In this paper, we introduce an implementation of the extended finite element method for fracture problems within the finite element software ABAQUS TM . User subroutine (UEL) in Abaqus is used to enable the incorporation of extended finite element capabilities. We provide details on the data input format together with the proposed user element subroutine, which constitutes the core of the finite element analysis; however, pre-processing tools that are necessary for an X-FEM implementation, but not directly related to Abaqus, are not provided. In addition to problems in linear elastic fracture mechanics, non-linear frictional contact analyses are also realized. Several numerical examples in fracture mechanics are presented to demonstrate the benefits of the proposed implementation.

SUMMARYThe application of the extended finite element method (XFEM) to fracture mechanics problems enables one to obtain accurate solutions more efficiently than with the standard finite element method. A component can be modelled without the need to build a mesh that matches the crack geometry, and thus remeshing as the crack grows is unnecessary. In the XFEM approach, the interpolation on certain elements is enriched with functions that make it feasible to represent the crack tip asymptotic displacement fields by using a local partition of unity method. However, the enrichment is only partial in the blending elements connecting the enriched zone with the rest of the mesh, and consequently pathological terms appear in the interpolation, which lead to increased error. In this study we propose enhancing the blending elements by adding hierarchical shape functions where appropriate; this permits compensating for the unwanted terms in the interpolation. This technique is an extension of the study of Chessa et al. (Int. J. Numer. Meth. Engng. 2003; 57:1015-1038) to fracture mechanics problems. The numerical results show that the proposed enhancement always results in greater accuracy. Moreover, enhancing the blending elements makes it possible to recover the convergence rate that is decreased when the degrees of freedom gathering technique is used to improve the condition number of the stiffness matrix.

In this work, the orientation and propagation of a crack in a fretting fatigue problem is analyzed numerically and correlated experimentally. The analysis is performed using 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 use the extended finite element method (X-FEM), allowing for crack face contact during the corresponding parts of the fatigue cycle. The problem is highly non-linear and nonproportional and an orientation criterion is introduced to predict the crack direction in each step of the crack growth simulation. It is shown that the proposed criterion predicts crack orientation directions that are in good agreement with those found experimentally, in contrast to the directions found by application of conventional orientation criteria used in LEFM, such as the MTS criterion.

a b s t r a c tIn this paper, the extended finite element method (X-FEM) is considered for the analysis of fretting fatigue problems. A two-dimensional implementation of the X-FEM is carried out within the finite element software ABAQUS TM by means of user subroutines, and crack propagation in fretting fatigue problems is investigated. On utilizing the non-linear contact capabilities of this code, the numerical technique is applied to a specimen-indenter model. The use of the X-FEM facilitates very accurate stress intensity factor computations on relatively coarse meshes, and furthermore, no remeshing is required for crack growth simulations. The implementation is applied to complete and incomplete contact fretting problems. A study of crack growth is conducted for several bulk loads applied to the specimen, and the influence of the initial crack angle is ascertained. The numerical simulations reveal the merits of applying the X-FEM to fretting fatigue problems.

WileyGonzález Albuixech, VF.; Giner Maravilla, E.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ.; Gravouil, A. (2013). Convergence of domain integrals for stress intensity factor extraction in 2-D curved cracks problems with the extended finite element method. International Journal for Numerical Methods in Engineering. 94(8):740-757. doi:10.1002/nme.4478. This is the peer reviewed version of the following article: Int. J. Numer. Meth. Engng 2013; 94:740-757, which has been published in final form at Wiley Online Library (wileyonlinelibrary.com SUMMARYThe aim of this study is the analysis of the convergence rates achieved with domain energy integrals for the computation of the stress intensity factors (SIF) when solving 2-D curved crack problems with the extended finite element method (XFEM). Domain integrals, specially the J-integral and the interaction integral, are widely used for SIF extraction and provide high accurate estimations with finite element methods. The crack description in XFEM is usually realized using level sets. This allows to define a local basis associated with the crack geometry. In this work the effect of the level set local basis definition on the domain integral has been studied. The usual definition of the interaction integral involves hypotheses that are not fulfilled in generic curved crack problems and we introduce some modifications to improve the behavior in curved crack analyses. Despite the good accuracy of domain integrals, convergence rates are not always optimal and convergence to the exact solution cannot be assured for curved cracks. The lack of convergence is associated with the effect of the curvature on the definition of the auxiliary extraction fields. With our modified integral proposal, the optimal convergence rate is achieved by controlling the q-function and the size of the extraction domain.

A variety of methods have been proposed to calculate the dynamic response caused by a railway vehicle affected by a wheelflat. Most of the sophisticated procedures evaluate the elastic properties of the wheel-rail contact by means of the Hertz model. However, the hypotheses that must be satisfied in order to apply the Hertzian contact model are not fulfilled when the wheel-rail contact occurs in the area of wheel affected by the flat. This gives rise to deviations in the results of the dynamic model compared to the real situation. With the objective of analysing the influence of the elastic wheel-rail contact model, a procedure was developed to determine the dynamic response caused by a geometric irregularity (in rail or wheel) by means of Hertzian and non-Hertzian contact models. Results of the wheelflat impact simulations given by both types of contact model have been compared in this work.

In this work, we present two strategies for the numerical modeling 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.

Cutting operations in bone are involved in surgical treatments in orthopaedics and traumatology.The importance of guaranteeing the absence of damage in the living workpiece is equivalent in this case to ensuring surface quality. The knowledge in this field is really far from the expertise in industrial cutting of mechanical components. Modeling of bone cutting is a challenge strongly dependent on the accurate modeling of mechanical behaviour of the bone. This paper focuses on modeling of orthogonal cutting of cortical bone. The intrinsic anisotropic nature of the cortical bone that makes it comparable to a compos-ite material is taken into account. The influence of anisotropy is analysed comparing this behaviour with an isotropic approach. It is shown that both chip morphology and temperature are affected by the anisot-ropy of the cortical bone that acts as a workpiece.