An exact reanalysis algorithm using incremental cholesky. Numerical applications article in international journal of solids and structures 4026. Prevost, modeling quasistatic crack growth with the extended finite element method part i. The basic concept of the extended finite element method is discussed in the context of mechanical and thermal discontinuities. Modeling crack propagation with the extended scaled. You can study the onset and propagation of cracking in quasistatic problems using the extended finite element method xfem. For crack modeling in the xfem, a discontinuous function and. In this paper, the stress intensity factors of a slantcracked plate, which is made of 6061t651 aluminum, have been calculated using extended finite element method. Cracktip and associated domain integrals from momentum. Modeling quasistatic crack growth with the extended finite element.
Application of the extended finite element method in crack propagationj. The numerical simulation of fatigue crack growth using extended. Modeling quasistatic crack growth with the extended finite element method part i. The extended finite element method is also used to compute the stress and displacement field near the crack tip in order to determine the angle of the crack propagation. Preevost b a department of civil and environmental engineering, university of california, one shields avenue, davis, ca 95616, usa b department of civil and environmental engineering, princeton university, princeton, nj 08544, usa. Modeling quasistatic crack growth with the extended finite element method, part i. This enables the domain to be modeled by finite element with no explicit meshing of the crack. Extended finite element method for cohesive crack growth. Numerical study of quasistatic crack growth problems. Quasistatic crack propagation is conducted using the extended finite element method xfem and microstructures are simulated using a kinetic monte carlo potts algorithm.
In the xfem, special functions are added to the finite element approximation using the framework of partition of unity. International journal of solids and structures 40, no. Thepurpose of this paper is to determine the sifs for a number of 2d crack problems by the two ap. Modeling discontinuities as an enriched feature using the. A discontinuous function and the twodimensional asymptotic cracktip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. For crack modeling in the xfem, a discontinuous function and the neartip asymptotic functions are added to the finite element approximation using the framework of partition of unity. In the xfem, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the twodimensional. Experimental and xfem modelling of high cycle fatigue crack growth in steel. References extended finite element method wiley online. This work aims to present a complete full coupling extended finite element formulation of the thermomechanical problem of cracked bodies. Prevost, modeling quasistatic crack growth with the extended finite element method part ii.
In this work, we have exposed a recent method for modeling crack growth without remeshing. Analysis of multicrack growth in asphalt pavement based. In part i sukumar and prevost 2003, we described the implementation of the extended finite element method xfem within dynaflow, a standard finite element package. Modeling crack in viscoelastic media using the extended finite. In this paper, the high concrete dam of longtan was used as an example, using the abaqus program based on the extended finite element method to analyze the longtan dam under static and dynamic conditions which has been commonly used for the study of crack growth.
Based on the algorithm of xfem, the major factors such as integral domain factor and mesh density which all influence the calculation accuracy of stress intensity factor sif are discussed, and the proper parameters to calculate the sif are given. The kinked crack growth in an element is performed using the concept of virtual nodes to model and improve the accuracy of the solution. The extended finite element method allows one to model. Wolf, chongmin song, the scaled boundary finiteelement method. In our implementation, we focused on twodimensional crack modeling in linear elasticity. Computer implementation december 2003 international journal of solids and structures 4026. We provide a historical perspective on the development. Analysis of threedimensional crack initiation and propagation using the extended finite element method. The stress intensity factor sif is an important parameter for estimating the life of the cracked structure. Computer implementation, international journal for solids and structures, vol. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
For crack modeling in the xfem, a discontinuous function and the neartip asymptotic functions are added to the finite. Numerical applications author links open overlay panel r. Application of the extended finite element method in crack. Modelling of crack propagation in layered structures using. Xfem is available only for threedimensional solid and twodimensional planar models. The paper covers the formulation and implementation of xfem, and discusses various aspects of the approach enrichments. Computer implementation, international journal of solids and structures, vol. Modelling of stationary and growing cracks in fe framework without remeshing.
Modeling quasistatic crack growth with the extended finite element method, part ii. In this paper, we provide a retrospective examination of the developments and applications of the extended finite element method xfem in computational fracture mechanics. Modelling crack growth by level sets in the extended. Simulation of cracking in high concrete gravity dam using. The methodology adopted for modeling crack discontinuities falls within the purview of the xfem.
International journal of solids and structures 40 2003. Extended finite element method in computational fracture. Stochastic fracture response and crack growth analysis of. Modeling quasistatic crack growth with the extended finite element method part ii. The two most promising approaches to determine stress intensity factor sif developedover the past decade are the symmetric galerkin boundary element method finite element methodsgbemfem based alternating method and the extended finite element xfem method. Numerical study of quasistatic crack growth problems based on extended finite element method. This permits the crack to be represented without explicitly meshing the crack surfaces and crack propagation simulations can be carried out without the need for any remeshing. Finally, in section 4, a quasistatic crack growth problem is used as a test problem to evaluate the effectiveness of the proposed reanalysis method with respect to computational time and level of mesh re. Modeling quasistatic crack growth with the extended finite element method.
Xfem allows you to study crack growth along an arbitrary, solutiondependent path without needing to remesh your model. Comparison of sgbemfem alternating method and xfem. The design and analysis of the generalized finite element. A numerical prediction of crack propagation in concrete gravity dams is presented.
Full thermomechanical coupling using extended finite element. Use the link below to share a fulltext version of this article with your friends and colleagues. Using extended finite element method for computation of. Sukumar and prevost utilized xfem in quasistatic crack growth problems 9. Parametric sensitivities of xfem based prognosis for quasi. The extended finite element method xfem is a numerical method for modeling discontinuities within a classical finite element framework. The virtual nodes are enriched with additional degrees of freedom. An extended finite element method for modeling crack growth with.
Our main attention is placed on the modeling of cracks strong discontinuities for quasistatic crack growth simulations in isotropic linear elastic continua. Full thermomechanical coupling using extended finite. In a prior study sukumar and prevost, 2003 referred to hereafter as part i, we have described the implementation of the extended finite element method x fem. A quasitransient crack propagation model, subjected to transient thermal. An extended finite element method xfem for multiple crack growth in asphalt pavement is described. Coupled finite volume methods and extended finite element.
The 6061t651 aluminium alloy is one of the most common aluminium alloys for marine components and general structures. The main advantage of this method is its capability in modeling discontinuities independently, so the mesh is prepared without any considering the existence of discontinuities. A numerical hydraulic fracture model using the extended. Horst, combination of the material force concept and the extended finite element method for mixed mode crack growth simulations, international journal for numerical methods in engineering, 85, 12, 15221542, 2010. We assume quasistatic loading by a body force b and tractions t imposed on the part ct of the. In our implementation, we focused on 2dimensional crack modeling in linear elasticity.
The extended finite element method xfem is a relatively recent concept developed for modeling geometric discontinuities and singularities by introducing the addition of new terms to the classical shape functions in order to allow the finite element formulation to remain the same. Motamedi and mohammadi used this method for analyzing dynamic stationary cracks for both and orthotropic materials isotropic 7, 8. Modeling quasistatic crack growth with the extended. Vahedi, using extended finite element method for computation of the stress intensity factor, crack growth simulation and predicting fatigue crack growth in a slantcracked plate of 6061t651 aluminum, world journal of mechanics, vol.
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