Fahmi Chaari

Identification of the spongy bone mechanical behavior under compression loads: numerical simulation versus experimental results

Abstract In the fields of crashworthiness, ballistic protections, and other medical applications, the accurate material constitutive law of spongy bone is needed to carry out valid finite element analyses. The direct identification of bone mechanical behavior law is not easy since it is a complex network of intersecting osseous spans (trabeculae), where the space in and around the trabeculae contains bone marrow and fluids. We propose in this work to overtake the bone geometrical dispersion by applying an inverse scheme identification method, based on the global mechanical response, correlated with the exact geometry. First step study was made on spongy bone cylindrical samples cut in beef ribs. Compression tests on these samples showed a large dispersion and suggested that the fluid effect can be neglected during the quasi-linear part of the mechanical response. The micro-architecture of each sample was acquired thanks to microcomputed tomography technique (μCT). After applying a threshold, we used the μCT data to build a micro-FE model of the spongy bone. This model is introduced in FE code in order to simulate quasi-static compression of the sample. An elastic plastic constitutive law is assigned to the spongy bone. An optimization procedure is then applied in order to identify the spongy bones behavior. The optimization function is based on the global response (force versus displacement) of the sample. This procedure was repeated for different samples in order to obtain average spongy bone behavior.

On the effect of marrow in the mechanical behavior and crush response of trabecular bone

The present paper focuses on the mechanical behavior analysis of bones at mesoscopic scale, paying a special attention to the trabecular bone and the bone marrow filling the porosities. Uni-axial quasi-static compression tests under unconfined conditions have been performed to identify the mechanical behavior of 46 trabecular bone samples. The bone marrow for 22 samples has been preserved to analyze the fluid flow effects on the crushing response. Although deformation patterns do not differ significantly, the average crush behavior of the trabecular bone shows an unexpected decrease of the mechanical properties when the marrow is kept in the sample (26% for the elastic modulus (E(a)), 38% for the maximum compressive stress (σ(max)) and 33% for the average stress (σ(mean))). An explanation is given by analyzing the contribution of the bone marrow viscosity which smooths the mechanical response. A numerical analysis on an idealized trabecula confirms that the marrow induces transverse pressure and extra local stress on trabeculae during its flow, causing the premature collapse of the trabecular network.

Micromechanical Modeling of the Anisotropy of Elastic Biological Composites

In this paper, a Mori–Tanaka micromechanical modeling of effective elastic properties of trabecular bone is coupled with experimental measurements of morphology obtained from X-ray microtomography. The principle of modeling is based on the Eshelby and Hill polarization tensors of isolated ellipsoidal inclusions embedded in an infinite matrix. The problem is entirely geometrized and is treated in terms of averages of Walpoles components of the fourth-order tensors describing the problem. The structural anisotropy of trabecular bone was determined in three-dimensional space by means of the mean intercept length method and expressed by a fabric tensor, which is a second rank tensor describing the orientation distribution of inclusions volume fractions and degree of anisotropy of trabecular bone. Modeling results showed the high effects of the aspect ratio and orientation distribution of pores on the effective elastic properties of trabecular bone.

Spongy bone deformation mechanisms: Experimental and numerical studies.

In order to identify the spongy bones mechanical behaviour, we performed compression tests on cylindrical samples. Experimental results show important dispersions and an unexpected inverse strain rate dependency at low range of loading velocities. The origin of the dispersions can be attributed to the combination of the architecture effect and the mechanical properties variation of the constitutive material. In order to understand the inverse strain rate sensitivity, we used a controlled constitutive material to build new equivalent samples with the spongy bones architecture. These samples were subjected to compression tests. Numerical simulations of compression tests on the same architecture have been carried out with FE models built from μCt data. The obtained results are compared in term of final sample shape and the evolution of the compression force.

Macro-modeling of spot weld strength and failure: Formulation and identification procedure based on pure and mixed modes of loading

Purpose This paper aims to propose a macro modeling approach to simulate the mechanical behavior and the failure of spot welded joints in structural crashworthiness computations. Design/methodology/approach A connector element is proposed to simulate the behavior and failure of spot weld joints. An elastic-plastic damageable model is used to describe the non-linear response and rupture. The connector model involves several parameters that have to be defined. Some are directly identified based on mechanical interpretations and experimental tests characteristics. The remaining parameters are identified through a finite element model updating approach using Arcan tests. Resulting from a sensitivity analysis, an original two steps optimization methodology, using the Modes I and II Arcan tests results sequentially, has been implemented to identify the remaining model parameters. Findings The numerical results for Arcan tests in mixed Modes I/II are in a good agreement with the experimental ones. The model is also validated on tensile pull-out, single lap shear and coach-peel tests. Originality/value By comparison with previous published results, the proposed model brings a significant improvement. The main innovative aspects of this work are as follows: the proposed formulation, a reduced number of parameters to optimize, an original sequential optimization methodology based on physical and mechanical analyses and a mesh size independent connector element.

Brittle Fracture: Experimental and Numerical Modeling Using Phase-Field Approach

Crack paths prediction is one of the most challenging of fracture mechanics. The difficulty in this seek is how to obtain numerical models able of predicting unknown crack paths. One of these models is called the phase-field approach. It represents cracks by means of an additional continuous field variable. This model approximates a sharp crack with a diffuse crack phase-field where a characteristic length regularizes the crack topology and a crack energy density describes the energy dissipated in order to break a brittle piece. This method avoids some of the drawbacks of a sharp interface description of cracks. The phase-field model for brittle fracture assumes quasi-static loading conditions. However, dynamic effects have a great impact on the crack growth in many practical applications. Therefore, this investigation presents an extension of the quasi-static phase-field model for the fracture to the dynamic case. Experiment tests will be presented in this work in order to study the efficiency and the robustly of phase-field approach for modeling brittle fracture and capturing complex crack topologies.

Anisotropy and strain rate effects on bovine cortical bone: combination of high-resolution imaging and dynamic loading.

Biomechanics of impact requires high accuracy responses at both mesoand macro-scales of the skeleton. The effect of strain rate and the direction of loading are also crucial for a goodpredictionof injuries.Bone isdescribed in the literature as a hard-mineralised tissue composed of fibres, an organic matrix and inorganic salts. Cortical bone has porosity under 30%, whereas the porosity in cancellous bone varies from 30% to 90%. Anisotropies, heterogeneities and nonlinearity aspects of cortical bone have already been studied through different mechanical tests (Lindhom et al. 1964; Novitskaya et al. 2011).Nevertheless, the accurate investigation of strain rate effect is still one of the challenges in bone characterisation. This study combines high-resolution imaging techniquewith themechanical responses of cortical bone under compression loadings at high strain rates.

Analysis of the cortical bone thickness of human thorax based on multi-scale imaging techniques

Recent studies issued by the World Health Organization (2009) reported that road accidents will be the third highest cause of premature deaths in 2020. Besides these general considerations, research aiming to improve road safety is still needed to provide advanced numerical tools for future evaluations of new cars. Numerous models of the human body have already been developed butwere limited in their biofidelity. The thorax is one of the segments frequently involved in road accidents and the complex ribs geometry complicates the characterisation tasks. One such task concerns the description of rib geometry and more precisely the thinness of cortical bone. The cortical bone distribution in the ribs is one of the major factors influencing the thorax response when submitted to an impact (Kemper et al. 2007). Previous studies investigating this parameter using physical measurements (Roberts and Chen 1972) and photographs (Yoganandan andPintar 1998) suffer froma lack of accuracy. Recently, medical CT scans, vet CT scans (Charpail et al. 2005) and mCT scans (Li et al. 2009) have been used for a better characterisation. This study presents a new method to investigate the whole rib geometry using accurate multilevel scale acquisition devices.

A micro-finite element reconstruction for identifing spongy bone mechanical behaviour

In the fields of transportations safety, ballistic protections and other medical applications, the accurate material constitutive law of spongy bone is needed for finite element analyses. Bones are made up of two different types of tissue, the compact bone (cortical) and the spongy bone (trabeculare). In contrast to the structure of cortical bone, trabeculare bone is a complex network of intersecting curve plates and tubes (trabeculae). The spaces in and around the trabeculae contain fluids and bone marrow. The identification of bone mechanical behaviour law is complex because of the random distribution of the osseous spans. The mechanical properties depend both on geometrical and physical parameters. Global mechanical testing give so information of the structure behaviour, but not the trabeculae properties. More over such global properties reported in literature show a large dispersion (Van Rietbergen 1995). An inverse parametric method seems to be an appropriate method to identify these parameters. During this identification, geometry information is needed to access the mechanical property of the bone. Thanks to the Micro-Computed Tomography (mCT),such informations can be probed. We propose in this work a methodolody of a reconstruction of the geometry of spongy bone in order to realise a finite element analyse.