focus on the 2D and 3D planar geometry in their models. As gender comparison has yet to be addressed, we intended to fill this gap by exploring the stress contours of the local flap designs in different genders. Create a 3D face model from two opposite genders which is capable of simulating closure of wounds using local flaps with a focus on advancement, rotation, and rhomboid flaps.

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A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials

Cited by 18 publications

References 55 publications

The Use of Contravariant Tensors to Model Anisotropic Soft Tissues

The Use of Contravariant Tensors to Model Anisotropic Soft Tissues

Modeling and Implementing Compressible Isotropic Finite Deformation without the Isochoric–Volumetric Split

Anticipating local flaps closed‐form solution on 3D face models using finite element method

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