scholarly journals Cast3M implementation of the extended finite element method for cohesive crack

2011 ◽  
Vol 33 (1) ◽  
pp. 55-64
Author(s):  
Nguyen Truong Giang ◽  
Ngo Huong Nhu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Extended Finite Element Method ◽  
Brittle Materials ◽  
Cohesive Crack ◽  
Numerical Calculations ◽  
Extended Finite Element ◽  
Element Method

In this paper, the finite element for cohesive crack for quasi-brittle materials is constructed by the displacement discontinuities in the element. The algorithm of construction and procedures for involving this finite element into code Cast3M are presented. The numerical calculations in fracture mechanics are presented to demonstrate the benefits of the proposed implementation.

scholarly journals A Hybrid Finite Volume and Extended Finite Element Method for Hydraulic Fracturing with Cohesive Crack Propagation in Quasi-Brittle Materials

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 1921 ◽  
Author(s):  
Chong Liu ◽  
Zhenzhong Shen ◽  
Lei Gan ◽  
Tian Jin ◽  
Hongwei Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Volume ◽  
Extended Finite Element Method ◽  
Brittle Materials ◽  
Cohesive Crack ◽  
Picard Iteration ◽  
Extended Finite Element ◽  
Static Conditions ◽  
Element Method

High-pressure hydraulic fractures are often reported in real engineering applications, which occur due to the existence of discontinuities such as cracks, faults, or shear bands. In this paper, a hybrid finite volume and extended finite element method (FVM-XFEM) is developed for simulating hydro-fracture propagation in quasi-brittle materials, in which the coupling between fluids and deformation is considered. Flow within the fracture is modelled using lubrication theory for a one-dimensional laminar flow that obeys the cubic law. The solid deformation is governed by the linear momentum balance equation under quasi-static conditions. The cohesive crack model is used to analyze the non-linear fracture process zone ahead of the crack tip. The discretization of the pressure field is implemented by employing the FVM, while the discretization of the displacement field is accomplished through the use of the XFEM. The final governing equations of a fully coupled hydro-mechanical problem is solved using the Picard iteration method. Finally, the validity of the proposed method is demonstrated through three examples. Moreover, the fluid pressure distribution along the fracture, the fracture mouth width, and the pattern of the fracture are investigated. It is shown that the numerical results correlated well with the theoretical solutions and experimental results.

A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics

2019 ◽  
Vol 230 (7) ◽  
pp. 2385-2398 ◽  
Author(s):  
S. Z. Feng ◽  
S. P. A. Bordas ◽  
X. Han ◽  
G. Wang ◽  
Z. X. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Element Method

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bruna Caroline Campos ◽  
Felício Bruzzi Barros ◽  
Samuel Silva Penna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Content Type ◽  
Integration Techniques ◽  
Integration Strategies ◽  
Element Method

Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered. Design/methodology/approach Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results. Findings Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities. Originality/value This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

Extended Finite Element Method for Fracture Mechanics and Mesh Refinement Controlled by Density Function

2012 ◽  
Vol 525-526 ◽  
pp. 413-416
Author(s):  
Yi Cen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Method ◽  
Density Function ◽  
Extended Finite Element Method ◽  
Mesh Refinement ◽  
Extended Finite Element ◽  
Element Enrichment ◽  
Element Method

This paper discusses the combination of element enrichment by mesh refinement controlled by density function with the extended finite element method and its application in fracture mechanics. Extended finite element method (XFEM) is an effective numerical method for solving discontinuity problems in the finite element work frame. A numerical example of fracture mechanics is analyzed at the end of this paper to show the application of the above method.

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