Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS

Cheng, 2000, Effects of electric fields on the bending behavior of PZT-5Z piezoelectric laminates, Smart Mater. Struct., 9, 824, 10.1088/0964-1726/9/6/312

Kuna, 2010, Fracture mechanics of piezoelectric materials—where are we right now?, Eng. Fract. Mech., 77, 309, 10.1016/j.engfracmech.2009.03.016

Parton, 1976, Fracture mechanics of piezoelectric materials, Acta Astronaut., 3, 671, 10.1016/0094-5765(76)90105-3

Pak, 1990, Crack extension force in a piezoelectric material, J. Appl. Mech., 57, 647, 10.1115/1.2897071

Sosa, 1990, Three-dimensional eigenfunction analysis of a crack in a piezoelectric material, Int. J. Solids Struct., 26, 1, 10.1016/0020-7683(90)90090-I

McMeeking, 1990, A J-integral for the analysis of electrically induced mechanical stress at cracks in elastic dielectrics, Internat. J. Engrg. Sci., 28, 605, 10.1016/0020-7225(90)90089-2

Pak, 1992, Linear electro-elastic fracture mechanics of piezoelectric materials, Int. J. Fract., 54, 79, 10.1007/BF00040857

Suo, 1992, Fracture mechanics for piezoelectric ceramics, J. Mech. Phys. Solids, 40, 739, 10.1016/0022-5096(92)90002-J

Chen, 1999, Fundamental solution for a penny-shaped crack in a piezoelectric medium, J. Mech. Phys. Solids, 47, 1459, 10.1016/S0022-5096(98)00114-8

Park, 1995, Fracture criteria for piezoelectric ceramics, J. Am. Ceram. Soc., 78, 1475, 10.1111/j.1151-2916.1995.tb08840.x

Xu, 2000, A theoretical study of branched cracks in piezoelectrics, Acta Mater., 48, 1865, 10.1016/S1359-6454(99)00469-3

Kumar, 1996, Crack propagation in piezoelectric materials under combined mechanical and electric loadings, Acta Mater., 44, 173, 10.1016/1359-6454(95)00175-3

Kumar, 1997, Energy release rate and crack propagation in piezoelectric materials, Part II, combined mechanical and electric loads, Acta Mater., 45, 849, 10.1016/S1359-6454(96)00175-9

Abendroth, 2002, Finite element computation of the electromechanical J-Integral for 2-D and 3-D crack analysis, Int. J. Fract., 114, 359, 10.1023/A:1015725725879

Enderlein, 2005, Finite element techniques for dynamic crack analysis in piezoelectrics, Int. J. Fract., 134, 191, 10.1007/s10704-005-0522-9

Gruebner, 2003, Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium, Eng. Fract. Mech., 70, 1399, 10.1016/S0013-7944(02)00117-0

Janski, 2010, Adaptive finite element computation of dielectric and mechanical intensity factors in piezoelectrics with impermeable cracks, Internat. J. Numer. Methods Engrg., 81, 1492, 10.1002/nme.2742

Kuna, 1998, Finite element analyses of crack problems in piezoelectric structures, Comput. Mater. Sci., 13, 67, 10.1016/S0927-0256(98)00047-0

Kuna, 2006, Finite element analyses of cracks in piezoelectric structures: A survey, Arch. Appl. Mech., 76, 725, 10.1007/s00419-006-0059-z

Pan, 1999, A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids, Eng. Anal. Bound. Elem., 23, 67, 10.1016/S0955-7997(98)00062-9

Rajapakse, 2001, Boundary element modeling of cracks in piezoelectric solids, Eng. Anal. Bound. Elem., 25, 771, 10.1016/S0955-7997(01)00058-3

Garcia-Sanchez, 2007, 2D transient dynamic crack analysis in piezoelectric solids by BEM, Comput. Mater. Sci., 39, 179, 10.1016/j.commatsci.2006.03.021

Garcia-Sanchez, 2008, 2-D transient dynamic analysis of cracked piezoelectric solids by a time-domain BEM, Comput. Methods Appl. Mech. Engrg., 197, 3108, 10.1016/j.cma.2008.02.013

Lei, 2015, Comparison of several BEM-based approaches in evaluating crack-tip field intensity factors in piezoelectric materials, Int. J. Fract., 189, 111, 10.1007/s10704-014-9964-2

Lei, 2015, Transient dynamic interface crack analysis in magnetoelectroelastic bi-materials by a time-domain BEM, Eur. J. Mech. A Solids, 49, 146, 10.1016/j.euromechsol.2014.07.010

Wünsche, 2010, A 2D time-domain collocation-Galerkin BEM for dynamic crack analysis in piezoelectric solids, Eng. Anal. Bound. Elem., 34, 377, 10.1016/j.enganabound.2009.11.004

Sladek, 2007, Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG, Comput. Model. Eng. Sci., 19, 247

Sladek, 2007, Evaluation of fracture parameters in continuously nonhomogeneous piezoelectric solids, Int. J. Fract., 145, 313, 10.1007/s10704-007-9130-1

Sladek, 2008, Dynamic 3-D axisymmetric problems in continuously nonhomogeneous piezoelectric solids, Int. J. Solids Struct., 45, 4523, 10.1016/j.ijsolstr.2008.03.027

Liew, 2007, Boundary element-free method for fracture analysis of 2-D anisotropic piezoelectric solids, Internat. J. Numer. Methods Engrg., 69, 729, 10.1002/nme.1786

Li, 2013, Fracture analysis of piezoelectric materials using the scaled boundary finite element method, Eng. Fract. Mech., 97, 52, 10.1016/j.engfracmech.2012.10.019

Li, 2014, 2D dynamic analysis of cracks and interface cracks in piezoelectric composites using the SBFEM, Int. J. Solids Struct., 51, 2096, 10.1016/j.ijsolstr.2014.02.014

Béchet, 2009, Application of the X-FEM to the fracture of piezoelectric materials, Internat. J. Numer. Methods Engrg., 77, 1535, 10.1002/nme.2455

Shama, 2013, Analysis of a subinterface crack in piezoelectric bimaterials with the extended finite element method, Eng. Fract. Mech., 104, 114, 10.1016/j.engfracmech.2013.03.012

Bui, 2012, Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading, Comput. Mater. Sci., 62, 243, 10.1016/j.commatsci.2012.05.049

Bui, 2013, Analysis of generalized dynamic intensity factors of cracked magnetoelectroelastic solids by X-FEM, Finite Elem. Anal. Des., 69, 19, 10.1016/j.finel.2013.02.001

Liu, 2013, Transient dynamic crack analysis in non-homogeneous functionally graded piezoelectric materials by the X-FEM, Comput. Mater. Sci., 69, 542, 10.1016/j.commatsci.2012.11.009

Liu, 2014, Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method, Int. J. Solids Struct., 51, 2167, 10.1016/j.ijsolstr.2014.02.024

Belytschko, 2009, A review of extended/generalizad finite element methods for material modeling, Modelling Simul. Mater. Sci. Eng., 17, 043001, 10.1088/0965-0393/17/4/043001

Fries, 2010, The generalized/extended finite element method: An overview of the method and its application, Internat. J. Numer. Methods Engrg., 84, 253, 10.1002/nme.2914

Bhattacharya, 2013, Fatigue crack growth simulations of interfacial cracks in bi-layered FGMs using XFEM, Comput. Mech., 52, 799, 10.1007/s00466-013-0845-8

Yu, 2015, A stabilized discrete shear gap extended finite element for the analysis of cracked Reissner–Mindlin plate vibration problems involving distorted meshes, Int. J. Mech. Des.

Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008

Yu, 2015, A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates, Finite Elem. Anal. Des., 96, 1, 10.1016/j.finel.2014.11.003

Shojaee, 2012, Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method, Compos. Struct., 94, 677, 10.1016/j.compstruct.2012.01.012

Yin, 2014, Bordas SPA. Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates, Compos. Struct., 118, 121, 10.1016/j.compstruct.2014.07.028

Valizadeh, 2013, NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter, Compos. Struct., 99, 309, 10.1016/j.compstruct.2012.11.008

Valizadeh, 2013, Isogeometric simulation for buckling, free and forced vibration of orthotropic plates, Int. J. Appl. Mech., 05, 1350017, 10.1142/S1758825113500178

Nguyen, 2014, Isogeometric analysis for unsaturated flow problems, Comput. Geotech., 62, 257, 10.1016/j.compgeo.2014.08.003

Benson, 2010, A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM, Internat. J. Numer. Methods Engrg., 83, 765, 10.1002/nme.2864

De Luycker, 2011, X-FEM in isogeometric analysis for linear fracture mechanics, Internat. J. Numer. Methods Engrg., 87, 541, 10.1002/nme.3121

Ghorashi, 2011, Extended isogeometric analysis for simulation of stationary and propagating cracks, Internat. J. Numer. Methods Engrg., 89, 1069, 10.1002/nme.3277

Haasemann, 2011, Development of a quadratic finite element formulation based on the XFEM and NURBS, Internat. J. Numer. Methods Engrg., 86, 598, 10.1002/nme.3120

Bayesteh, 2015, Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method, Eur. J. Mech. A Solids, 51, 123, 10.1016/j.euromechsol.2014.12.004

Ghorashi, 2015, T-spline based XIGA for fracture analysis of orthotropic media, Comput. Struct., 147, 138, 10.1016/j.compstruc.2014.09.017

Jia, 2014, Extended isogeometric analysis for material interface problems, IMA J. Appl. Math., 1

Bhardwaj, 2015, Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA, Comput. Methods Appl. Mech. Engrg., 284, 186, 10.1016/j.cma.2014.08.015

Bhardwaj, 2015, Fatigue crack growth analysis of a homogeneous plate in the presence of multiple defects using extended isogeometric analysis, J. Braz. Soc. Mech. Sci. Eng., 10.1007/s40430-014-0232-1

Bhardwaj, 2015, Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions, Compos. Struct., 126, 347, 10.1016/j.compstruct.2015.02.066

Singh, 2015, A new criterion for modeling multiple discontinuities passing through an element using XIGA, J. Mech. Sci. Technol., 29, 1141, 10.1007/s12206-015-0225-8

Pisarenko, 1985, Anisotropy of fracture toughness of piezoelectric ceramics, J. Am. Ceram. Soc., 68, 259, 10.1111/j.1151-2916.1985.tb15319.x

Piegl, 1997

Laborde, 2005, High-order extended finite element method for cracked domains, Internat. J. Numer. Methods Engrg., 64, 354, 10.1002/nme.1370

Wang, 2010, An improved NUBRS-based isogeometric analysis with enhanced treatment of essential boundary conditions, Comput. Mech. Appl. Mech. Eng., 199, 2425, 10.1016/j.cma.2010.03.032

Yin, 2015, Two improved treatment methods for Dirichlet-type boundary conditions in isogeometric analysis, Eur. J. Mech. A Solids

Koo, 2013, Isogeometric shape design sensitivity analysis using transformed basis functions for Kronecker delta property, Comput. Methods Appl. Mech. Engrg., 253, 505, 10.1016/j.cma.2012.08.014

Fernandez-Mendez, 2004, Imposing essential boundary conditions in mesh-free methods, Comput. Methods Appl. Mech. Engrg., 193, 1257, 10.1016/j.cma.2003.12.019

Rao, 2008, Interaction integrals for fracture analysis of functionally graded piezoelectric materials, Int. J. Solids Struct., 45, 5237, 10.1016/j.ijsolstr.2008.05.020

Liu, 2012, The singular edge-based smoothed finite element method for stationary dynamic crack problems in 2D elastic solids, Comput. Methods Appl. Mech. Engrg., 233–236, 68, 10.1016/j.cma.2012.04.008

Hao, 1994, A new electric boundary condition of electric fracture mechanics and its applications, Eng. Fract. Mech., 47, 793, 10.1016/0013-7944(94)90059-0

Shindo, 2009, Effect of the electrical boundary condition at the crack face on the mode I energy release rate in piezoelectric ceramics, Appl. Phys. Lett., 94, 081902, 10.1063/1.3088855

Wang, 2003, On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics, Internat. J. Engrg. Sci., 41, 633, 10.1016/S0020-7225(02)00149-0

Janski, 2011, Crack propagation simulations in piezoelectric structures with an efficient adaptive finite element tool, 163

Meschke, 2007, Energy-based modeling of cohesive and cohesionless cracks via X-FEM, Comput. Methods Appl. Mech. Engrg., 196, 2338, 10.1016/j.cma.2006.11.016

Yu, 2015, Interfacial dynamic impermeable cracks analysis in dissimilar piezoelectric materials under coupled electromechanical loading with the extended finite element method, Int. J. Solids Struct., 67–68, 205, 10.1016/j.ijsolstr.2015.03.037