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Destrade, Michel
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Destrade, Michel
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Destrade, Michel
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- PublicationDeficiencies in numerical models of anisotropic nonlinearly elastic materialsIncompressible nonlinearly hyperelastic materials are rarely simulated in finite element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial finite element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a 'compressibility parameter' (or 'penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a 'bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in 'Poisson’s ratio' close to the perfect incompressibility limit of 1/2 are made.
622Scopus© Citations 35 - PublicationInfluence of preservation temperature on the measured mechanical properties of brain tissueThe large variability in experimentally measured mechanical properties of brain tissue is due to many factors including heterogeneity, anisotropy, age dependence and post-mortem time. Moreover, differences in test protocols also influence these measured properties. This paper shows that the temperature at which porcine brain tissue is stored or preserved prior to testing has a significant effect on the mechanical properties of brain tissue, even when tests are conducted at the same temperatures. Three groups of brain tissue were stored separately for at least 1 h at three different preservation temperatures, i.e., ice cold, room temperature (22 °C) and body temperature (37 °C), prior to them all being tested at room temperature (∼22 °C). Significant differences in the corresponding initial elastic shear modulus μ (Pa) (at various amounts of shear, 0≤K≤1.0) were observed. The initial elastic moduli were 1043±271 Pa, 714±210 Pa and 497±156 Pa (mean±SD) at preservation temperatures of ice cold, 22 °C and 37 °C, respectively. Based on this investigation, it is strongly recommended that brain tissue samples must be preserved at an ice-cold temperature prior to testing in order to minimize the difference between the measured in vitro test results and the in vivo properties. A by-product of the study is that simple shear tests allow for large, almost perfectly homogeneous deformation of brain matter.
715Scopus© Citations 33 - PublicationMechanical characterization of brain tissue in simple shear at dynamic strain ratesDuring severe impact conditions, brain tissue experiences a rapid and complex deformation, which can be seen as a mixture of compression, tension and shear. Diffuse axonal injury (DAI) occurs in animals and humans when both the strains and strain rates exceed 10% and 10/s, respectively. Knowing the mechanical properties of brain tissue in shear at these strains and strain rates is thus of particular importance, as they can be used in finite element simulations to predict the occurrence of brain injuries under different impact conditions. However, very few studies in the literature provide this information. In this research, an experimental setup was developed to perform simple shear tests on porcine brain tissue at strain rates ≤120/s. The maximum measured shear stress at strain rates of 30, 60, 90 and 120/s was 1.15±0.25 kPa, 1.34±0.19 kPa, 2.19±0.225 kPa and 2.52±0.27 kPa, (mean±SD), respectively at the maximum amount of shear, K =1. Good agreement of experimental, theoretical (Ogden and Mooney–Rivlin mod)and numerical shear stresses was achieved (p =0.7866–0.9935). Specimen thickness effects (2.0–10.0 mm thick specimens) were also analyzed numerically and we found that there is no significant difference (p =0.9954) in the shear stress magnitudes, indicating a homogeneous deformation of the specimens during simple shear tests. Stress relaxation tests in simple shear were also conducted at different strain magnitudes (10–60% strain) with the average rise time of 14 ms. This allowed us to estimate elastic and viscoelastic parameters (initial shear modulus, μ=4942.0 Pa, and Prony parameters: g1=0.520, g2=0.3057, τ1=0.0264 s, and τ2=0.011 s) that can be used in FE software to analyze the non-linear viscoelastic behavior of brain tissue. This study provides new insight into the behavior in finite shear of brain tissue under dynamic impact conditions, which will assist in developing effective brain injury criteria and adopting efficient countermeasures against traumatic brain injury.
1066Scopus© Citations 148 - PublicationAutomated Estimation of Collagen Fibre Dispersion in the Dermis and its Contribution to the Anisotropic Behaviour of SkinCollagen fibres play an important role in the mechanical behaviour of many soft tissues. Modelling of such tissues now often incorporates a collagen fibre distribution. However, the availability of accurate structural data has so far lagged behind the progress of anisotropic constitutive modelling. Here, an automated process is developed to identify the orientation of collagen fibres using inexpensive and relatively simple techniques. The method uses established histological techniques and an algorithm implemented in the MATLAB image processing toolbox. It takes an average of 15 s to evaluate one image, compared to several hours if assessed visually. The technique was applied to histological sections of human skin with different Langer line orientations and a definite correlation between the orientation of Langer lines and the preferred orientation of collagen fibres in the dermis (p<0.001,R 2 =0.95) was observed. The structural parameters of the Gasser–Ogden–Holzapfel (GOH) model were all successfully evaluated. The mean dispersion factor for the dermis was κ=0.1404±0.0028. The constitutive parameters μ, k 1 and k 2 were evaluated through physically-based, least squares curve-fitting of experimental test data. The values found for μ, k 1 and k 2 were 0.2014 MPa, 243.6 and 0.1327, respectively. Finally, the above model was implemented in ABAQUS/Standard and a finite element (FE) computation was performed of uniaxial extension tests on human skin. It is expected that the results of this study will assist those wishing to model skin, and that the algorithm described will be of benefit to those who wish to evaluate the collagen dispersion of other soft tissues.
709Scopus© Citations 152 - PublicationThird- and fourth-order constants of incompressible soft solids and the acousto-elastic effectAcousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third- and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for ρv2, where ρ is the mass density and v the wave speed, in terms of the elongation e of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: ρv2=a+be+ce2, say, a depends linearly on μ; b on μ and A; and c on μ, A, and D, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.
465Scopus© Citations 55 - PublicationAutomated Estimation of Collagen Fibre Dispersion in the Dermis and its Contribution to the Anisotropic Behaviour of Skin(Springer, 2012-08)
; ; ; ; Collagen fibres play an important role in the mechanical behaviour of many soft tissues. Modelling of such tissues now often incorporates a collagen fibre distribution. However, the availability of accurate structural data has so far lagged behind the progress of anisotropic constitutive modelling. Here, an automated process is developed to identify the orientation of collagen fibres using inexpensive and relatively simple techniques. The method uses established histological techniques and an algorithm implemented in the MATLAB image processing toolbox. It takes an average of 15 s to evaluate one image, compared to several hours if assessed visually. The technique was applied to histological sections of human skin with different Langer line orientations and a definite correlation between the orientation of Langer lines and the preferred orientation of collagen fibres in the dermis (p<0.001,R2=0.95) was observed. The structural parameters of the Gasser–Ogden–Holzapfel (GOH) model were all successfully evaluated. The mean dispersion factor for the dermis was κ=0.1404±0.0028. The constitutive parameters μ, k 1 and k 2 were evaluated through physically-based, least squares curve-fitting of experimental test data. The values found for μ, k 1 and k 2 were 0.2014 MPa, 243.6 and 0.1327, respectively. Finally, the above model was implemented in ABAQUS/Standard and a finite element (FE) computation was performed of uniaxial extension tests on human skin. It is expected that the results of this study will assist those wishing to model skin, and that the algorithm described will be of benefit to those who wish to evaluate the collagen dispersion of other soft tissues.350Scopus© Citations 152 - PublicationInhomogeneous deformation of brain tissue during tension testsMechanical characterization of brain tissue has been investigated extensively by various research groups over the past fifty years. These properties are particularly important for modelling Traumatic Brain Injury (TBI) by using finite element human head models to simulate brain injuries under different impact conditions. They are also increasingly important for computer assisted neurosurgery. During severe impact conditions, brain tissue experiences compression, tension and shear; however only limited tests have been performed in tension. Typically, cylindrical specimen are prepared and glued to platens to perform tensile tests which produce an inhomogeneous deformation field near the boundaries, thus contributing to higher magnitudes of stresses. In this research, we present the design and calibration of a High Rate Tension Device (HRTD) capable of performing tests up to a maximum strain rate of 90/s. We use experimental and numerical methods to investigate the effects of inhomogeneous deformation of porcine brain tissue during tension at different specimen thicknesses (4.0 – 14.0 mm), by performing tension tests at a strain rate of 30/s. One-term Ogden material parameters ( = 4395.0 Pa, a = - 2.8) were derived by performing an inverse finite element analysis to model all experimental data. A similar procedure was adopted to determine the Young’s modulus ( E = 11200 Pa) of the linear elastic regime. Based on this analysis, brain specimens of aspect ratio (diameter/thickness) S = 10/10 or lower (10/12, 10/13) are considered suitable for minimizing the effects of inhomogeneous deformation during tension tests.
512Scopus© Citations 37 - PublicationMechanical characterization of brain tissue in compression at dynamic strain ratesTraumatic brain injury (TBI) occurs when local mechanical load exceeds certain tolerance levels for brain tissue. Extensive research has been done previously for brain matter experiencing compression at quasistatic loading; however, limited data is available to model TBI under dynamic impact conditions. In this research, an experimental setup was developed to perform unconfined compression tests and stress relaxation tests at strain rates ≤90/s. The brain tissue showed a stiffer response with increasing strain rates, showing that hyperelastic models are not adequate. Specifically, the compressive nominal stress at 30% strain was 8.83 ± 1.94, 12.8 ± 3.10 and 16.0 ± 1.41 kPa (mean ± SD) at strain rates of 30, 60 and 90/s, respectively. Relaxation tests were also conducted at 10%–50% strain with the average rise time of 10 ms, which can be used to derive time dependent parameters. Numerical simulations were performed using one-term Ogden model with initial shear modulus μo=6.06±1.44, 9.44 ± 2.427 and 12.64 ± 1.227 kPa (mean ± SD) at strain rates of 30, 60 and 90/s, respectively. A separate set of bonded and lubricated tests were also performed under the same test conditions to estimate the friction coefficient μ, by adopting combined experimental–computational approach. The values of μ were 0.1 ± 0.03 and 0.15 ± 0.07 (mean ± SD) at 30 and 90/s strain rates, respectively, indicating that pure slip conditions cannot be achieved in unconfined compression tests even under fully lubricated test conditions. The material parameters obtained in this study will help to develop biofidelic human brain finite element models, which can subsequently be used to predict brain injuries under impact conditions.
630Scopus© Citations 196 - PublicationNon-invasive evaluation of skin tension lines with elastic waves(Wiley, 2016-11-20)
; ; ; ; Background: Since their discovery by Karl Langer in the 19th Century, Skin Tension Lines (STLs) have been used by surgeons to decide the location and orientation of an incision. Although these lines are patient-specific, most surgeons rely on generic maps to determine their orientation. Beyond the imprecise pinch test, there still exists no accepted method for determining the STLs in vivo. Methods: (i) The speed of an elastic motion travelling radially on the skin of canine cadavers was measured with a commercial device called the Reviscometer R . (ii) Similar to the original experiments conducted by Karl Langer, circular excisions were made on the skin and the subsequent geometric changes to the resulting wounds and excised samples were used to determine the orientation of STLs. Results A marked anisotropy in the speed in the elastic wave travelling radially was observed. The orientation of the fastest wave was found to correlate with the orientation of the elongated wound (P < 0.001, R2 = 74%). Similarly, the orientation of fastest wave was the same for both in vivo and excised isolated samples, indicating that the STLs have a structural basis. Resulting wounds expanded by an average area of 9% (+16% along STL and −10% across) while excised skin shrunk by an average of 33% (23% along STL and 10% across). Conclusion: Elastic surface wave propagation has been validated experimentally as a robust method for determining the orientation of STLs nondestructively and non-invasively. This study has implications for the identification of STLs and for the prediction of skin tension levels, both important factors in reconstructive surgeries for both medicine and veterinary medicine.638Scopus© Citations 24 - PublicationMechanical characterization of brain tissue in tension at dynamic strain ratesMechanical characterization of brain tissue at high loading velocities is crucial for modeling Traumatic Brain Injury (TBI). During severe impact conditions, brain tissue experiences compression, tension and shear. Limited experimental data is available for brain
623Scopus© Citations 169