A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

Brown, Leslee W.; Smith, L. M.

doi:10.1115/1.4003517

Cited by 18 publications

(32 citation statements)

References 30 publications

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“…where F is the deformation gradient. Ψ can also be written as a function of three invariants of C namely I 1 , I 2 and I 3 , which are given by equation 3.1 [134][135][136][137][138].…”

Section: Numerical Modelmentioning

confidence: 99%

“…The strain energy stored in the fibers is modeled as a function of , which is based on the assumption that the strain energy stored in the fibers depends mainly on the fiber elongation, where 4 F I   is the actual fiber stretch. To account for nonlinear dependence of strain energy on fiber stretch, and also to account for the three-dimensional aspect of the fiber, the strain energy stored in fibers is written as is related to stretch-dependent shear modulus of the fiber[134][135][136][137][138].…”

mentioning

confidence: 99%

“…Using 2 e as the rotation axis, 1 is rotated back to 1 2 e -e plane. The new deformation gradient tensor * are rigid body rotations, point of the following multiplicative decomposition of deformation gradient[134][135][136][137][138].From definition of * F in the current deformation considered inFigure 3.6, ,e ,e coordinate system is given by equation3.17[134][135][136][137][138].…”

mentioning

confidence: 99%

“…In this step, the composite is treated as neo-Hookean matrix embedded with neo-Hookean fibers where 4 ( ) f I is ratio of the fiber and matrix stiffnesses. The quantity of shear deformation is computed by adding the terms as shown in equation 3.21, where of the neo-Hookean composite is given by equation 3.22, where 3c is the effective neo-Hookean modulus, and 1 1 ( ) remaining after deformation * s[134][135][136][137][138].…”

mentioning

confidence: 99%

“…function for the anisotropic composite model is sum of the strain energies of the two steps (equations 3.20 and 3.22), which is given by equation 3.23[134][135][136][137][138]…”

mentioning

confidence: 99%

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Biofidelic soft composites–experimental and computational modeling

Chanda¹

2018

Preprint

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Biofidelic soft composites or tissues form the building blocks of the human body. Understanding the complex mechanics of these soft composites is the key to understanding the genesis and progression of disease. Biomechanically, soft composites exhibit anisotropic mechanical behavior and comprise of multiple fiber layers within a soft matrix. To date, there is a lack of understanding of the anisotropic mechanical behavior of soft composites, primarily due to unavailability of a robust characterization framework. In this dissertation, novel multiscale computational and experimental investigation models are developed to simulate and characterize anisotropic soft composite mechanical behavior. Soft composite surrogates were first developed to simulate various tissues in the human body namely the skin, brain, artery and vaginal tissues. Novel anisotropic soft composite models were also fabricated taking into consideration the tissue anisotropy and multifunctional properties. Hyperelastic anisotropic constitutive relationships were formulated to precisely characterize the mechanical behavior of soft composite considering varying fiber and matrix contributions, fiber-matrix interactions, fiber orientations and multiple fiber layers. Coupled with high fidelity experimental and computational models, microscopy, and Digital Image Correlation (DIC) studies, the damage and repair of soft composite surrogates are also discussed in this dissertation, with relevance to soft tissue wounds and suture. Computational modeling to understand the interaction between multiple soft composite systems and its effect on soft composite damage are also highlighted in this work. Some specific soft composite interaction systems modeled were the female pelvic system under abdominal loads, whole body impact due to blast, and ulceration in diabetic foot. This dissertation lays the foundation for micro and macro scale anisotropic soft composite modeling and characterization using high fidelity experimental and numerical techniques which will be indispensable for studying tissue mechanics and other soft composite applications in engineering and medicine.

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“…where F is the deformation gradient. Ψ can also be written as a function of three invariants of C namely I 1 , I 2 and I 3 , which are given by equation 3.1 [134][135][136][137][138].…”

Section: Numerical Modelmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…function for the anisotropic composite model is sum of the strain energies of the two steps (equations 3.20 and 3.22), which is given by equation 3.23[134][135][136][137][138]…”

mentioning

confidence: 99%

See 3 more Smart Citations

Biofidelic soft composites–experimental and computational modeling

Chanda¹

2018

Preprint

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Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers

Kiran

Khandelwal

2014

Comput Mech

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Hyperelastic Energy Densities for Soft Biological Tissues: A Review

Chagnon

Rebouah

Favier

2014

J Elast

225

136

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International audienceMany soft tissues are naturally made of a matrix and fibres that present some privileged directions. They are known to support large reversible deformations. The mechanical behaviour of these tissues highlights different phenomena as hysteresis, stress softening or relaxation. A hyperelastic constitutive equation is typically the basis of the model that describes the behaviour of the material. The hyperelastic constitutive equation can be isotropic or anisotropic, it is generally expressed by means of strain components or strain invariants. This paper proposes a review of these constitutive equations

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A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

Cited by 18 publications

References 30 publications

Biofidelic soft composites–experimental and computational modeling

Biofidelic soft composites–experimental and computational modeling

Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers

Hyperelastic Energy Densities for Soft Biological Tissues: A Review

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