Three-Scale Multiphysics Modeling of Transport Phenomena within Cortical Bone

Bone tissue can adapt its properties and geometry to its physical environment. This ability is a key point in the osteointegration of bone implants since it controls the tissue remodeling in the vicinity of the treated site. Since interstitial fluid and ionic transport taking place in the fluid compartments of bone plays a major role in the mechanotransduction of bone remodeling, this theoretical study presents a three-scale model of the multiphysical transport phenomena taking place within the vasculature porosity and the lacunocanalicular network of cortical bone. These two porosity levels exchange mass and ions through the permeable outer wall of the Haversian-Volkmann canals. Thus, coupled equations of electrochemohydraulic transport are derived from the nanoscale of the canaliculi toward the cortical tissue, considering the intermediate scale of the intraosteonal tissue. In particular, the Onsager reciprocity relations that govern the coupled transport are checked

Bone orthotropic remodeling as a thermodynamically-driven evolution

International audienceIn this contribution we present and discuss a model of bone remodeling set up in the framework of the theory of generalized continuum mechanics and first introduced by DiCarlo et al.[1]. Bone is described as an orthotropic body experiencing remodeling as a rotation of its microstruc-ture. Thus, the complete kinematic description of a material point is provided by its position in space and a rotation tensor describing the orientation of its microstructure. Material motion is driven by energetic considerations , namely by the application of the Clausius-Duhem inequality to the microstructured material. Within this framework of orthotropic re-modeling, some key features of the remodeling equilibrium configurations are deduced in the case of homogeneous strain or stress loading conditions. First, it is shown that remodeling equilibrium configurations correspond to energy extrema. Second, stability of the remodeling equilibrium configurations is assessed in terms of the local convexity of the strain and complementary energy functionals hence recovering some classical energy theorems. Eventually, it is shown that the remodeling equilibrium configurations are not only highly dependent on the loading conditions, but also on the material properties

Influence des flux de calcium sur la contrainte de cisaillement agissant sur les ostéocytes dans l'os cortical

Nous avons modélisé l'écoulement du fluide encerclant les cellules osseuses mécano-sensibles (ostéocytes). Le but de cette étude est d'améliorer nos modèles précédents en incluant des flux de calcium apparaissant lors de la dissolution ou de la précipitation de la matrice osseuse. Même si ces flux ne semblent pas altérer de manière significative la vitesse du fluide, ils peuvent changer le cisaillement ressenti par les ostéocytes. Par conséquent, nous avons examiné la façon dont de tels échanges chimiques affectent l'écoulement du fluide et donc la mécano-sensibilité des ostéocytes

Surface Waves for Anisotropic Material Characterization-A Computer Aided Evaluation System

Along with a wide application of nondestructive evaluation methods by ultrasonic techniques, Rayleigh surface waves are being studied for their applications in material characterization. Because surface waves can offer some sensitive measurement features of wave propagation, it is suggested that surface waves be conveniently used as an experimental technique for the solution of the inverse problem of determining elastic constants and/or other characteristics in materials [1–3]. The most common direct problem is to obtain wave propagation features by theoretical analysis, experimental measurement, or numerical calculation. A desired problem in material evaluation however, is to solve an inverse problem to find material characteristics from a set of field measurement data. In surface wave problems, the closed form solutions may not even exist for some direct problems. Moreover, often material constants collectively influence the ultrasonic wave propagation in anisotropic medium, and we can not decouple them and evaluate them individually by each single ultrasonic measurement. Therefore, a numerical computational procedure is proposed.</p

Anisotropic diffusion of water molecules in hydroxyapatite nanopores

Funded by EPSRC Grant EP/K000128/1

Computational Homogenization of Architectured Materials

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials

A numerical investigation of structure-property relations in fibre composite materials.

A multifield continuous model is adopted to investigate the mechanical behaviour of heterogeneous materials made of short, stiff and tough fibres embedded in a more deformable matrix. This continuum accounts for the presence of internal structure by means of non-standard field descriptors. The constitutive relations, obtained by a multiscale approach linking the material description at different scales, depend on the geometry and the arrangement of the internal phases and include internal scale parameters, which allow taking into account size effects. A multiscale finite element technique has been used for obtaining the numerical solution of the multifield and the corresponding Cauchy model. The numerical results obtained on a sample fibre reinforced composite show the effectiveness of the former in pointing out the influence of the size, the shape and the orientation of the fibres on the gross behaviour of the material

Coupling Continuum and Discrete Models of Materials with Microstructure: a Multiscale Algorithm

International audienc

Multifield continuum modelling for materials with lattice microstructure

multiscale computational coarse-grainin