RE: Simulating XFEM using LS-DYNA
James M. Kennedy
Dear Masha,
XFEM method
The extended finite element method (XFEM), is a numerical technique based on the
generalized finite element method (GFEM) and the partition of unity method (PUM). It
extends the finite element method (FEM) approach by enriching the solution space for
solutions to differential equations with discontinuous functions. The extended finite
element method (XFEM), is a numerical technique based on the generalized finite
element method (GFEM) and the partition of unity method (PUM). It extends the classical
XFEM was developed by Belytschko and collaborators [1999, 2000, and 2010] to help alleviate
shortcomings of the finite element method and has been used to model the propagation of
various discontinuities: strong (cracks) and weak (material interfaces). The idea behind XFEM
is to retain most advantages of meshfree methods while alleviating their negative sides. XFEM
was developed to ease difficulties in solving problems with localized features that are not
efficiently resolved by mesh refinement.
Enriched finite element methods extend, or enrich, the approximation space so that it is able
to naturally reproduce the challenging feature associated with the problem of interest: the
discontinuity, singularity, boundary layer, etc. It was shown that for some problems, such an
embedding of the problem's feature into the approximation space can significantly improve
convergence rates and accuracy. Moreover, treating problems with discontinuities with XFEM
suppresses the need to mesh and remesh the discontinuity surfaces, thus alleviating the
computational costs and projection errors associated with conventional finite element
methods, at the cost of restricting the discontinuities to mesh edges
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Several LS-DYNA presentations that might be of help:
Wu, C.T., Guo, Y., and Lu, H.S., "The Development of XFEM Fracture and Mesh-Free
Adaptivity", 5th German LS-DYNA Forum, Ulm, Germany, October, 2006.
Song, J.-H, Wang, H., and Belytschko, T., "A Comparative Study on Finite Element
Methods for Dynamic Fracture", Computational Mechanics, Vol. 42, No. 2, pp. 239-250,
July, 2008.
The performance of finite element methods for dynamic crack propagation in brittle materials
is studied. Three methods are considered: the extended finite element method (XFEM),
element deletion method and interelement crack method. The extended finite element
method is a method for arbitrary crack propagation without remeshing. In element deletion
methods, elements that meet a fracture criterion are deleted. In interelement crack methods,
the crack is limited to element edges; the separation of these edges is governed by a cohesive
law. We show that XFEM and interelement method show similar crack speeds and crack paths.
However, both fail to predict a benchmark experiment without adjustment of the energy release
rate. The element deletion method performs very poorly for the refinements studied, and is
unable to predict crack branching.
Guo, Y., and Wu. C.T., "XFEM and EFG Cohesive Fracture Analysis for Brittle and Semi-
Brittle Materials", 11th International LS-DYNA Users Conference, Dearborn, Michigan, June, 2010.
http://www.dynalook.com/international-conf-2010/Simulation-2-3.pdf
Guo, Y., and Wu. C.T., "EFG and XFEM Cohesive Fracture Analysis Methods in LS-DYNA",
New Methodologies and Developments in LS-DYNA, DYNAmore Gmbh, Stuttgart, Germany,
November, 2010.
https://pdfs.semanticscholar.org/bc27/3ce7feb9c00e49a13b4fc45986465d405141.pdf
This study involved FEM with erosion, EFG, and XFEM techniques for three point bending of
crack propagation problems of a beam subjected to eccentric impact loading. The simulations
were evaluated for the effectiveness of each technique through a comparison with the experiment
result:
Tsuda, T., Ohnishi, Y., Ohtagaki, R., Cho, K., and Fujimoto, T., "Three-Point Bending Crack
Propagation Analysis of Beam Subjected to Eccentric Impact Loading by X-FEM", 10th
European LS-DYNA Users Conference, Wurzburg, Germany, May, 2015.
Four different numerical methods implemented in LS-DYNA were evaluated to determine
their abilities and limitations in fracture problems, especially 3D crack propagation problems.
Those methods were: Finite Element method (FEM), Discrete Element Method (DEM), Element
Free Galerkin (EFG), and Extended Finite Element Method (XFEM). Their methodologies were
briefly described and several numerical simulations were carried out and compared with experi-
mental results:
Tabiei, A., and Zhang, W., "Evaluation of Various Numerical Methods in LS-DYNA for 3D
Crack Propagation", 14th International LS-DYNA Users Conference, Dearborn, Michigan, June,
2016.
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Hu, W., Wu, C.T., Guo. Y., Ren, B., and Wu, Y., "LS-DYNA Advanced FEM and Meshfree
Methods for Solid and Structural Analyses – Manufacturing Applications", 14th International
LS-DYNA Users Conference, Dearborn, Michigan, June, 2016.
http://ftp.lstc.com/anonymous/outgoing/whu/Class/AdvFem_Meshfree_2016Class.pdf
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In this study, the extended finite element method was used for modeling dynamic fracture in
Kirchhoff plate and shell problems. A new set of tip functions was extracted from analytical
solutions of Kirchhoff plates. The semi-discrete method was used to simulate the dynamic
behavior. An unconditionally stable implicit Newmark scheme was used for temporal discreti-
zation.
Rouzegar, S.J., and Mirzaei, M., “Modeling Dynamic Fracture in Kirchhoff Plates and Shells
Using the Extended Finite Element Method”, Scientia Iranica, Vol. 20, Issue 1, pp. 120-130,
February, 2013.
https://www.sciencedirect.com/science/article/pii/S1026309812002969
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Post-Conference Training (2 day) Wed & Thurs, June 13th & 14th, 2018, 9am-5pm Edward
Hotel & Convention Center, Dearborn, MI
Fracture, Damage and Failure Using LS-DYNA
http://www.ls-dynaconferences.com/2018/post_classes/Failure%20Fracture_2018_post.pdf
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From the LS-DYNA User’s Manual:
7 - Cohesive solid
*MAT_185: *MAT_COHESIVE_TH [7]
For XFEM, the only cohesive law that can be used right now is *MAT_185
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See if this example is of some help:
http://ftp.lstc.com/anonymous/outgoing/yguo/XFEM/xfemshell.k
http://ftp.lstc.com/anonymous/outgoing/yguo/XFEM/XFEM_User_Manual.pdf
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https://www.lstc-cmmg.org/xfem
Presentation illustrating that XFEM provides an effective tool for dynamic analysis in 2D
and shell structures, minimizes mesh sensitivity, such as mesh orientation effect and mesh
size effect, and can solve fracture and propagation problems in both brittle and ductile
materials:
Wu, C.T., Hu, W., Guo. Y., Ren, B., Wu, Y., and Pan, X, "LS-DYNA XFEM Shell for
Dynamic Fracture Analysis", 3rd China LS-DYNA Users’ Conference, Shanghai, China,
October, 2017.
http://www.lsdyna.cn/document/2017_Session_Guoyong.pdf
Three advanced numerical methods for material failure simulation in LS-DYNA were
presented, Smoothed Particle Galerkin (SPG) method for 3D ductile failure analysis,
Peridynamics for 3D brittle fracture analysis, and Extended Finite Element Method
(XFEM) for shell ductile failure analysis:
Wu, C.T., Hu, W., Guo. Y., Ren, B., Wu, Y., Pan, X, and Liu, Z., "Recent Progress on
Material Failure Analysis Using LS-DYNA Advanced FEM and Meshfree Methods",
3rd China LS-DYNA Users’ Conference, Shanghai, China, October, 2017.
http://www.lsdyna.cn/document/2017_Keynote_CTWu.pdf
This paper presented an enhancement of LS-DYNA XFEM shell method for dynamic
ductile failure in shell structures. The XFEM shell formulation adopted the finite element
continuous-discontinuous approach. The continuum damage model based on continuous
displacements was used in the continuous stage to describe the diffuse micro-cracking
in ductile failure before a macro-crack was formed. In the context of first-order shear
deformable shell finite method, a nonlocal modelling procedure based on a projection of
mid-plane reference surface was introduced to regularize the element-wise strain induced
by the continuum damage model. In the discontinuous stage, an incorporation of velocity
discontinuities in shell elements was pursued by XFEM method when the damage variable
exceeded a critical value and the transition from a continuous to a discontinuous model
was permitted. A phantom-node approach was employed in XFEM method to simplify
the numerical treatment of velocity discontinuities in the shell element formulation:
Guo, Y., Wu. C.T., Hu, W., Takada, K., Okada, H., Ma, N., and Saito, K., "An Enhance-
ment of LS-DYNA XFEM Shells for Dynamic Ductile Fracture Analysis", 15th Inter-
national LS-DYNA
Users Conference, Dearborn, Michigan, June, 2018.
This paper investigated the potential of combining the extended finite element method
(XFEM) and cohesive zone method (CZM), available through LS-DYNA commercial
finite element software, for effectively modeling delamination buckling and crack
propagation in fiber metal laminates (FML). The investigation included modeling the
response of the standard double cantilever beam test specimen, and delamination-
buckling of a 3D-FML under axial impact loading:
De Cicco, D., and Taheri, F., “Delamination Buckling and Crack Propagation Simulations
in Fiber-Metal Laminates Using XFEM and Cohesive Elements”, Applied Sciences, Vol. 8,
Issue 12, pp. 1-19, December, 2018.
https://www.mdpi.com/2076-3417/8/12/2440/htm
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*BOUNDARY_PRECRACK
Purpose: Define pre-cracks in XFEM shell formulations 52 or 54 for purposes of fracture
analysis.
Pre-Crack Point Cards. Include NP cards, one for each point in the pre-crack.
Data entry example. Use an editor if LS-PrePost does not offer complete input.
*BOUNDARY_PRECRACK
$# PID, CTYPE, NP
1, 1, 2
$# Pre-Crack Point Cards. Include NP cards, one for each point in the pre-crack.
$# X, Y, Z
0.5, 0.0, 12.5
0.5, 26.0, 12.5
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Sincerely,
James M. Kennedy
KBS2 Inc.
October 23, 2021
From: Mahsa Alimohammadi [mailto:mahsa.ali...@queensu.ca]
Sent: Friday, October 22, 2021 6:52 PM
To: j...@kbs2.com
Subject: Simulating XFEM using LS-DYNA
Dear Dr. Kennedy,
This is Mahsa Alimohammadi. I am a visiting PhD student at Queen’s University. I am using LS-DYNA for my PhD thesis. I am simulating a 3-point bend test using XFEM. I do not know how I can plot the force-displacement curve for my model as a result. Also, I want to simulate the hoop stress in a circular cross section composed of two materials in another Finite element model. I would be grateful if you can help me in this regard and send me some sources that can help me.
Kind regards,
Mahsa Alimohammadi
James M. Kennedy
Dear Masha,
Thermal
The examples in this section present the thermal capabilities of LS-DYNA. They are provided by Dr. Art Shapiro. Art is working since decades on topics reated to DYNA3D, LS-DYNA and TOPAZ. He is the key developer for the thermal capabilities of LS-DYNA. Art is one of the co-founders of LSTC. You may access the examples separately by using the menu on the left.
https://www.dynaexamples.com/thermal
LS DYNA BASIC TUTORIAL: Thermal Tutorial
https://www.youtube.com/watch?v=I3A96om3a20
This chapter builds on the simple example presented in the previous chapter.
https://www.dynasupport.com/tutorial/getting-started-with-ls-dyna/the-next-step
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A number of years back, I upgraded an Examples Manual for LS-DYNA Users (several thermal examples):
Kennedy, J.M., "Introductory Examples Manual for LS-DYNA Users", Livermore Software Technology Corporation, Livermore, California, June, 2013.
http://ftp.lstc.com/anonymous/outgoing/jday/manuals/Intro_Examples_Manual_DRAFT.pdf
(accompanying input decks)
http://ftp.lstc.com/anonymous/outgoing/jday/manuals/Intro_Examples_Manual.input_decks.zip
-------------------------------
Sincerely,
James M. Kennedy
KBS2 Inc.
October 24, 2021
From: Mahsa Alimohammadi [mailto:mahsa.ali...@queensu.ca]
Sent: Saturday, October 23, 2021 10:42 AM
To: James M. Kennedy <j...@kbs2.com>; 'LS-DYNA2' <ls-d...@googlegroups.com>
Subject: Re: Simulating XFEM using LS-DYNA
Dear Dr. Kennedy
Thank you so much for your kind help. I simulated my model using XFEM and LS-DYNA. I just want to model hoop stress by modeling thermal elements. I want to model a circular model consisting of 2 materials and model thermal elements for expansion and have hoop stress. I am looking for modeling thermal elements using LS-DYNA. I would be grateful if you can send me such similar cases using LS-DYNA.
Kind regards,
Mahsa
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