Study of Growth of Cohesive Crack in two Phase Environments with Extended Finite Element Method

Document Type : Research Article

Authors

Ferdowsi University of Mashhad

Abstract

Initiation and progression of cracks in a saturated porous media is an important topic which has attracted considerable attention from researchers in the recent years. Extended finite element method (EFEM) is a contemporary technique removing the necessity of consecutive meshing of the problem in the analysis process. In the EFEM by enriching the elements whose discontinuity there exists, there is no need for re-meshing at each step of the analysis. .In this paper, EFEM is used to evaluate progression of cohesive crack in a two phase saturated porous media. To analyze the saturated porous media, at the first, the equations of mass conservation, momentum conservation, and energy conservation are established to consider simultaneous effects of displacement, pressure, and temperature on the crack progression. The cohesive model is used to simulate crack progression. Heavy-side functions are used to enrich finite elements and the resulting system of equations are solved by Newton Raphson method. Finally, the numerical model were analyzed by other researchers is considered to evaluate the derived relationships. Numerical result show that maximum variation by other researchers is 5%.

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References

[1] T.Belytschko and T.Black, Elastic crack growth in finite element with minimum remeshing. International Journal of Numerical Methods in Engineering, 1999. 45: p. 601620.
[2] N.Moes, J.Dolbow, and T.Belytschko, A finite element method for crack growth without remeshing. International Jounal of Numerical Methods in Engineering, 1999. 46: p. 131-150.
[3] J.Dolbow, An extended finite element method with discontinuous enrichment  for  applied  mechanics. 1999, Northwestern  University.
[4] J.J.C.Remmers, R.d. Borst, and A.Needleman, The simulation of dynamic crack propagation using the cohesive segment method. Journal of the Mechanics and Physics of Solids, 2008. 56: p. 70-92.
[5] T.Belystchko, et al., Arbitrary discontinuities in finite elements. International Journal of Numerical Methods in Engineering, 2001. 50: p. 993-1013.
[6] N.Sukumar, et al., Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering, 2001. 190: p. 6183-6200.
[7] J.Chessa and T.Belytschko, An extended finite element method for two phase fluids. J Appl Mech, 2003. 70: p. 10-17.
[8] A.Pirec and E.Detouranay, An implicit level set method for modeling hydraulically driven fractures. Computer Methods in Applied Mechanics and Engineering, 2008. 197.
[9] J.Rethore, R.d. Borst, and M.A.Abellan, A two-scale approach for fluid flow in fractured porous media. Computer Methods in Applied Mechanics and Engineering, 2007. 71: p. 780-800.
[10] B.Lecampion, An  extended  finite  element  method  for hydraulic  fracture problems. Commun.  Numer.  Methods Eng, 2009. 25: p. 121-133.
[11] E.Gordeliy and A.Peirce, Coupling  schemes  for modeling  hydraulic  fracture propagation  using  the XFEM. Comput.  Methods  Appl.  Mech.  Eng, 2013. 253: p. 305-322.
[12] E.Gordeliy and A.Peirce, Enrichment  strategies  and convergence  properties  of the  XFEM  for  hydraulic fracture  problems. Comput.  Methods  Appl.  Mech.  Eng, 2015. 283: p. 474-502.
[13] J.Vignollet, S.May, and R.d. Borst, Isogeometric  analysis of  fluid-saturated porous  media  including  flow  in  the cracks. Int. J. Numer. Methods Eng, 2016.
[14] R.de.Borst, Fluid  flow  in  fractured  and  fracturing porous  media:  A  unified  view. Mechanics Research Communications, 2017. 80: p. 47-57.
[15] K.Terzaghi, Theoretical Soil Mechanics. 1943: John Wiley & Sons.
[16] D.Gawin and P.Klemm, Coupled heat and moisture transfer with phase change in porous building materials. Arch Civil Engng, 1994. 40: p. 89-104.
[17] B.A.Schrefler, X.Y.Zhan, and L.Simoni, A coupled model for water flow, air flow and heat flow in deformable porous media. Int J Numer Meth Heat Fluid Flow, 1995. 5: p. 531.745
[18] H.Vaziri, Theory and application of a fully coupled thermo-hydro-mechanical finite element model. Compos Struct, 1996. 61: p. 131-146.
[19] B.Gatmiri and C.Arson, a powerful tool of thermohydromechanical behaviour and damage modeling of unsaturated porous media. Comput Geotech, 2008. 35: p. 890-915.
[20] J.Taron and D.Elsworth, Thermal–hydrologic– mechanical–chemical  processes in the evolution of engineered geothermal reservoirs. Int. J. Rock Mech. Min. Sci, 2009. 46: p. 855-864.
[21] R.Gelet, B.Loret, and N.Khalili, A  thermo-hydromechanical  coupled  model  in local  thermal  nonequilibrium  for  fractured  HDR  reservoir  with  double porosity. J.  Geophys.  Res, 2012.
[22] S.N.Pandey, A.Chaudhuri, and S.Kelkar, A  coupled thermo-hydro-mechanical  modeling  of  fracture  aperture alteration  and  reservoir  deformation  during  heat extraction  from  a geothermal  reservoir. Geothermics, 2017. 65: p. 17-31.
[23] I.Asareh, Y.Cheol, and J.HoonSong, A numerical method for dynamic fracture using the extended finite element method with non-nodal enrichment parameters. International Journal of Impact Engineering, 2018. 121  p. 63-76.
[24] H.Hyynh, et al., An extended polygonal finite element method for large deformation fracture analysis. Engineering Fracture Mechanics, 2019. 209 p. 344-406.
[25] J. Deng, N.L., H. Zhou, and W. Xue, Predicting plastic and fracture properties of silicon oxycarbide thin films using extended finite element method. Journal of Alloys and Compounds, 2019. 792 p. 481-486.
[26] J. Deng, N.L., H. Zhou, and W. Xue, Predicting plastic and fracture properties of silicon oxycarbide thin films using extended finite element method. Journal of Alloys and Compounds, 2019. 792 p. 481-486.
[27] J.Chen and Z.Xiao, The enhanced extended finite element method for the propagation of complex branched cracks. Engineering Analysis With Boundary Elements, 2019. 104: p. 46-62.
[28] M.W.Lai, D.Rubin, and E.Kremple, Introduction  to Continuum Mechanics. 1993, Pergamon Press.
[29] R.T.Fernandez, Natural  Convection  from  cyllinders buried  in  porous media. 1972, Engineering University of California
[30] J.P.Holman, Heat Transfer. 1968: Mc Grow-Hill.
[31] O.C.Zienkiewicz, AHC.Chan, and M.Pastor,  Computational  geomechanics  with  especial  refrence  to earthquake engineering, ed. Wiley. 1999.
[32] R.W.Zimmerman and G.S.Bodvarsson, Hydraulic Conductivity of Rock Fracturess. Transport in Porous Media, 1996. 23: p. 1-30.
[33] F.Irzala, J.C.Remmers, and M.Huyghe, A large deformation formulation for fluid flow in a progressively fracturing porous material. Computer Methods in Applied Mechanics and Engineering, 2013. 256(1(: p. 29-37.
Amirkabir Journal of Civil Engineering
Volume 52, Issue 9
December 2020
Pages 2289-2300

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