The present work focuses on the dynamic compressive response of dynamically crushed auxetic structures. The aim is to propose a simplified methodology to assess the influence of geometrical/topological and material parameters on the impact response of these structures. The response also depends on the impact velocity. Based on an analogy with the propagation of shock waves in a rigid, perfectly plastic, locking (RPPL) material model, two approaches are developed to study the collapse of the structure crushed by a rigid impactor: (i) an analytical development and (ii) an iterative procedure, are proposed to evaluate the energy transfer and the impactor deceleration, thus allowing the physical quantities of interest to be deduced: dynamic stress, crushed length and strain, time for densification, stop time for the impactor. The methodology is presented and illustrated with the conventional 2D re-entrant auxetic, of which every range of geometrical data can be taken into account in the proposed formulas. Finite Element explicit simulations were carried out to confirm the analytical prediction. Results show good agreement between analytical and Finite Element results.

This paper investigates the characterization and numerical modeling of the elastic behavior of the human humerus bone using a recently developed micromechanical approach coupled to nanoindentation measurements. At first, standard three-point bending experiments were conducted under low static loading, using several humerus diaphysis in order to identify the apparent elastic modulus of the bone in static regime. Then, a drop tower impact experiment was used on the same set of humerus diaphysis specimens, in order to assess the elastic modulus in dynamic regime. These measurements will be used as reference bases for comparison purpose. The originality of this work, lies in the coupling between a two-phase micromechanical approach based on Mori-Tanaka homogenization scheme for cylindrical voids and nanoindentation measurements of the elastic modulus of the bone matrix phase. This model has been implemented using a user defined material subroutine VMAT in ABAQUS© Explicit code. The bone mechanical response prediction using the proposed methodology was validated against previous standard experimental data. Finally, it was shown that the numerical predictions are consistent with the physical measurements obtained on human humerus via the good estimation of the ultimate impact load.

This paper deals with the formulation, development and validation of a newly developed micromechanical-based model for the modeling of the nonlinear ductile fracture of human humerus. The originality of the present works concerns the coupling between the micromechanical formulation based on the Mori-Tanaka homogenization scheme for cylindrical voids and the Marigo nonlinear ductile damage model based on the porosity growth. The proposed model was implemented as a User Material UMAT within the explicit dynamic software LS-DYNA and validated by numerical and experimental analysis conducted by a drop tower impact of human humerus. The outcome of the proposed multi-scale model appears to correctly predict the general trends observed experimentally via the good estimation of the ultimate impact load and the fracture patterns of the human humerus.

The relevance and biofidelity level of the human numerical models are key issues in car accidents related trauma research. To limit the risk of injury of upper extremities and plan a preventive intervention, the humerus mechanical properties must be correctly assessed. However, the constitutive models used nowadays are still mainly derived from experimental characterizations carried out at the macroscopic scale without taking into account the bone microarchitecture. A multiscale approach coupled with nanoindentation experiments revealed to be more appropriate when the robustness of computation and accuracy of results are of interest. In this study, we propose a multi-scale approach for the accurate characterization and modeling of the mechanical behavior of the human humerus under low velocityimpact. The present model is based on the coupling between the Mori-Tanaka homogenization scheme 0 for the estimation of the elastic properties of the humeral cortical bone 0 0, and an isotropic damage model 0 for the prediction of the bone damage evolution. In order to consider the strain rate effects on the humerus behavior, the standard model of Johnson-Cook is adopted as a preliminary guess 0. The obtained model is implemented using a User Material subroutine (UMAT) within the explicit dynamic code LS-DYNA 0. The validity of the resulting finite element model has been validated by comparing numerical predictions with experimental observations at different length-scales. The outcome of the proposed multi-scale model appears to correctly predict the general trends observed experimentally through the good estimation of the ultimate impact load that a human humerus may encounter before fracture. The fracture patterns predicted by the proposed damage model are consistent with the physical humerus rupture even if this model is limited only to the failure initiation. Further improvements will be performed to the present model to take into account the marrow effects and rupture propagation paths.

Modeling the mechanical behavior of bone is very complex due to substantial variability of the mechanical response of bone. The objective of this study is to investigate the link between morphology of the human parietal bone and its mechanical behavior in compression with two different strain rates. Five formalin-preserved human skulls were used, and 10 specimens were taken from the parietal bone of each subject. The internal geometry of the osseous material was studied with a micro-tomography device. For mechanical testing, quasi-static (0.02 s–1) tests on a conventional compression machine and dynamic tests (1500 s–1) on a split Hopkinson pressure bar (SHPB) were conducted on 9 mm diameter samples. The results were used to examine relationships between the morphological parameters to find morphological correlations. Linkages between mechanical behavior and morphology of the human parietal bone were also analyzed to develop a behavior model based on micro-structure parameters as determined by micro-scanning.

The use of highly sensitive soft materials has become increasingly apparent in the last few years in numerous industrial fields, due to their viscous and damping nature. Unfortunately these materials remain difficult to characterize using conventional techniques, mainly because of the very low internal forces supported by these materials especially under high strain-rates of deformation. The aim of this work is to investigate the dynamic response of a polymer gel brain analog material under specific rotational-impact experiments. The selected polymer gel commercially known as Sylgard 527 has been studied using a specific procedure for its experimental characterization and numerical modeling. At first an indentation experiment was conducted at several loading rates to study the strain rate sensitivity of the Sylgard 527 gel. During the unloading several relaxation tests were performed after indentation, to assess the viscous behavior of the material. A specific numerical procedure based on moving least square approximation and response surface method was then performed to determine adequate robust material parameters of the Sylgard 527 gel. A sensitivity analysis was assessed to confirm the robustness of the obtained material parameters. For the validation of the obtained material model, a second experiment was conducted using a dynamic rotational loading apparatus. It consists of a metallic cylindrical cup filled with the polymer gel and subjected to an eccentric transient rotational impact. Complete kinematics of the cup and the large strains induced in the Sylgard 527 gel, have been recorded at several patterns by means of optical measurement. The whole apparatus was modeled by the Finite Element Method using explicit dynamic time integration available within Ls-dyna(®) software. Comparison between the physical and the numerical models of the Sylgard 527 gel behavior under rotational choc shows excellent agreements.

"On the influence of marrow on the mechanical behavior of porcine trabecular bone under dynamic loading: a numerical investigation." Computer Methods in Biomechanics and Biomedical Engineering, 18(sup1), pp. 1974–1975

With the aim to improve the safety of people, it is essential to know the phenomena of deformation, damage, and fracture of the various parts of the human body. This kind of study necessitates the creation of numerical models allowing making biologically relevant simulations of accidents. Several models of skull are proposed in the literature, the homogeneous macroscopic models of the bone of the human skull brands, the macroscopic models making the difference between cortical bone and spongy bone (Raul et al. 2006), or the microscopic models of Halgrin 2011. For the macroscopic models, the modeling is not refined enough to represent the bone of the skull in a correct way. With regards to the microscopic models, the setups allow good modeling but ask for a significant calculation time in order to be usable in simulations of crash of vehicle. There are also several studies which tried to identify the mechanical parameters of the human bone according to the morphological parameters, these equations do not allow to obtain a good precision in the calculation of the modulus. We can quote Van Eijden et al. (2006), Van Lenthe et al. (2006), and Chatelin et al. (2011) who identified the Eapp modulus according to morphological parameters in particular BV/TV (percentage of bone in a volume). The main criticism that can be made for this kind of model is the globalized vision of the morphology of the bone; while the geometry of the skull bone makes that there are differences inside the same sample having an impact on the mechanical behavior. This article suggests an intermediate model, precise enough to model with finite elements the human skull bone by taking into account the morphology of the head and with a reasonable calculation time. The consideration of the variability of the bone will be represented as layers of elements of different mechanical properties. We limit ourselves for this study to the linear modeling of a quasi-static compression test.

It has been shown through recent investigations in biomechanics, that marrow can play a critical role upon the cancellous bone behavior [1]. Besides its direct influence on the transport properties including pressure drop, shear dissipated energy an d tortuosity of the bone geometry, the marrow is also responsible in transmitting and regulating the int r-lamellas pressure [2], due to external loadi ng especially in case of impacts and crash accidents c au ing bone fracture. It is also worthy to notice, that for biological and clinical reasons such as bone re modeling, aging effects and drugs use, it is important to understand and quantify the mechanical behavior of cancellous bone in the presence of the marrow [3], [4]. A quick review in the biomechanics field shows an a bundant literature related to the mechanical characterization of cancellous bone, yet only very f w investigations have considered the influence of the marrow effects [1]-[4]. In the present investig a on a new numerical procedure is proposed, to study the marrow effects on the mechanical behavior of the cancellous bone. The proposed approach is based on fluid-structure interactions using part icles methods for the modeling of the trabecular bo ne and marrow environment. The Smoothed Particle Hydro dynamics method (SPH) is used for the modeling of the trabecular lamella while the Lattic e-Boltzmann method (LBM) is used for the marrow flow modeling. Based on their previous work, the authors proposed an efficient shell-based SPH method which shows to be a real alternative to the conventional finite element, especially under large strains [5], [6]. This method has been adopte d in the present investigation for the modeling of trabeculea using the Total Lagrangian Formulation. The present approach has been validated in the mode ling of the marrow flow through a cancellous bone of a rabbit femoral head sample [7] (Fig 1-a). At first, a two-dimensional slice of micro-CT image of 0.0185mm resolution [7] has been used. A meso-scale rectangu l r area of 1.23 1mm has been extracted as a domain of study (Fig 1-b). The 2D-domain has been discretized using 123 100 particles, where Lattice particles have been used f or the marrow areas and SPH particles for the bone trabeculea. For the boundary conditions, an imposed velocity flow of the marrow was imposed on the upper side (inlet), while free conditions were impo sed on the two lateral edges. At the bottom side (outlet) no pressure variation was imposed. As a fi rst attempt, the bone lamellas were assumed to be elastic isotropic (on the domain of study) and the marrow is considered as an incompressible fluid. The numerical results obtained using the proposed F SI coupling approach between SPH and LBM (Fig 1-c), have been compared to those obtained usi ng OpenFOAM® CFD software [8]. The preliminary comparisons show that the proposed appr oach is very promising and may constitute an efficient and elegant alternative to the convention al mesh based methods. a) Rabbit femoral head sample [7] b) 2D Micro-CT scan image c) Bone marrow flow modeling using FSI by coupling LB and SPH methods Fig 1: Rabbit cancellous Bone/Marrow modeling using FSI by coupling LBM and SPH methods

This paper is devoted to the experimental characterization and micromechanical modeling of the elastic behavior of the human cranial bone. Three points bending tests on the frontal, parietal and temporal bone specimens have been performed to determine their mechanical characteristics under quasi-static loading. It is shown that Young's modulus and the bending stiffness are significantly influenced by the bone morphology and orientation. The anis otropic bone elastic properties have been then estimated by means of the Mori-Tanaka homogenization scheme coupled to experimental measurements of structural anisotropy by microtomography techniques. The obtained micromechanical model has been implemented as an UMAT routine within the explicit dynamics code LS-DYNA (R) and applied successfully for the estimation of the mechanical properties of the human cranial frontal bone. The obtained numerical results show an overall good agreement when compared to the experimental data. (C) 2014 Elsevier Ltd. All rights reserved.

The present study aims at providing quantitative data for the personalisation of geometrical and mechanical characteristics of the adult cranial bone to be applied to head FE models. A set of 351 cranial bone samples, harvested from 21 human skulls, were submitted to three-point bending tests at 10 mm/min. For each of them, an apparent elastic modulus was calculated using the beam's theory and a density-dependant beam inertia. Thicknesses, apparent densities and percentage of ash weight were also measured. Distributions of characteristics among the different skull bones show their symmetry and their significant differences between skull areas. A data analysis was performed to analyse potential relationship between thicknesses, densities and the apparent elastic modulus. A specific regression was pointed out to estimate apparent elastic modulus from the product of thickness by apparent density. These results offer quantitative tools in view of personalising head FE models and thus improve definition of local injury criteria for this body part.

Brain injury constitutes one of the major causes of death in road accidents. Finite element (FE) models are commonly used to investigate the biomechanics of head impact since they enable an enhance...

Click to increase image sizeClick to decrease image sizeKeywords:: damageappendicular boneexperimental characterisation AcknowledgementsThis work was supported by International Campus on Safety and Intermodality in Transportation, the European Community, the Délégation Régionale à la Recherche et à la Technologie, the Ministère de l'Enseignement supérieur et de la Recherche, the Région Nord Pas de Calais and the Centre National de la Recherche Scientifique. The authors also thank Régis Bry and Maurice De Meulaere for their helpful contribution to this work.

Density, structural anisotropy and mechanical strength are important features when evaluating and describing bone tissues. Many theories on bone material have attempted to predict the quasi-static failure of bones, but very few have attempted to study the fracture behaviour of long bones under impact. To estimate fracture and plan a preventive intervention, the strength of the humerus must be precisely quantified (Duprey et al. 2007a, 2007b). To this end, micromechanical approaches combined with CT-based finite element (FE) models have been proved to be more appropriate when the robustness of computation and accuracy of results are of interest. The aim of this study was to propose a consistent multiscale approach for the accurate characterisation and modelling of mechanical behaviour of the human humerus under impact. The present micromechanical model (Rahmoun et al. 2009) is based on the combination of the Mori–Tanaka homogenisation scheme (Mori and Tanaka 1973) for the estimation of elastic properties of the humerus bone and a 3D hexahedral FE model at the macro-level for the prediction of the global response of the humerus.

"Evaluation of wrist guard effectiveness for snowboarders." Computer Methods in Biomechanics and Biomedical Engineering, 16(sup1), pp. 187–188Keywords:: wrist guardimpact biomechanicsinjury mechanisms AcknowledgementsThis research was supported by the Nord-Pas-de-Calais Region, the European Community, the Regional Delegation for Research and Technology, the Ministry of Higher Education and Research and the National Center for Scientific Research.

This two-part paper described the results of the research programme PROCAB for train driver protection during rail collisions. In Part I, a methodology was proposed to analyse driver survivability in train crash. Appropriate experimental devices and associated numerical models were developed which were able to reproduce the loads and accelerations imparted to the train driver and on the interior elements of the driver's cabin. A full validation programme was realised involving correlation between experimental methods and computer model outputs. Experiments and computer results indicated that during a collision, the driver was likely to strike the desk at the lower chest. Since actual desk was extremely rigid due to maintenance requirements, chest deflection exceeded human tolerance. Part II deals with the development of an interior driver protection.

This two-part paper described the results of the research programme PROCAB (French acronym for PROtection CABine) for train driver protection in rail collisions. In the part I, virtual and physical testing were developed to predict the train driver dynamics and related injuries due to secondary impact with cabin furniture. The conclusion was that the desk represented a hostile secondary impact environment for the locomotive engineer by inducing severe thoracic injuries. Part II included the design, fabrication and testing of an improved command desk. The concept selected was a movable rigid desk with energy-absorbing aluminium honeycomb to slow the desk motion, coupled with knee bolsters. A prototype of the protection device was fabricated and evaluated in a dynamical sled test under a 5g, 0.1s deceleration pulse. Preliminary results demonstrated the effectiveness of this concept in reducing the thoracic injury risk without increasing risk in another area (head, neck, chest, femurs and tibias).

Click to increase image sizeClick to decrease image sizeKeywords:: train collisionsecondary impactdriver protectionimpact biomechanicsinjury mechanisms AcknowledgementsThis research was supported by the Nord-Pas-de-Calais Region, the European Community, the Regional Delegation for Research and Technology, the Ministry of Higher Education and Research and the National Center for Scientific Research.