Vittorio Sansalone

A mixed solution strategy for the nonlinear analysis of brick masonry walls

The paper presents a discrete mechanical model for masonry walls based on a Lagrangean description where each brick is described as a rigid body and each mortar joint as an interface element. Constitutive assumptions, characterized by elasticity, damage and friction, are associated to the joints only. A numerical solution strategy, based on a mixed path-following approach in terms of stresses, strains, displacements, damage and load parameters, is proposed for avoiding convergence problems related to the joint softening behaviour. Some numerical results are also presented showing the robustness and effectiveness of this proposal.

What is the importance of multiphysical phenomena in bone remodelling signals expression? A multiscale perspective.

Cortical bone, constituting the outer shell of long bones, is continuously renewed by bone cells in response to daily stimuli. This process, known as bone remodelling, is essential for proper bone functioning in both physiological and pathological conditions. Classical bone remodelling models do not, or only implicitly do, take into account physico-chemical phenomena, focussing on the mechanosensitivity property of the tissue. The aim of this paper is to carry out an investigation of the multiphysical phenomena occuring in bone life. Using a recent multiscale model combining piezoelectricity and electrokinetics to poromechanics, the usual viewpoint of bone remodelling models is questioned and new research avenues are proposed.

Multiphysical modelling of fluid transport through osteo-articular media

In this study, a multiphysical description of fluid transport through osteo-articular porous media is presented. Adapted from the model of Moyne and Murad, which is intended to describe clayey materials behaviour, this multiscale modelling allows for the derivation of the macroscopic response of the tissue from microscopical information. First the model is described. At the pore scale, electrohydrodynamics equations governing the electrolyte movement are coupled with local electrostatics (Gauss-Poisson equation), and ionic transport equations. Using a change of variables and an asymptotic expansion method, the macroscopic description is carried out. Results of this model are used to show the importance of couplings effects on the mechanotransduction of compact bone remodelling.

Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu: a multi-parametric sensitivity analysis.

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells’ metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte’s dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.

Do calcium fluxes within cortical bone affect osteocyte mechanosensitivity

Bone reacts to local mechanical environment by adapting its structure. Bone is also a key source of calcium for the body homeostasis. Osteocytes, cells located within the bone tissue, are thought to play a major role in sensing mechanical signals and regulating bone remodeling. Interestingly, osteocytes were also shown to directly participate in the calcium homeostasis by regulating dissolution and deposition of calcium in the perilacuno-pericanalicular space. However, it is not known if osteocytes roles in mechanoregulation and calcium homeostasis have any significant crosstalk. Previously, a multi-scale mathematical model of the interstitial fluid flow through the canaliculus was developed, which took into account physicochemical phenomena including hydraulic effects, formation of electrical double layer, osmosis and electro-osmosis. We extended this model to include the directional movement of calcium from and into the bone tissue, and assessed the shear stress at the osteocyte membrane. We have found that in the bulk of the canalicular space the fluid flow due to chemical gradient generated by deposition or dissolution of calcium is negligible compared to the fluid flow due to hydraulic pressure. However, at the osteocyte proximity, the presence of calcium gradient generated sufficient fluid flow to induce significant changes in the shear stress on the osteocyte membrane. Calcium deposition and dissolution on the canalicular wall resulted in increased or decreased shear stress on the osteocyte membrane respectively. Thus, our data demonstrate that strong calcium fluxes due to whole body calcium homeostasis may affect mechanical forces experienced by osteocytes.

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.

On the rotary remodelling equilibrium of bone

The amazing mechanical properties of bone, coupling stiffness, strength and lightweight, are due to a lifelong reorganisation of bone material in response to the prevailing mechanical and chemical ...

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

The importance of a multiscale modeling to describe the behavior of materials with microstructure is commonly recognized. In general, at the different scales the material may be described by means of different models. In this paper we focus on a specific class of materials for which it is possible to identify (at the least) two relevant scales: a macroscopic scale, where continuum mechanics applies; and a microscale, where a discrete model is adopted. The conceptual framework and the theoretical model were discussed in previous work. This approach is well suited to study multifield and multiphysics problems. We present here the multiscale algorithm and the computer code that we developed to implement this strategy. The solution of the problem is searched for at the macroscale using nonlinear FEM. During the construction of the FE solution, the material behavior needs to be described at Gauss points. This step is performed numerically, formulating an equivalent problem at the microscale where the inner structure of the material is described through a lattice-like model. The two scales are conceptually independent and bridged together by means of a suitable localization-homogenization procedure. We show how different macroscopic models (e.g. Cauchy vs. Cosserat continuum) can be easily recovered starting from the same discrete system but using different bridges. The interest of this approach is shown discussing its application to few examples of engineering interest (composite materials, masonry structures, bone tissue).

How (and why) twisting cycles make individual MWCNTs stiffer

Torsion of MWCNTs entails bumpy nanoscopic interwall phenomena, which gradually enhance the microscopic interwall coupling. This effect is likely to be confined at the ends of the suspended portions of the CNT, the structural changes required to link the outer wall to the inner ones being probably triggered by a complex interaction with the metal deposited onto the nanotube.

A thermodynamically consistent model of bone rotary remodeling: a 2D study

Bone remodeling characterizes the lifelong turnover and adaptation of bone tissue to its mechanical and biochemical environment. This phenomenon is of major importance, as it governs healing as well as osseointegration around implants (Haiat et al. 2014). Several scales and physics are involved in bone remodeling. Indeed, changes of the mechanical environment of bone at the organ scale lead to apposition and resorption of bone material at the microstructural scale which, in turn, result in an evolution of the mechanical properties of bone tissue, at the tissue scale. Moreover, biochemical stimuli can also trigger bone remodeling. In this work, we present a thermodynamically consistent framework for describing the evolution of bone elastic properties at the tissue scale. Such an approach allows to consider not only mechanics, but also phenomena related to biological activity. In particular, we focus on the stress driven rotation of the principal axes of the elastic tensor of bone. Rotation of bone material axes describes, at the tissue scale, the reorientation of bone microstructure induced by the macroscopic loading.