A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method

Abstract The extended finite element method is applied on the two-dimensional (2-D) finite piezoelectric media weakened by a crack. The fourfold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors. Four sequence of analysis, namely crack–mesh alignment, aspect ratio, mesh with local refinement and domain independency is done on the center and edge crack problems. These four analyses when combined together give an optimum result to study the finite specimen. It is observed that for smaller values of strip width to crack length ratio the finiteness of the specimen size affects the intensity factors.

[1]  Y. Mai,et al.  A piezoelectric material strip with a crack perpendicular to its boundary surfaces , 2002 .

[2]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[3]  T. Hughes,et al.  Finite element method for piezoelectric vibration , 1970 .

[4]  M. Kuna.  Finite element analyses of cracks in piezoelectric structures: a survey , 2006 .

[5]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[6]  Martin Abendroth,et al.  Finite element-computation of the electromechanical J-Integral for 2-D and 3-D crack analysis , 2002 .

[7]  M. Kuna,et al.  Calculation of the J-integral for limited permeable cracks in piezoelectrics , 2005 .

[8]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[9]  T. Belytschko,et al.  A review of extended/generalized finite element methods for material modeling , 2009 .

[10]  B. Rao,et al.  Interaction integrals for fracture analysis of functionally graded piezoelectric materials , 2008 .

[11]  Meinhard Kuna,et al.  Application of the X‐FEM to the fracture of piezoelectric materials , 2009 .

[12]  Hamouine Abdelmadjid,et al.  A state-of-the-art review of the X-FEM for computational fracture mechanics , 2009 .

[13]  Horacio Sosa,et al.  On the fracture mechanics of piezoelectric solids , 1992 .

[14]  M. Kuna,et al.  Finite Element Techniques for Dynamic Crack Analysis in Piezoelectrics , 2005 .

[15]  M. Kuna.  Fracture mechanics of piezoelectric materials – Where are we right now? , 2010 .

[16]  Y. E. Pak,et al.  Linear electro-elastic fracture mechanics of piezoelectric materials , 1992 .

[17]  S. Kumar,et al.  Crack propagation in piezoelectric materials under combined mechanical and electrical loadings , 1995 .

[18]  G. P. Cherepanov.  Invariant Γ-integrals and some of their applications in mechanics: PMM vol. 41, n≗ 3, 1977, pp. 399–412 , 1977 .

[19]  Y. Murakami.  Stress Intensity Factors Handbook , 2006 .

[20]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[21]  Meinhard Kuna,et al.  Towards the computation of electrically permeable cracks in piezoelectrics , 2004 .

[22]  T.J.C. Liu.  Anomalies associated with energy release parameters for cracks in piezoelectric materials , 2009 .

[23]  Raj N. Singh,et al.  Energy Release rate and crack propagation in piezoelectric materials. Part I: Mechanical/electrical load , 1997 .