Poynting effect of brain matter in torsion

Balbi, Valentina; Trotta, Antonia; Destrade, Michel; Annaidh, Aisling Ní

doi:10.1039/c9sm00131j

Cited by 38 publications

(31 citation statements)

References 27 publications

(31 reference statements)

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“…where I 1 and I 2 are the first and second invariants of the left Cauchy‐Green deformation tensor. Several researchers used the Mooney‐Rivlin model to characterize the elastic response during multi‐modal mechanical (Balbi et al., 2019; Budday et al., 2017a; Destrade et al., 2015; Eskandari et al., 2021b; Hosseini‐Farid et al., 2017; Hrapko et al., 2008a; Laksari et al., 2012; Liu et al., 2019; Mihai et al., 2015; Rashid et al., 2013b; Shafieian et al., 2012) and indentation experiments (MacManus et al., 2016; MacManus et al., 2017c; MacManus et al., 2018; Pierrat et al., 2018; Sundaresh et al., 2021). However, similar to the neo‐Hookean model, it fails to capture compression, tension, and shear loadings simultaneously (Budday et al., 2017a).…”

Section: Extended Data Analysis: Constitutive Modeling and Parameter ...mentioning

confidence: 99%

Tissue‐Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

et al. 2022

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Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time‐dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. This article was corrected on 16 April 2022. See the end of the full text for details.

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Section: Extended Data Analysis: Constitutive Modeling and Parameter ...mentioning

confidence: 99%

Tissue‐Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

et al. 2022

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“…The choice for 𝑊 is motivated by many experimental observations on soft tissues. In particular, it has been observed that the brain behaves as a Mooney-Rivlin material in torsion [20] and in simple shear [21]. Moreover, the Mooney-Rivlin model has the key feature of predicting a linear elastic response in torsion, i.e.…”

Section: Simple Torsionmentioning

confidence: 99%

“…(68) without loss of generality. Furthermore, we set 𝑐 2 = 𝑐 1 /2 according to the observed values of 𝑐 1 and 𝑐 2 for brain tissues [20].…”

Section: Torquementioning

confidence: 99%

“…This deformation can be performed with commercially available rheometers which measure both the torque and the normal force required to twist a cylindrical sample, giving access to two independent sets of data. Torsion has been successfully used to characterise the elastic properties of the brain in large deformations [20] suggesting that the tissue behaves as a Mooney-Rivlin material. The same behaviour was previously observed in simple shear experiments [21].…”

Section: Introductionmentioning

confidence: 99%

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Foundations of viscoelasticity and application to soft tissues mechanics

Righi¹,

Balbi²

2021

Preprint

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Soft tissues are complex media, they display a wide range of mechanical properties such as anisotropy and non-linear stress-strain behaviour. They undergo large deformations and they exhibit a time-dependent mechanical behaviour, i.e. they are viscoelastic. In this chapter we review the foundations of the linear viscoelastic theory and the theory of Quasi-Linear Viscoelasticity (QLV) in view of developing new methods to estimate the viscoelastic properties of soft tissues through model fitting. To this aim, we consider the simple torsion of a viscoelastic Mooney-Rivlin material in two different testing scenarios: step-strain and ramp tests. These tests are commonly performed to characterise the time-dependent properties of soft tissues and allow to investigate their stress relaxation behaviour. Moreover, commercial torsional rheometers measure both the torque and the normal force, giving access to two sets of data. We show that for a step test, the linear and the QLV models predict the same relaxation curves for the torque. However, when the strain history is in the form of a ramp function, the non-linear terms appearing in the QLV model affect the relaxation curve of the torque depending on the final strain level and on the rising time of the ramp. Furthermore, our results show that the relaxation curve of the normal force predicted by the QLV theory depends on the level of strain both for a step and a ramp tests. To quantify the effect of the non-linear terms, we evaluate the maximum and the equilibrium (as 𝑡 → ∞) values of the relaxation curves. Our results provide useful guidelines to accurately fit QLV models in view of estimating the viscoelastic properties of soft tissues.

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“…16,17 In such small-to-moderate deformation ranges, W (I 1 ) models have been shown to produce high levels of relative error when fitted to the experimental data. 10,[18][19][20] Indeed, there is a plethora of experimental evidence [21][22][23] as well as theoretical analyses by way of deriving universal relationships 19,21,24,25 that prove the necessity of the inclusion of I 2 , the second principal invariant of the Cauchy-Green deformation tensor, within the strain energy function W. Although a consensus is yet to be reached among rubber practitioners as to whether the addition of the second invariant term is always necessary (see also the next section for further discussion), the inclusion of I 2 into W significantly improves the fitting quality in small-to-moderate deformation ranges and reduces the relative error. [18][19][20][21] Accordingly, to enjoy the best of modeling features, that is, having a simple functional form while including the I 2 invariant for improved modeling predictions, an advantageous strain energy function W for application to practical problems of rubberlike materials should ideally have the following features: (i ) a small number of model parameters so as to avoid uniqueness problems of the kind discussed by Ogden et al 15 , (ii ) structurally relevant model parameters so as to embody physical and mathematical objectivity, and (iii ) a degree of universality in that various deformation behaviors of a specific sample can be captured and predicted by a single set of model parameter values.…”

Section: Introductionmentioning

confidence: 99%

Assessment of a New Isotropic Hyperelastic Constitutive Model for a Range of Rubberlike Materials and Deformations

Anssari-Benam

Bucchi

Horgan

et al. 2021

Rubber Chemistry and Technology

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The choice of an appropriate strain energy function W is key to accurate modeling and computational finite element analysis of the mechanical behavior of unfilled non-crystalizing rubberlike materials. Despite the existing variety of models, finding a suitable model that can capture many deformation modes of a rubber specimen with a single set of parameter values and satisfy the a priori mathematical and structural requirements remains a formidable task. Previous work proposed a new generalized neo-Hookean W (I1) function, showing a promising fitting capability and enjoying a structural basis. We now use two extended forms of that model that include an I1 term adjunct, W (I1, I2), for application to various boundary value problems commonly encountered in rubber mechanics applications. Specifically, two functional forms of the I2 invariant are considered: a linear function and a logarithmic function. The boundary value problems of interest include the in-plane uniaxial, equi-biaxial, and pure shear deformations and simple shear, inflation, and nonhomogeneous deformations such as torsion. By simultaneous fitting of each model to various deformation modes of rubber specimens, it is demonstrated that a single set of model parameter values favorably captures the mechanical response for all the considered deformations of each specimen. It is further shown that the model with a logarithmic I2 function provides better fits than the linear function. Given the functional simplicity of the considered W (I1, I2) models, the low number of model parameters (three in total), the structurally motivated bases of the models, and their capability to capture the mechanical response for various deformations of rubber specimens, the considered models are recommended as a powerful tool for practical applications and analysis of rubber elasticity.

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Poynting effect of brain matter in torsion

Cited by 38 publications

References 27 publications

Tissue‐Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Tissue‐Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Foundations of viscoelasticity and application to soft tissues mechanics

Assessment of a New Isotropic Hyperelastic Constitutive Model for a Range of Rubberlike Materials and Deformations

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