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Jacquelin E.,University of Lyon | Jacquelin E.,University Claude Bernard Lyon 1 | Jacquelin E.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs | Friswell M.I.,University of Swansea | And 4 more authors.
Mechanical Systems and Signal Processing | Year: 2016

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments. © 2016 Elsevier Ltd. All rights reserved.

Sinou J.-J.,CNRS Tribology and Dynamic Systems Laboratory | Jacquelin E.,University Claude Bernard Lyon 1 | Jacquelin E.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs
Mechanical Systems and Signal Processing | Year: 2015

A stochastic harmonic balance method with a recursive procedure is developed to evaluate the steady-state response of a rotor system with uncertain stiffness and asymmetric coupling that involves time-dependent terms. The Polynomial Chaos (PC) expansion is proposed to evaluate the mean and the standard deviation of the responses and the harmonic amplitudes of orders 1-4 involving 288 degrees-of-freedom. To determine the coefficients of the expansion requires to solve a large system of equations. To achieve this and to avoid numerical problems related to the size of the system, the first contribution of the study consists of a recursive evaluation of the Polynomial Chaos coefficients to be able to estimate the stochastic response for a high order of the Polynomial Chaos expansion. From the methodology implemented, the steady-state responses and n× harmonic components (for n=1, 2, 3 and 4 in the present study) of the asymmetric rotor with uncertainty are evaluated for several PC orders. Then, the second main contribution focuses on a clarification and analysis of the use of Polynomial Chaos expansion around the critical speeds. First, it is observed that the convergence is slow: the response obtained with 30 PCs is twice the one obtained with 200 PCs. Second, it is noted that the parity of the PC order has a strong influence on the response level: whereas two responses obtained with two consecutive even PC orders (or two consecutive odd PC orders) are almost the same for a given rotation speed, the ratio of the responses evaluated with two consecutive PC orders (one even order and one odd order) may be large (e.g. oscillations between two consecutive PC orders greater than 10 are noticeable if the PC order is about 30). © 2014 Elsevier Ltd. All rights reserved.

Jacquelin E.,University of Lyon | Jacquelin E.,University Claude Bernard Lyon 1 | Jacquelin E.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs | Adhikari S.,University of Swansea | And 3 more authors.
Journal of Sound and Vibration | Year: 2015

Abstract Polynomial chaos solution for the frequency response of linear non-proportionally damped dynamic systems has been considered. It has been observed that for lightly damped systems the convergence of the solution can be very poor in the vicinity of the deterministic resonance frequencies. To address this, Aitken's transformation and its generalizations are suggested. The proposed approach is successfully applied to the sequences defined by the first two moments of the responses, and this process significantly accelerates the polynomial chaos convergence. In particular, a 2-dof system with respectively 1 and 2 parameter uncertainties has been studied. The first two moments of the frequency response were calculated by Monte Carlo simulation, polynomial chaos expansion and Aitken's transformation of the polynomial chaos expansion. Whereas 200 polynomials are required to have a good agreement with Monte Carlo results around the deterministic eigenfrequencies, less than 50 polynomials transformed by the Aitken's method are enough. This latter result is improved if a generalization of Aitken's method (recursive Aitken's transformation, Shank's transformation) is applied. With the proposed convergence acceleration, polynomial chaos may be reconsidered as an efficient method to estimate the first two moments of a random dynamic response. © 2015 Elsevier Ltd.

Gras L.-L.,Arts et Metiers ParisTech | Gras L.-L.,University of Lyon | Gras L.-L.,University Claude Bernard Lyon 1 | Gras L.-L.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs | And 5 more authors.
Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine | Year: 2014

In models developed for impact biomechanics, muscles are usually represented with one-dimensional elements having active and passive properties. The passive properties of muscles are most often obtained from experiments performed on animal muscles, because limited data on human muscle are available. The aim of this study is thus to characterize the passive response of a human muscle in tension. Tensile tests at different strain rates (0.0045, 0.045, and 0.45s-1) were performed on 10 extensor carpi ulnaris muscles. A model composed of a nonlinear element defined with an exponential law in parallel with one or two Maxwell elements and considering basic geometrical features was proposed. The experimental results were used to identify the parameters of the model. The results for the first- and second-order model were similar. For the first-order model, the mean parameters of the exponential law are as follows: Young's modulus E (6.8MPa) and curvature parameter α (31.6). The Maxwell element mean values are as follows: viscosity parameter η (1.2MPas) and relaxation time Δ(0.25s). Our results provide new data on a human muscle tested in vitro and a simple model with basic geometrical features that represent its behavior in tension under three different strain rates. This approach could be used to assess the behavior of other human muscles. © IMechE 2014.

Helfenstein-Didier C.,University Claude Bernard Lyon 1 | Helfenstein-Didier C.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs | Tanter M.,ESPCI ParisTech | Gennisson J.-L.,ESPCI ParisTech | And 2 more authors.
Journal of Biomechanics | Year: 2015

A protocol based on ultrafast ultrasonography was developed to study the internal response of isolated perfused human (n=3) and porcine (n=11) kidneys subjected to loading at 0.003. m/s and 0.3. m/s respectively.Regional uniaxial strains were calculated based on natural target tracking. The effect of loading speed and regional differences could be statistically detected on the porcine specimens. However, despite the inhomogeneity of their anatomical structures, strains' responses appeared relatively homogeneous at 0.3. m/s in both porcine and human kidneys.Failure, identified as a sudden change on the ultrasonography movie, also appeared at similar compression levels for both species (38.3% of applied strain in average for human and 35.8% of applied strain in average for porcine). © 2015 Elsevier Ltd.

Lacour J.-R.,University of Lyon | Lacour J.-R.,University Claude Bernard Lyon 1 | Lacour J.-R.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs | Bourdin M.,University of Lyon | And 3 more authors.
European Journal of Applied Physiology | Year: 2015

Metabolic measurement is still the criterion for investigation of the efficiency of mechanical work and for analysis of endurance performance in running. Metabolic demand may be expressed either as the energy spent per unit distance (energy cost of running, Cr) or as energy demand at a given running speed (running economy). Systematic studies showed a range of costs of about 20 % between runners. Factors affecting Cr include body dimensions: body mass and leg architecture, mostly calcaneal tuberosity length, responsible for 60–80 % of the variability. Children show a higher Cr than adults. Higher resting metabolism and lower leg length/stature ratio are the main putative factors responsible for the difference. Elastic energy storage and reuse also contribute to the variability of Cr. The increase in Cr with increasing running speed due to increase in mechanical work is blunted till 6–7 m s−1 by the increase in vertical stiffness and the decrease in ground contact time. Fatigue induced by prolonged or intense running is associated with up to 10 % increased Cr; the contribution of metabolic and biomechanical factors remains unclear. Women show a Cr similar to men of similar body mass, despite differences in gait pattern. The superiority of black African runners is presumably related to their leg architecture and better elastic energy storage and reuse. © 2015, Springer-Verlag Berlin Heidelberg.

Haupert S.,University Pierre and Marie Curie | Guerard S.,Arts et Metiers ParisTech | Mitton D.,University of Lyon | Mitton D.,University Claude Bernard Lyon 1 | And 3 more authors.
Journal of the Mechanical Behavior of Biomedical Materials | Year: 2015

The objective of this study was to investigate the sensitivity of the nonlinear elastic properties of cortical bone to the presence of a single submillimetric crack. Nonlinear elasticity was measured by nonlinear resonant ultrasound spectroscopy (NRUS) in 14 human cortical bone specimens. The specimens were parallelepiped beams (50×2×2mm3). A central notch of 500μm was made to control crack initiation and propagation during four-point bending. The nonlinear hysteretic elastic and dissipative parameters αf and αQ, and Young[U+05F3]s modulus Eus were measured in dry condition for undamaged (control) specimens and in dry and wet conditions for damaged specimens. The length of the crack was assessed using synchrotron radiation micro-computed tomography (SR-μCT) with a voxel size of 1.4μm. The initial values of αf, measured on the intact specimens, were remarkably similar for all the specimens (αf =-5.5±1.5). After crack propagation, the nonlinear elastic coefficient αf increased significantly (p<0.006), with values ranging from -4.0 to -296.7. Conversely, no significant variation was observed for αQ and Eus. A more pronounced nonlinear elastic behavior was observed in hydrated specimens compared to dry specimens (p<0.001) after propagation of a single submillimetric crack. The nonlinear elastic parameter αf was found to be significantly correlated to the crack length both in dry (R=0.79, p<0.01) and wet (R=0.84, p<0.005) conditions. Altogether these results show that nonlinear elasticity assessed by NRUS is sensitive to a single submillimetric crack induced mechanically and suggest that the humidity must be strictly controlled during measurements. © 2015 Elsevier Ltd.

Tran D.,University of Lyon | Tran D.,University Claude Bernard Lyon 1 | Tran D.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs | Mitton D.,University of Lyon | And 7 more authors.
Journal of Biomechanics | Year: 2014

A better understanding of the abdominal wall biomechanics could help designing new treatments for incisional hernia. In the current study, an experimental protocol was developed to evaluate the contributions of the abdominal wall components to the structural response of the anterior part of the abdominal wall. The specimens underwent 3 dissections (removal of (1) skin and subcutaneous fat, (2) anterior rectus sheath, (3) rectus abdominis muscles). After each dissection, they were subjected to air pressure up to 3. kPa. Ultrasound images and associated elastographic maps were collected at 0, 2 and 3. kPa in the intact state and strains on the internal surface were calculated using stereo-correlation in all states. Strains on the rectus abdominis and linea alba were analyzed. After the dissection of the anterior sheath of the rectus abdominis, longitudinal strain was found significantly different on the linea alba (5% at 3. kPa) and on the rectus abdominis area (11% at 3. kPa). The current results highlight the importance of the rectus sheath in the structural response of the anterior part of the abdominal wall ex vivo. Geometrical characteristics such as thicknesses and radii of curvature and mechanical properties (shear modulus of the rectus abdominis, e.g. at 0 pressure the average value is 14. kPa) were provided in order to facilitate future modeling efforts. © 2014 Elsevier Ltd.

Jayyosi C.,University of Lyon | Jayyosi C.,University Claude Bernard Lyon 1 | Jayyosi C.,Lbmc Laboratoire Of Biomecanique Et Mecanique Des Chocs | Coret M.,CNRS Research Institute in Civil Engineering and Mechanics | And 3 more authors.
Journal of the Mechanical Behavior of Biomedical Materials | Year: 2016

The characterization of biological tissue at the microscopic scale is the starting point of many applications in tissue engineering and especially in the development of structurally based constitutive models. In the present study, focus is made on the liver capsule, the membrane encompassing hepatic parenchyma, which takes a huge part in liver mechanical properties. An in situ bulge test experiment under a multiphoton microscope has been developed to assess the microstructure changes that arise with biaxial loading. Multiphoton microscopy allows to observe the elastin and collagen fiber networks simultaneously. Thus a description of the microstructure organization of the capsule is given, characterizing the shapes, geometry and arrangement of fibers. The orientation of fibers is calculated and orientation distribution evolution with loading is given, in the case of an equibiaxial and two non equibiaxial loadings, thanks to a circular and elliptic set up of the bulge test. The local strain fields have also been computed, by the mean of a photobleaching grid, to get an idea of what the liver capsule might experience when subjected to internal pressure. Results show that strain fields present some heterogeneity due to anisotropy. Reorientation occurs in non equibiaxial loadings and involves fibers layers from the inner to the outer surface as expected. Although there is a fiber network rearrangement to accommodate with loading in the case of equibiaxial loading, there is no significant reorientation of the main fibers direction of the different layers. © 2015 Elsevier Ltd.

Amabile C.,Arts et Metiers ParisTech | Amabile C.,Hospital for Special Surgery | Choisne J.,Arts et Metiers ParisTech | Nerot A.,Arts et Metiers ParisTech | And 3 more authors.
Journal of Biomechanics | Year: 2016

Body segment parameters (BSP) for each body's segment are needed for biomechanical analysis. To provide population-specific BSP, precise estimation of body's segments volume and density are needed. Widely used uniform densities, provided by cadavers' studies, did not consider the air present in the lungs when determining the thorax density. The purpose of this study was to propose a new uniform thorax density representative of the living population from 3D external body shape modeling. Bi-planar X-ray radiographies were acquired on 58 participants allowing 3D reconstructions of the spine, rib cage and human body shape. Three methods of computing the thorax mass were compared for 48 subjects: (1) the Dempster Uniform Density Method, currently in use for BSPs calculation, using Dempster density data, (2) the Personalized Method using full-description of the thorax based on 3D reconstruction of the rib cage and spine and (3) the Improved Uniform Density Method using a uniform thorax density resulting from the Personalized Method. For 10 participants, comparison was made between the body mass obtained from a force-plate and the body mass computed with each of the three methods. The Dempster Uniform Density Method presented a mean error of 4.8% in the total body mass compared to the force-plate vs 0.2% for the Personalized Method and 0.4% for the Improved Uniform Density Method. The adjusted thorax density found from the 3D reconstruction was 0.74g/cm3 for men and 0.73g/cm3 for women instead of the one provided by Dempster (0.92g/cm3), leading to a better estimate of the thorax mass and body mass. © 2016 Elsevier Ltd.

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