J.E. Tarancón

Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models

Mineralized collagen fibrils have been usually analyzed like a two-phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that when Halpin–Tsai equations are applied to estimate elastic constants from typical constituent properties, not all crystal dimensions yield a model that satisfy thermodynamic restrictions. We provide the ranges of platelet dimensions that lead to positive definite stiffness matrices. On the other hand, a finite element model of a mineralized collagen fibril unit cell under periodic boundary conditions is analyzed. By applying six canonical load cases, homogenized stiffness matrices are numerically calculated. Results show a monoclinic behavior of the mineralized collagen fibril. In addition, a 5-layer lamellar structure is also considered where crystals rotate in adjacent layers of a lamella. The stiffness matrix of each layer is calculated applying Lekhnitskii transformations, and a new finite element model under periodic boundary conditions is analyzed to calculate the homogenized 3D anisotropic stiffness matrix of a unit cell of lamellar bone. Results are compared with the rule-of-mixtures showing in general good agreement.

Method for obtaining the modal properties of articulated trains equipped with independently rotating wheels

Independently rotating wheels in railway vehicles could represent an alternative to standard technology as a solution to dynamic problems such as hunting instability or steering forces in curves. Among the proposed design solutions, the train with independently rotating wheels and with the most practical applications is that developed by Talgo. The Talgo technology is based on the use of a passive steering technique of the wheelset through a mechanism. The absence of automatic control systems means that a careful selection of the mechanical parameters of the vehicle is required to improve its dynamic characteristics. Aspects such as dynamic stability or the effect of vibration on passenger comfort could be analysed by extracting the modal properties of the train from mathematical models. In this article, a methodology for determining the low-frequency modal properties of articulated trains equipped with independently rotating wheels and passive steering system (Talgo-type) is proposed. The singularity of this application based on the use of non-conventional wheelsets necessarily involves the development of a specific methodology. †This article includes a word (Talgo) that is or is asserted to be a proprietary term or trade mark. Its inclusion does not imply it has acquired for legal purposes a non-proprietary or general significance, nor is any other judgement implied concerning its legal status.

Stochastic Monte Carlo simulations of the pantograph–catenary dynamic interaction to allow for uncertainties introduced during catenary installation

ABSTRACT The simulation of the pantograph–catenary dynamic interaction is at present mainly based on deterministic approaches. However, any errors made during the catenary stringing process are sources of variability that can affect the dynamic performance of the system. In this paper, we analyse the influence of dropper length, dropper spacing and support height errors on the current collection quality by applying a classic Monte Carlo method to obtain the probability density functions of several output quantities. The effects of installation errors are also studied for a range of train speeds. Finally, the pre-sag that, on average, produces the best behaviour of the system is identified, allowing for the uncertainty in the catenary installation. The results obtained show the convenience to consider variability in pantograph–catenary dynamic simulations.

Crack growth in fretting-fatigue problems using the extended finite element method

The aim of this work is to apply the extended finite element method (X-FEM) to the analysis of crack orientation and propagation in a 2D fretting-fatigue problem. The X-FEM approach features some important advantages in the computational modelling of crack growth problems. The main advantage is that the mesh generation does not need to conform to the geometric discontinuity caused by the crack presence. The discontinuous behavior is introduced via special functions that enrich the classical finite element formulation. In this way, the initial mesh can be used for any further variation in crack length and orientation.