Modeling pressurized fracture propagation with the isogeometric BEM

Leilei Chen1,2, Zhongwang Wang1,2, Xuan Peng3, Jianfeng Yang4, Pengfei Wu5, Haojie Lian6,2
1College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang, People’s Republic of China
2School of Architectural Engineering, Huanghuai University, Zhumadian, People’s Republic of China
3Department of Mechanical Engineering, Suzhou University of Science and Technology, Suzhou, People’s Republic of China
4School of Energy Engineering, Xi’an University of Science and Technology, Xi’an, People’s Republic of China
5College of Mining Engineering, Taiyuan University of Technology, Taiyuan, People’s Republic of China
6Key Laboratory of In-situ Property-Improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan, People’s Republic of China

Tóm tắt

Từ khóa


Tài liệu tham khảo

Areias P, Msekh M, Rabczuk T (2016) Damage and fracture algorithm using the screened poisson equation and local remeshing. Eng Fract Mech 158:116–143. https://doi.org/10.1016/j.engfracmech.2015.10.042

Becker A (1992) The boundary element methods in engineering. McGraw-Hill Book Company, New York

Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45(5):601–620

Bruno M, Nakagawa F (1991) Pore pressure influence on tensile fracture propagation in sedimentary rock. Int J Rock Mech Mining Sci Geomech Abst 28(4):261–273. https://doi.org/10.1016/0148-9062(91)90593-B

Carrier B, Granet S (2012) Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng Fract Mech 79:312–328

Chen L, Liu C, Zhao W, Liu L (2018) An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution. Comput Methods Appl Mech Eng 336:507–532

Chen L, Marburg S, Zhao W, Liu C, Chen H (2019a) Implementation of isogeometric fast multipole boundary element methods for 2d half-space acoustic scattering problems with absorbing boundary condition. J Theoret Comput Acoust 27(02):1850024

Chen L, Lian H, Liu Z, Chen H, Atroshchenko E, Bordas S (2019b) Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods. Comput Methods Appl Mech Eng 355:926–951

Chen L, Zhang Y, Lian H, Atroshchenko E, Ding C, Bordas S (2020a) Seamless integration of computer-aided geometric modeling and acoustic simulation: Isogeometric boundary element methods based on catmull-clark subdivision surfaces. Adv Eng Softw 149:102879

Chen L, Lu C, Lian H, Liu Z, Zhao W, Li S, Chen H, Bordas S (2020b) Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods. Comput Methods Appl Mech Eng 362:112806

Chen L, Lu C, Zhao W, Chen H, Zheng CJ (2020c) Subdivision surfaces–boundary element accelerated by fast multipole for the structural acoustic problem. J Theoret Comput Acoust 28(2):2050011–1–27

Cox M (1972) The numerical evaluation of B-splines. IMA J Appl Math 10(2):134–1492

Cruse T (1996) Bie fracture mechanics analysis: 25 years of developments. Comput Mech 18(1):1–11

Cruse T, Rizzo F (1968) A direct formulation and numerical solution of the general transient elastodynamic problem i. J Math Anal Appl 22(1):244–259

De Boor C (1972) On calculating with B-splines. J Approx Theory 6(1):50–62

Duan K, Li Y, Yang W (2021) Discrete element method simulation of the growth and efficiency of multiple hydraulic fractures simultaneously-induced from two horizontal wells. Geomech Geophys Geo-Energy Geo-Resour. https://doi.org/10.1007/s40948-020-00196-4

Erdogan F, Sih G (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85(4):519

Gordeliy E, Peirce A (2015) Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems. Comput Methods Appl Mech Eng 283:474–502

Guiggiani M, Krishnasamy G, Rudolphi T, Rizzo F (1992) A general algorithm for the numerical solution of hypersingular boundary integral equations. J Appl Mech 59(3):604–614

He B, Zhuang X (2018) Modeling hydraulic cracks and inclusion interaction using XFEM. Underground space 3(3):218–228

Hong H, Chen J (1988) Derivations of integral equations of elasticity. J Eng Mech 114(6):1028–1044

Hu Y, Li X, Zhang Z, He J, Li G (2020) Numerical investigation on the hydraulic stimulation of naturally fractured longmaxi shale reservoirs using an extended discontinuous deformation analysis (DDA) method. Geomech Geophys Geo-Energy Geo-Resour 6(4):1–21

Hughes T, Cottrell J, Bazilevs Y (2005) Isogeometric analysis: Cad, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39–41):4135–4195

Khoei A, Hirmand M, Vahab M, Bazargan M (2015) An enriched FEM technique for modeling hydraulically driven cohesive fracture propagation in impermeable media with frictional natural faults: Numerical and experimental investigations. Int J Numer Meth Eng 104(6):439–468

LaGreca R, Daniel M, Bac A (2005) Local deformation of NURBS curves. Math Methods Curves Surf Tromso 2004:243–252

Lecampion B (2009) An extended finite element method for hydraulic fracture problems. Commun Numer Methods Eng 25(2):121–133

Li K, Qian X (2011) Isogeometric analysis and shape optimization via boundary integral. Comput Aided Des 43(11):1427–1437

Li C, Niu Z, Hu Z, Hu B, Cheng C (2019) Effectiveness of the stress solutions in notch/crack tip regions by using extended boundary element method. Eng Anal Boundary Elem 108:1–13

Li Z, Li X, Yu J, Cao W, Wang X (2020) Influence of existing natural fractures and beddings on the formation of fracture network during hydraulic fracturing based on the extended finite element method. Geomech Geophys Geo-Energy Geo-Resour 6(4):58

Lian H, Kerfriden P, Bordas S (2016) Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity. Int J Numer Meth Eng 106(12):972–1017

Lian H, Kerfriden P, Bordas S (2017) Shape optimization directly from CAD: An isogeometric boundary element approach using t-splines. Comput Methods Appl Mech Eng 317:1–41

Liu Y, Rudolphi T (1991) Some identities for fundamental solutions and their applications to non-singular boundary element formulations. Eng Anal Boundary Elem 8(6):301–311

Liu C, Chen L, Zhao W, Chen H (2017) Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions. Eng Anal Boundary Elem 85:142–157

Lo L (2014) Interaction of growing cracks in hydraulic fracturing. Ph.D. thesis

Miehe C, Hofacker M, Welschinger F (2010a) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199(45–48):2765–2778

Miehe C, Welschinger F, Hofacker M (2010b) Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations. Int J Numer Meth Eng 83(10):1273–1311

Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng

Mohammadnejad T, Khoei A (2013) An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elem Anal Des 73:77–95

Nguyen B, Tran H, Anitescu C, Zhuang X, Rabczuk T (2016) An isogeometric symmetric galerkin boundary element method for two-dimensional crack problems. Comput Methods Appl Mech Eng 306:252–275

Nguyen V, Lian H, Rabczuk T, Bordas S (2017) Modelling hydraulic fractures in porous media using flow cohesive interface elements. Eng Geol 225:68–82

Niu Z, Cheng C, Zhou H, Hu Z (2007) Analytic formulations for calculating nearly singular integrals in two-dimensional BEM. Eng Anal Boundary Elem 31(12):949–964

Niu Z, Cheng C, Ye J, Recho N (2009) A new boundary element approach of modeling singular stress fields of plane V-notch problems. Int J Solids Struct 46(16):2999–3008

Niu Z, Hu Z, Cheng C, Zhou H (2015) A novel semi-analytical algorithm of nearly singular integrals on higher order elements in two dimensional BEM. Eng Anal Bound Elem 61:42–51

Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Meth Eng 44(9):1267–1282

Paluszny A, Zimmerman R (2013) Numerical fracture growth modeling using smooth surface geometric deformation. Eng Fract Mech 108:19–36

Peng X, Atroshchenko E, Kerfriden P, Bordas S (2017a) Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth. Comput Methods Appl Mech Eng 316:151–185

Peng X, Atroshchenko E, Kerfriden P, Bordas S (2017b) Linear elastic fracture simulation directly from CAD: 2d NURBS-based implementation and role of tip enrichment. Int J Fract 204(1):55–78

Rogers D (2000) An introduction to NURBS: with historical perspective. Elsevier, New York

Rudolphi T (1991) The use of simple solutions in the regularization of hypersingular boundary integral equations. Math Comput Model 15(3–5):269–278

Scott M, Simpson R, Evans J, Lipton S, Bordas S, Hughes T, Sederberg T (2013) Isogeometric boundary element analysis using unstructured t-splines. Comput Methods Appl Mech Eng 254:197–221

Seybert A, Soenarko B, Rizzo F, Shippy D (1985) An advanced computational method for radiation and scattering of acoustic waves in three dimensions. J Acoust Soc Am 77(2):362–368

Simpson R, Trevelyan J (2011) A partition of unity enriched dual boundary element method for accurate computations in fracture mechanic. Comput Methods Appl Mech Eng 200(1–4):1–10

Simpson R, Bordas S, Trevelyan J, Rabczuk T (2012) A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput Methods Appl Mech Eng 209:87–100

Simpson R, Bordas S, Lian H, Trevelyan J (2013) An isogeometric boundary element method for elastostatic analysis: 2d implementation aspects. Comput Struct 118:2–12

Simpson R, Scott M, Taus M, Thomas D, Lian H (2014) Acoustic isogeometric boundary element analysis. Comput Methods Appl Mech Eng 269:265–290

Sneddon I (1995) Fourier transforms. McGraw-Hill, New York

Telles J (1987) A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. Int J Numer Methods Eng 24(5):959–973

Yau J, Wang W, Corten H (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47(2):335–341

Zhang B, Ji B, Liu W (2017) The study on mechanics of hydraulic fracture propagation direction in shale and numerical simulation. Geomechanics and Geophysics for Geo-Energy and Geo-Resources 4:119–124

Zienkiewicz O, Taylor R (1977) The finite element method. McGraw-Hill Book Company, New York