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

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Li Ming Zhou ◽  
Guang Wei Meng ◽  
Feng Li ◽  
Hui Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Closure ◽  
Piezoelectric Materials ◽  
Piezoelectric Element ◽  
Fracture Analysis ◽  
Virtual Crack Closure Technique ◽  
Closure Technique ◽  
Smoothed Finite Element Method ◽  
Element Method

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.

scholarly journals Analysis of Dynamic Fracture Parameters in Functionally Graded Material Plates with Cracks by Graded Finite Element Method and Virtual Crack Closure Technique

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Li Ming Zhou ◽  
Guang Wei Meng ◽  
Xiao Lin Li ◽  
Feng Li
Keyword(s):  
Finite Element ◽  
Crack Closure ◽  
Dynamic Fracture ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Interface Element ◽  
Virtual Crack Closure Technique ◽  
Closure Technique ◽  
Graded Material ◽  
Element Method

Based on the finite element software ABAQUS and graded element method, we developed a dummy node fracture element, wrote the user subroutines UMAT and UEL, and solved the energy release rate component of functionally graded material (FGM) plates with cracks. An interface element tailored for the virtual crack closure technique (VCCT) was applied. Fixed cracks and moving cracks under dynamic loads were simulated. The results were compared to other VCCT-based analyses. With the implementation of a crack speed function within the element, it can be easily expanded to the cases of varying crack velocities, without convergence difficulty for all cases. Neither singular element nor collapsed element was required. Therefore, due to its simplicity, the VCCT interface element is a potential tool for engineers to conduct dynamic fracture analysis in conjunction with commercial finite element analysis codes.

A COMBINED EXTENDED AND EDGE-BASED SMOOTHED FINITE ELEMENT METHOD (ES-XFEM) FOR FRACTURE ANALYSIS OF 2D ELASTICITY

2011 ◽  
Vol 08 (04) ◽  
pp. 773-786 ◽  
Author(s):  
L. CHEN ◽  
G. R. LIU ◽  
K. Y. ZENG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Partition Of Unity ◽  
Fracture Analysis ◽  
Softening Effect ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
2D Elasticity ◽  
Element Method

This study combines the edge-based smoothed finite element method (ES-FEM) and the extended finite element method (XFEM) to develop a new simulation technique (ES-XFEM) for fracture analysis of 2D elasticity. In the XFEM, the need for the mesh alignment with the crack and remeshing, as the crack evolves, is eliminated because of the use of partition of unity. The ES-FEM uses the generalized smoothing operation over smoothing domain associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions for the numerical model. Taking advantage of both ES-FEM and XFEM, the present method introduces the edge-based strain smoothing technique into the context of XFEM. Thanks to strain smoothing, the necessity of sub-division in elements cut by discontinuities is suppressed via transforming interior integration into boundary integration. Hence, it simplifies the numerical integration procedure in the XFEM. Numerical examples showed that the proposed method improves significantly the accuracy of stress intensity factors and achieves a quasi optimal convergence rate in the energy norm without geometrical enrichment or blending correction.

scholarly journals A Cell-Based Smoothed XFEM for Fracture in Piezoelectric Materials

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Li Ming Zhou ◽  
Guang Wei Meng ◽  
Feng Li ◽  
Shuai Gu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Piezoelectric Materials ◽  
Crack Tip ◽  
Extended Finite Element ◽  
Boundary Integration ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Element Method

This paper presents a cell-based smoothed extended finite element method (CS-XFEM) to analyze fractures in piezoelectric materials. The method, which combines the cell-based smoothed finite element method (CS-FEM) and the extended finite element method (XFEM), shows advantages of both methods. The crack tip enrichment functions are specially derived to represent the characteristics of the displacement field and electric field around the crack tip in piezoelectric materials. With the help of the smoothing technique, integrating the singular derivatives of the crack tip enrichment functions is avoided by transforming interior integration into boundary integration. This is a significant advantage over XFEM. Numerical examples are presented to highlight the accuracy of the proposed CS-XFEM with the analytical solutions and the XFEM results.

scholarly journals A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Bin Cai ◽  
Liming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Piezoelectric Materials ◽  
Continuous System ◽  
Functionally Graded ◽  
Gaussian Integration ◽  
Functionally Graded Piezoelectric Materials ◽  
Smoothed Finite Element Method ◽  
Functionally Graded Piezoelectric ◽  
Element Method

To accurately simulate the continuous property change of functionally graded piezoelectric materials (FGPMs) and overcome the overstiffness of the finite element method (FEM), we present an electromechanical inhomogeneous cell-based smoothed FEM (ISFEM) of FGPMs. Firstly, ISFEM formulations were derived to calculate the transient response of FGPMs, and then, a modified Wilson-θ method was deduced to solve the integration of the FGPM system. The true parameters at the Gaussian integration point in FGPMs were adopted directly to replace the homogenization parameters in an element. ISFEM provides a close-to-exact stiffness of the continuous system, which could automatically and more easily generate for complicated domains and thus significantly decrease numerical errors. The accuracy and trustworthiness of ISFEM were verified as higher than the standard FEM by several numerical examples.

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