It is believed osteocytes embedded in mineralized bone matrix play an important role as a mechanosensor cell in bone remodeling. Osteocyte processes are thought to be stimulated by the interstitial fluid flow in canaliculi. In order to understand the mechanical behavior of the osteocyte process in the interstitial fluid, a mathematical model of osteocyte cell membrane was developed. Together with the lattice Boltzmann method to calculate the fluid velocity field, we simulated the deformation of a single osteocyte process due to interstitial fluid flow. The fluid flow induced the tensile strain at the upstream region and the compressive strain at the downstream region of the osteocyte cell membrane. In addition, inhomogeneous flow patterns produced by the projection on the wall of flow channel deformed the osteocyte process in the direction perpendicular to its longitudinal direction. These results show the importance of the effect of geometric complexity of the canaliculus on the flow profiles that drive cellular mechanotransduction.
As one of the analytical models of the thermal stress problem for composite materials, we consider an infinite plate composed of multilayered composite laminate and discuss the transient thermal stress problems of a laminated plate due to moving heat source from the upper surface. In order to develop the analysis for a multilayered composite plate, we introduce the methods of Fourier cosine and Laplace transform for the temperature field and Airy's stress function method for the thermoelastic field, and then evaluate the temperature and thermal stress distributions in a transient state. Extending the theoretical developments proposed in the present paper to the analysis of an infinite plate with nonhomogeneous material properties, we examine the thermal stress distributions and the effect of relaxation of stress values in nonhomogeneous plate made of functionally gradient materials.
Trabecular bone is a microstructural component of cancellous bone, forming a three-dimensional network structure. The typical individual trabecula is regarded as a cylindrical porous material which is composed of a calcified bone matrix and interstitial fluid in a lacuno-canalicular porosity. For a physiological range of activities excluding shocks, trabeculae in vivo are usually subjected to lowfrequency cyclic loading due to locomotion and the maintenance of posture. A number of experimental and theoretical studies have shown that the flow of interstitial fluid caused by deformation of the bone matrix under external loading plays an important role in cellular mechanosensing to initiate bone remodelling [1]. In order to quantitatively evaluate the interstitial fluid flow in bone tissue, poroelastic theory formulated by Biot has been widely used [2]. Poroelasticity is a continuum theory that considers the coupling behavior between the elastic solid matrix and the fluid-filled pores. In our previous study, we derived a closed-form solution for the fluid pressure in a two-dimensional poroelastic slab subjected to cyclic loading [3, 4]. However, this solution is insufficient to describe the mechanical behavior of interstitial fluid in a three-dimensional trabecula. The purpose of this study is to investigate the fluid pressure response to cyclic loading in a cylindrical trabecula based on a poroelastic approach. We developed an analytical solution for the interstitial fluid pressure in a single trabecula by solving the governing equations in the cylindrical coordinate system with the help of the Laplace transformation technique. The obtained solution contained both transient and steady-state responses depending on the loading frequency. The calculated results showed that the transient stage decayed within the first period of cyclic loading. In the steady state, the fluid pressure gradient around the trabecular surface was larger than that around the central axis of trabecula. Furthermore, the fluid pressure gradient close to the surface built up with the increase in the loading frequency. These results suggest that bone cells embedded in the neighborhood of the trabecular surface are significantly stimulated by the load-induced interstitial fluid flow, and the loading rate is one of the essential factors that can influence the process of cellular mechanosensing.
This paper is concerned with the theoretical treatment of transient thermoelastic problems involving a functionally graded hollow cylinder with piecewise power law due to asymmetrical heating from its surfaces. The thermal and thermoelastic constants of each layer are expressed as power functions of the radial coordinate, and their values continue on the interfaces. The exact solution for the two-dimensional temperature change in a transient state, and thermoelastic response of a hollow cylinder under the state of plane strain is obtained herein. Some numerical results for the temperature change and the stress distributions are shown in figures. Furthermore, the influence of the functional grading on the thermal stresses is investigated.
In this paper, theoretical analysis of a three-dimensional transient thermal stress problem is developed for a nonhomogeneous hollow circular cylinder with respect to rotating heat source from the inner and/or outer surface. We assume that the hollow circular cylinder has nonhomogeneous thermal and mechanical material properties in the radial direction. The heat conduction problem and the associated thermoelastic behavior for such nonhomogeneous media are developed by introducing the theory of laminated composites as one theoretical approximation. The transient heat conduction problem is evaluated with the aid of the methods of Fourier cosine transform and Laplace transform. The associated thermoelastic field is analyzed by making use of the thermoelastic displacement potential, Michell's function and the Boussinesq function. Some numerical results for the temperature change and the stress distributions are shown in figures.
