E. Giner

Numerical Estimation of Fretting Fatigue Lifetime Using Damage and Fracture Mechanics

Fretting fatigue is a complex tribological phenomenon that can cause premature failure of connected components that have small relative oscillatory movement. The fraction of fretting fatigue lifetime spent in crack initiation and in crack propagation depends on many factors, e.g., contact stresses, amount of slip, frequency, environmental conditions, etc., and varies from one application to another. Therefore, both crack initiation and propagation phases are important in analysing fretting fatigue. In this investigation, a numerical approach is used to predict these two portions and estimate fretting fatigue failure lifetime under a conformal contact configuration. For this purpose, an uncoupled damage evolution law based on principles of continuum damage mechanics is developed for modelling crack initiation. The extended finite element method approach is used for calculating crack propagation lifetimes. The estimated results are validated with previously reported experimental data and compared with other available methods in the literature.

A review on recent advances in numerical modelling of bone cutting.

Common practice of surgical treatments in orthopaedics and traumatology involves cutting processes of bone. These operations introduce risk of thermo-mechanical damage, since the threshold of critical temperature producing thermal osteonecrosis is very low. Therefore, it is important to develop predictive tools capable of simulating accurately the increase of temperature during bone cutting, being the modelling of these processes still a challenge. In addition, the prediction of cutting forces and mechanical damage is also important during machining operations. As the accuracy of simulations depends greatly on the proper choice of the thermo-mechanical properties, an essential part of the numerical model is the constitutive behaviour of the bone tissue, which is considered in different ways in the literature. This paper focuses on the review of the main contributions in modelling of bone cutting with special attention to the bone mechanical behaviour. The aim is to give the reader a complete vision of the approaches commonly presented in the literature in order to help in the development of accurate models for bone cutting.

Numerical modelling of the mechanical behaviour of an osteon with microcracks

In this work, we present two strategies for the numerical modelling of microcracks and damage within an osteon. A numerical model of a single osteon under compressive diametral load is developed, including lamellae organized concentrically around the haversian canal and the presence of lacunae. Elastic properties have been estimated from micromechanical models that consider the mineralized collagen fibrils reinforced with hydroxyapatite crystals and the dominating orientation of the fibrils in each lamella. Microcracks are simulated through the node release technique, enabling propagation along the lamellae interfaces by application of failure criteria initially conceived for composite materials, in particular the Brewer and Lagacé criterion for delamination. A second approach is also presented, which is based on the progressive degradation of the stiffness at the element level as the damage increases. Both strategies are discussed, showing a good agreement with experimental evidence reported by other authors. It is concluded that interlaminar shear stresses are the main cause of failure of an osteon under compressive diametral load.

An implementation of the stiffness derivative method as a discrete analytical sensitivity analysis and its application to mixed mode in LEFM

Abstract In this work, an improvement in the stiffness derivative method based on a shape design sensitivity analysis is proposed, so that the error inherent in the finite difference procedure is avoided. For a global estimation of G from a given finite element solution, this approach is shown to be equivalent to the well-known J -integral when the latter is numerically implemented through its equivalent domain integral. However, it is verified that its direct application to 2D mixed mode problems of linear elastic fracture mechanics through the field decomposition technique yields estimates for G I and G II which are in general more accurate for the proposed method. The importance of the velocity field is also remarked and some suggestions for its choice are given.

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.

Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone

In this work, a three-dimensional finite element model of the staggered distribution of the mineral within the mineralized collagen fibril has been developed to characterize the lamellar bone elastic behavior at the sub-micro length scale. Minerals have been assumed to be embedded in a collagen matrix, and different degrees of mineralization have been considered allowing the growth of platelet-shaped minerals both in the axial and the transverse directions of the fibril, through the variation of the lateral space between platelets. We provide numerical values and trends for all the elastic constants of the mineralized collagen fibril as a function of the volume fraction of mineral. In our results, we verify the high influence of the mineral overlapping on the mechanical response of the fibril and we highlight that the lateral distance between crystals is relevant to the mechanical behavior of the fibril and not only the mineral overlapping in the axial direction.

3D analysis of the influence of specimen dimensions on fretting stresses

In this paper, the contact conditions and stresses that arise in a fretting test have been analyzed by means of a three-dimensional finite element model of the contact between a sphere and a flat surface. At h-adaptive process, based on element subdivision, has been used in order to obtain a low discretization error at a reasonable computational cost. The influence of finite dimensions of the specimen in the stress fields has been evaluated. The results have been compared with the classical Cattaneo-Mindlin solution.

Orientation of propagating crack paths emanating from fretting-fatigue contact problems

In this work, the orientation and propagation of cracks in fretting fatigue problems is analyzed numerically using the finite element method (FEM) and the extended finite element method (X-FEM). The analysis is performed by means of a 2D model of a complete-contact fretting problem, consisting of two square indenters pressed onto a specimen subjected to cyclic fatigue. For the simulation, we allow for crack face contact in the implementation during the corresponding parts of the fatigue cycle. The problem is highly nonlinear and non-proportional and we make use of the so-called minimum shear stress range orientation criterion, min(??), proposed by the authors in previous works. This criterion is introduced to predict the crack path in each step of the crack growth simulation. The objective of the work is to detect which is the relevant parameter affecting the crack path orientation. A parametric study of some a priori relevant magnitudes is carried out, such as normal load on the indenters, bulk load on the specimen, stress ratio and relative stiffness of the indenter and specimen materials. Contrary to previous expectations, it is shown that the relative magnitude of the applied loads has no significant effect. However, it is found that the stiffness of the indenter material with respect to the specimen material has the greatest effect. A simple explanation of this behavior is also provided.

Numerical Modelling of Femur Fracture and Experimental Validation Using Bone Simulant

Bone fracture pattern prediction is still a challenge and an active field of research. The main goal of this article is to present a combined methodology (experimental and numerical) for femur fracture onset analysis. Experimental work includes the characterization of the mechanical properties and fracture testing on a bone simulant. The numerical work focuses on the development of a model whose material properties are provided by the characterization tests. The fracture location and the early stages of the crack propagation are modelled using the extended finite element method and the model is validated by fracture tests developed in the experimental work. It is shown that the accuracy of the numerical results strongly depends on a proper bone behaviour characterization.

Simulation of the behavior of the calfskin used as shoe upper material in footwear CAD

The aim of this work is to propound a mechanical behavior model for simulating the deformation of the shoe upper material in gait for footwear CAD applications. The chosen material is calfskin. The proposed material behavior for the working range is a linear elastic orthotropic model which considers large deformation and membrane and bending loading. The model was obtained from tensile tests and validated with two experiments: a test to measure the leather resistance to damage on lasting and a test that models the shoe forming process using lasts. The framework of this work is the simulation of the footwear deformation while walking for footwear computer-aided design, and these tests have been chosen because, in them, the shoe upper material is deformed in a similar way to those deformations that occur during a complete step. The tests have been simulated using the Finite Element Method. The results of this simulation show that, in most of the cases, the orthotropic model closely represents the real behavior of the leathers analyzed in this work.