Wang Tiling Based Enrichment Functions for Extended Finite Element Method

2017 ◽  
Vol 1144 ◽  
pp. 102-108
Author(s):  
Martin Doškář ◽  
Jan Novák ◽  
Jan Zeman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Diffusion Problem ◽  
Two Dimensions ◽  
Extended Finite Element ◽  
Linear Diffusion ◽  
Wang Tiles ◽  
Element Method

The Extended Finite Element Method (XFEM) enhances the approximation space of the standard Finite Element Method (FEM) with functions reflecting local features in order to yield more accurate results with less degrees of freedom. XFEM performance is, thus, closely related to the quality of enrichment functions. Analogously to our previous works, in which we have employed the concept of Wang tiles to assembly microstructure geometries, in this contribution we use Wang tiles to assemble microstructure-informed enrichment functions. We compare two ways of generating the enrichments: (i) inspired by the first-order numerical homogenization and (ii) based on spectral analysis of the global stiffness matrix for the whole set. The methodology and performance of both approaches are illustrated through a linear diffusion problem in two dimensions

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

scholarly journals Feasibility of the Extended Finite Element Method for the Simulation of Composite Bonded Joints

2012 ◽  
Vol 730-732 ◽  
pp. 513-518 ◽  
Author(s):  
Raul D.S.G. Campilho ◽  
Arnaldo M.G. Pinto ◽  
Mariana D. Banea ◽  
Filipe J.P. Chaves ◽  
Lucas F.M. da Silva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Adhesive Bonding ◽  
Epoxy Adhesive ◽  
Pure Mode ◽  
Extended Finite Element ◽  
Damage Law ◽  
Element Method

Adhesive-bonding for the unions in multi-component structures is gaining momentum over welding, riveting and fastening. It is vital for the design of bonded structures the availability of accurate damage models, to minimize design costs and time to market. Cohesive Zone Models (CZM’s) have been used for fracture prediction in structures. The eXtended Finite Element Method (XFEM) is a recent improvement of the Finite Element Method (FEM) that relies on traction-separation laws similar to those of CZM’s but it allows the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom. This work proposes and validates a damage law to model crack propagation in a thin layer of a structural epoxy adhesive using the XFEM. The fracture toughness in pure mode I (GIc) and tensile cohesive strength (sn0) were defined by Double-Cantilever Beam (DCB) and bulk tensile tests, respectively, which permitted to build the damage law. The XFEM simulations of the DCB tests accurately matched the experimental load-displacement (P-d) curves, which validated the analysis procedure.

An Extended Finite Element Method Based Approach for Modeling Crevice and Pitting Corrosion

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Ravindra Duddu ◽  
Nithyanand Kota ◽  
Siddiq M. Qidwai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Electrical Potential ◽  
Chloride Concentration ◽  
Two Dimensions ◽  
Extended Finite Element ◽  
Level Set Function ◽  
Current Densities ◽  
Element Method

A sharp-interface numerical approach is developed for modeling the electrochemical environment in crevices and pits due to galvanic corrosion in aqueous media. The concentration of chemical species and the electrical potential in the crevice or pit solution environment is established using the steady state Nernst–Planck equations along with the assumption of local electroneutrality (LEN). The metal-electrolyte interface fluxes are defined in terms of the cathodic and anodic current densities using Butler–Volmer kinetics. The extended finite element method (XFEM) is employed to discretize the nondimensionalized governing equations of the model and a level set function is used to describe the interface morphology independent of the underlying finite element mesh. Benchmark numerical studies simulating intergranular crevice corrosion in idealized aluminum–magnesium (Al–Mg) alloy microstructures in two dimensions are presented. Simulation results indicate that corrosive dissolution of magnesium is accompanied by an increase in the pH and chloride concentration of the crevice solution environment, which is qualitatively consistent with experimental observations. Even for low current densities the model predicted pH is high enough to cause passivation, which may not be physically accurate; however, this model limitation could be overcome by including the hydrolysis reactions that potentially decrease the pH of the crevice solution environment. Finally, a mesh convergence study is performed to establish the accuracy of the XFEM and a sensitivity study examining the relationship between crevice geometry and species concentrations is presented to demonstrate the robustness of the XFEM formulation in handling complex corrosion interface morphologies.

scholarly journals A mesh-independent framework for crack tracking in elastodamaging materials through the regularized extended finite element method

2021 ◽  
Author(s):  
Elena Benvenuti ◽  
Nicola Orlando
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Damage Evolution ◽  
Extended Finite Element Method ◽  
Mesh Adaptivity ◽  
Extended Finite Element ◽  
Evolution Law ◽  
Crack Paths ◽  
Original Crack ◽  
Element Method

AbstractWe propose a formulation for tracking general crack paths in elastodamaging materials without mesh adaptivity and broadening of the damage band. The idea is to treat in a unified way both the damaging process and the development of displacement discontinuities by means of the regularized finite element method. With respect to previous authors’ contributions, a novel damage evolution law and an original crack tracking framework are proposed. We face the issue of mesh objectivity through several two-dimensional tests, obtaining smooth crack paths and reliable structural results.

scholarly journals An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 507
Author(s):  
K. Yakoubi ◽  
S. Montassir ◽  
Hassane Moustabchir ◽  
A. Elkhalfi ◽  
Catalin Iulian Pruncu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Extended Finite Element Method ◽  
Research Study ◽  
Extended Finite Element ◽  
T Stress ◽  
Cracked Structures ◽  
Element Method

The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

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