Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements

International audienceIn this article, a phenomenological numerical model of bone remodeling is proposed. This model is based on the poroelasticity theory in order to take into account the effects of fluid movements in bone adaptation. Moreover, the proposed remodeling law stands from the classical 'Stanford' law, enriched in order to take into account the loading frequency, through fluid movements. This coupling is materialized by a quadratic function of Darcy velocity. The numerical model is carried out, using a finite element method, and calibrated using experimental results at macroscopic level, from the literature. First results concern cyclic loadings on a mouse ulna, at different frequencies between 1 Hz and 30 Hz, for a force amplitude of 1.5 N and 2 N. Experimental results exhibit a sensitivity to the loading frequency, with privileged frequency for bone remodeling between 5 Hz and 10 Hz, for the force amplitude of 2 N. For the force amplitude of 1.5 N, no privileged frequencies for bone remodeling are highlighted. This tendency is reproduced by the proposed numerical computations. The model is identified on a single case (one frequency and one force amplitude) and validated on the other ones. The second experimental validation deals with a different loading regime: An internal fluid pressure at 20 Hz on a turkey ulna. The same framework is applied, and the numerical and experimental data are still matching in terms of gain in bone mass density

Experimental characterization of mechanical properties of the cement-aggregate interface in concrete

International audienceThe microstructure of the Interfacial Transition Zone (ITZ) between the aggregates and the cement paste is characterized by a higher porosity than that of the bulk paste. The particular properties of this zone strongly influence the mechanical behavior of concrete. Microscopic cracks, which develop during subsequent loading, appear either in the matrix (cement paste or mortar) or along the cement-aggregates interface. Cracks could be caused by either tensile, shear strengths or by combinations of both. In this work, the mechanical properties of the cement paste – aggregate sample are experimentally studied. The experimental tests are performed on parallelepipedic samples at classical aggregate scale (one centimeter sections). These samples are composed of limestone aggregates and Portland cement paste, hereafter named ''composite ". The cement paste is prepared with a water/cement ratio of 0.5. The shape of the prepared composites makes them convenient for direct tensile and shear tests. At different stages of hydration, we performed direct tensile and shear tests on the composites by means of specific devices. The same tests were carried out on the cement paste in order to compare with the composite results. The analysis of the experimental results showed that the tensile strength of the cement-aggregate interface was about 30% lower than that of the cement paste tensile strength. Also, the shear strength of the cement-aggregate interface was smaller than the shear strength of the cement paste. In the same way as macroscopic Mohr–Coulomb criterion, we observed an increase of shear strength when normal stress increased. It provides access to a local cohesion (c) and a local friction angle ðUÞ at classical aggregate scale

Permeability of rapid prototyped artificial bone scaffold structures

In this work, various three-dimensional (3D) scaffolds were produced via micro-stereolithography (µ-SLA) and 3D printing (3DP) techniques. This work demonstrates the advantages and disadvantages of these two different rapid prototyping methods for production of bone scaffolds. Compared to 3DP, SLA provides for smaller feature production with better dimensional resolution and accuracy. The permeability of these structures was evaluated experimentally and via numerical simulation utilizing a newly derived Kozeny–Carman based equation for intrinsic permeability. Both experimental and simulation studies took account of porosity percentage, pore size, and pore geometry. Porosity content was varied from 30% to 70%, pore size from 0.34 mm to 3 mm, and pore geometries of cubic and hexagonal closed packed were examined. Two different fluid viscosity levels of 1 mPa·s and 3.6 mPa·s were used. The experimental and theoretical results indicated that permeability increased when larger pore size, increased fluid viscosity, and higher percentage porosity were utilized, with highest to lowest degree of significance following the same order. Higher viscosity was found to result in permeabilities 2.2 to 3.3 times higher than for water. This latter result was found to be independent of pore morphology type. As well as demonstrating method for determining design parameters most beneficial for scaffold structure design, the results also illustrate how the variations in patient's blood viscosity can be extremely important in allowing for permeability through the bone and scaffold structures

Finite element-based micromechanical modeling of the influence of phase properties on the elastic response of cementitious mortars

This study reports the influence of inclusion stiffness and its distribution on the stress distributions in the microstructural phases of different cementitious mortars using microstructure-guided finite element simulations. Randomly generated periodic microstructures with single/multiple inclusion sizes and random spatial distribution, subjected to periodic boundary conditions and a strain-controlled virtual testing regime are chosen for final analysis. Numerical simulations reveal: (i) the differences in locations/magnitudes of stress concentrations as a function of inclusion stiffness and size distribution, and (ii) the sometimes detrimental influence of matrix and interface stiffening/strengthening on the overall composite response, leading to material design strategies when non-conventional inclusions are used in cementitious systems for special properties. The constitutive behavior in the linear elastic regime is extracted based on the predicted dominant principal stresses and strains in the representative area element. Thus, in addition to the microstructural phase stresses, this methodology also provides predictions of the composite elastic modulus, which are observed to be more reliable than those obtained from analytical prediction models

Numerical model of bone remodelling sensitive to loading frequency

International audienc

Numerical model of bone remodeling taking into account fluid phasis

ECCOMAS thematic conferenceInternational audienc

Modèle du remodelage osseux prenant en compte la phase fluide

L'os est un matériau en évolution permanente, la modification de l'architecture osseuse étant liée aux actions mécaniques externes qui lui sont appliquées. Ce phénomène, le remodelage osseux, est décrit mathématiquement par des lois liant la contrainte ou la déformation, et la variation de densité osseuse. Par ailleurs l'os est un milieu poreux, composé d'une partie fluide, d'une partie solide et d'intéractions entre elles. L'influence du fluide interne de l'os sur le remodelage est non négligeable. L'objectif de ce travail est de proposer un modèle numérique macroscopique de remodelage osseux, tenant compte des mouvements de fluide interne. Pour cela l'os est considéré, dans cette étude, comme un matériau poroélastique. Une méthode de résolution numérique du problème poroélastique, basée sur les éléments finis, est alors définie. Cette résolution est suivie d'un traitement numérique d'une loi de remodelage osseux, liant variation de densité osseuse et cumul de contrainte, et tenant compte des mouvements de fluide interne à travers la vitesse de Darcy. Ce modèle numérique est validé sur des études expérimentales, et il permet d'obtenir une prédiction de l'adaptation osseuse, selon le type d'os et le cas de chargement considérésMONTPELLIER-BU Sciences (341722106) / SudocSudocFranceF

Experimental and numerical identification of cortical bone permeability

International audienceBone is a complex system, and could be modeled as a poroelastic media. The aim of this paper is to identify the macroscopic value of the cortical bone permeability coefficient. A simple experimental method was designed in order to determine the permeability coefficient. Two bone samples taken from different ox femurs were filled with water, to place them under internal pressure. The measurements gave both the fluid flow through the lateral surfaces and the internal pressure. The originality of this work is the coupling between an experimental process and a structural computation performed with a finite element method. The mean cortical bone permeability coefficient identified was about k=1.1x10(-13)m(2). This value tends to confirm other values found in the literature, obtained by different methods and often at macroscopic scale. It confirms also the domination of vascular permeability (Haversian and Volkmann's canals)

A cohesive zone model for the characterisation of the interfacial transition zone (ITS) between cement paste and aggregates

International audienceCharacterization of concrete behavior needs to know mechanical properties of the two phases constituting them : mortar and aggregates. Nevertheless this bi-phasic approach reaches its limits when concrete leaves the elastic domain. At that stage and according to several studies, phenomena which occur at the interface between mortar and aggregates, or in mortar between cement paste and aggregates, must be taken into account. If the occurence of an Interfacial Transition Zone (ITZ), with weak mechanical properties in regard to the two others surrounding them is well knwon, the modeling of this third phase is not settled yet. This study focus on the characterization of the adhesion at interface between cement paste and aggregates. A mortar compounded by two limestone aggregates binded by a cement paste is considered, and tensile tests are performed on a sample of this composite. Based on these experimental results, a numerical study is developed in order to see influence of interface quality in tensile strength. For thar mortar is modeled by finite elements with a cohesive zone model at the interface, substituting ITZ. With the cohesive zone model used, coupling friction and adhesion at the interface, three parameters have to be fitted : normal and tangential stiffness, and decohesion energy. A strong correlation is found between these parameters and tensile strength, but numerical results show also low values of stiffness and decohesion energy at interface. This result could be explained by a partial adhesion between mortar and cement paste in the sample

Identification expérimentale et numérique de la perméabilité de l'os cortical pour la modélisation du remodelage

L'os est un système complexe qui peut-être considéré comme un milieu poroélastique. Le premier des paramètres à connaître pour cette intéraction fluide-structure est la perméabilité. La littérature fournit une grande variété de valeurs de perméabilité, obtenues par différentes méthodes à des échelles microscopiques. L'objectif de notre étude est d'identifier une valeur de la perméabilité de l'os cortical à une échelle macroscopique. Pour cela un dispositif expérimental simple a été élaboré. Un échantillon d'os provenant d'un fémur de boeuf est préparé et mis sous pression. Il est ainsi possible de mesurer le débit à travers les parois latérales et la pression interne. Afin d'interprêter ces résultats obtenus sur une structure, il est nécessaire d'effectuer une simulation numérique. Une méthode de calcul par éléments finis est choisie