Cell-Based Smoothed Finite Element Method-Virtual Crack Closure Technique for a Piezoelectric Material of Crack

In order to improve the accuracy and efficiency of solving fracture parameters of piezoelectric materials, a piezoelectric element, tailored for the virtual crack closure technique (VCCT), was used to study piezoelectric materials containing a crack. Recently, the cell-based smoothed finite element method (CSFEM) and VCCT have been used to simulate the fracture mechanics of piezoelectric materials. A center cracked piezoelectric materials with different material properties, crack length, mesh, and smoothing subcells at various strain energy release rates are discussed and compared with finite element method-virtual crack closure technique (FEM-VCCT). Numerical examples show that CSFEM-VCCT gives an improved simulation compared to FEM-VCCT, which generally simulates materials as too stiff with lower accuracy and efficiency. Due to its simplicity, the VCCT piezoelectric element demonstrated in this study could be a potential tool for engineers to practice piezoelectric fracture analysis. CSFEM-VCCT is an efficient numerical method for fracture analysis of piezoelectric materials.

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

[2]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[3]  M. Kanninen,et al.  A finite element calculation of stress intensity factors by a modified crack closure integral , 1977 .

[4]  Paul A. Wawrzynek,et al.  An interactive approach to local remeshing around a propagating crack , 1989 .

[5]  A. Jones.  10 – Rock Mechanics and Rock Engineering , 1989 .

[6]  Y. Pak,et al.  Crack Extension Force in a Piezoelectric Material , 1990 .

[7]  H. Sosa.  Plane problems in piezoelectric media with defects , 1991 .

[8]  Tong-Yi Zhang,et al.  Mode‐III cracks in piezoelectric materials , 1992 .

[9]  Zhigang Suo,et al.  Fracture mechanics for piezoelectric ceramics , 1992 .

[10]  S. K. Maiti.  Finite element computation of crack closure integrals and stress intensity factors , 1992 .

[11]  Biao Wang,et al.  Three-dimensional analysis of a flat elliptical crack in a piezoelectric material , 1992 .

[12]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[13]  T. Belytschko,et al.  A new implementation of the element free Galerkin method , 1994 .

[14]  E. Pan.  A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids , 1999 .

[15]  Glaucio H. Paulino,et al.  Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method , 2002 .

[16]  Yoon-Suk Chang,et al.  Numerical calculation of energy release rates by virtual crack closure technique , 2004 .

[17]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[18]  Ronald Krueger,et al.  The Virtual Crack Closure Technique : History , Approach and Applications , 2002 .

[19]  De Xie,et al.  Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: Formulation and validation , 2006 .

[20]  De Xie,et al.  Progressive crack growth analysis using interface element based on the virtual crack closure technique , 2006 .

[21]  De Xie,et al.  Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part II: Sensitivity study on modeling details , 2006 .

[22]  Xianghua Guo,et al.  Analysis of piezoelectric ceramic multilayer actuators based on an electro-mechanical coupled meshless method , 2006 .

[23]  K. Y. Dai,et al.  Theoretical aspects of the smoothed finite element method (SFEM) , 2007 .

[24]  K. Y. Dai,et al.  A Smoothed Finite Element Method for Mechanics Problems , 2007 .

[25]  Moussa Nait-Abdelaziz,et al.  A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics , 2007 .

[26]  Timon Rabczuk,et al.  A new crack tip element for the phantom‐node method with arbitrary cohesive cracks , 2008 .

[27]  H. Nguyen-Xuan,et al.  A smoothed finite element method for plate analysis , 2008 .

[28]  Guirong Liu,et al.  An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures , 2009 .

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

[30]  Shengchuan Wu,et al.  An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system , 2010 .

[31]  Guiyong Zhang,et al.  Dispersion error reduction for acoustic problems using the edge‐based smoothed finite element method (ES‐FEM) , 2011 .

[32]  T. Rabczuk,et al.  Extended finite element method for dynamic fracture of piezo-electric materials , 2012 .

[33]  Wei Gao,et al.  Fracture analysis of piezoelectric materials using the scaled boundary finite element method , 2013 .

[34]  Guirong Liu,et al.  An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order , 2013 .

[35]  Junping Shi,et al.  Extended meshless method based on partition of unity for solving multiple crack problems , 2013 .

[36]  Louis Ngai Yuen Wong,et al.  Dynamic Study on Fracture Problems in Viscoelastic Sedimentary Rocks Using the Numerical Manifold Method , 2013, Rock Mechanics and Rock Engineering.

[37]  Timon Rabczuk,et al.  Detection of multiple flaws in piezoelectric structures using XFEM and level sets , 2014 .