It is well argued that stability-initiated failure dominates, especially in older bone, because of the instability of single trabeculae which is prone to inelastic buckling at stresses far less than expected for strength-based failure. It is also well known that when several horizontal struts have disappeared, trabecula fails due to compression-buckling load. In this contribution, our main goal is to improve, from theoretical point of view, the mechanistic understanding of bone buckling failure which is known to be at the core of important clinical problems. For that and with respect to previous works, an attempt is made in order to establish a simplified adaptive-beam buckling model, formulated within the context of the nonlocal adaptive continuum mechanics, from which numerical computations were performed in order to get a better knowledge about bone-column buckling mechanism affected by both bone density and bone density gradient distributions restricted to Euler–Bernoulli beam theory. An attempt is made to compare the experimental data with the response of our simplified model. For that, controlled buckling tests of single trabeculae were carried out from three medial tibia end sections (knee joint).

The objective of this paper is to develop a global modelling approach, that simulates both the resin transfer molding (RTM) manufacturing and the prediction of the effective thermal conductivity (ETC) of a carbon–cpoxy (CE) laminated composite reinforced with particles. This numerical approach is based on two main stages. First, a numerical simulation of the suspension flow and the filtration of the charges during the RTM process. A method, for simulating the flow of a resin, loaded with particles in suspension through a fibrous medium, considering its double porosity scale, has been proposed. It is based on the description of the flow by Stokes–Darcy coupling, filtration phenomenon and particle dynamics. Secondly, the ETC of the composite thus produced is evaluated using a numerical homogenisation technique, considering the spherical particles inserted into the carbon–epoxy laminated composite. These obtained results have shown that, the incorporation of particles in the laminated composite leads to a significant increase in their effective thermal conductivity, which depends on their thermal conductivity. Finally, a simple linear thermal model has been proposed to predict the effective thermal conductivity of the composite carbon–epoxy–particles, as a function of that of the base composite carbon–epoxy and that of the particles.