An extended finite element method with analytical enrichment for cohesive crack modeling

2008 ◽  
Vol 78 (1) ◽  
pp. 48-83 ◽  
Author(s):  
James V. Cox
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Cohesive Crack ◽  
Extended Finite Element ◽  
Element Method

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.

Numerical Simulation of Quasi-Brittle Fracture in Concrete Structures with Extended Finite Element Method

2010 ◽  
Vol 163-167 ◽  
pp. 1837-1843 ◽  
Author(s):  
Hong Chang Qu ◽  
Xiao Zhou Xia ◽  
Zhi Qiang Xiong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Growth ◽  
Extended Finite Element Method ◽  
Circumferential Stress ◽  
Cohesive Crack ◽  
Shear Stresses ◽  
Extended Finite Element ◽  
Discrete Crack ◽  
Element Method

In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.

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.

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