We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.
This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite element (FE) implementation that are able to prevent oscillations which are seen when using the conventional Bubnov-Galerkin FE implementation. In addition, it is shown that the RfBF are able to provide stabilisation with very distorted meshes and curved interface boundaries. Comparison with the co...
An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap (DSG) technique using triangular meshes (ES-DSG) was recently proposed to enhance the accuracy of the existing FEM with the DSG for analysis of isotropic Reissner/Mindlin plates. In this paper, the ES-DSG is further formulated for static, free vibration and buckling analyses of functionally graded material (FGM) plates. The thermal and mechanical properties of FGM plates are assumed to vary across the thickn...
In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element is used for this study. The natural frequencies and mode shapes of simply supported and clamped square and rectangular plates are computed as a function of gradient index, crack length, crack orientation and crack loc...
#1E. De Luycker(UCSD: University of California, San Diego)H-Index: 2
#2David J. Benson(UCSD: University of California, San Diego)H-Index: 50
Last. Ming-Chen Hsu(UCSD: University of California, San Diego)H-Index: 39
view all 5 authors...
The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X-FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X-FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X-FEM with conventional finite elem...
By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress a...
Abstract Determining the lifetime of solder joints subjected to thermomechanical loads is crucial to guarantee the quality of electronic devices. The fatigue process is heavily dependent on the microstructure of the joints. We present a new methodology to determine the lifetime of the joints based on microstructural phenomena. Random microstructures are generated to capture the statistical variety of possible microstructures and crack growth calculations are performed. The extended finite elemen...
We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous a...
Last. Goangseup Zi(KU: Korea University)H-Index: 46
view all 3 authors...
This paper reviews different crack tracking techniques in three-dimensions applicable in the context of partition of unity methods, especially meshfree methods. Issues such as describing and tracking the crack surface are addressed. A crack tracking procedure is proposed in detail and implemented in the context of the extended element-free Galerkin method (XEFG). Several three-dimensional cracking examples are compared to other results from the literature or the experimental data and show good a...
Strain singularities appear in many linear elasticity problems. A very fine mesh has to be used in the vicinity of the singularity in order to obtain acceptable numerical solutions with the finite element method (FEM). Special enrichment functions describing this singular behavior can be used in the extended finite element method (X-FEM) to circumvent this problem. These functions have to be known in advance, but their analytical form is unknown in many cases. Li et al. described a method to cal...
Abstract A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack i...
Abstract This paper investigates the interfacial crack growth in the piezoelectric-piezomagnetic (PE-PM) bi-layered composite structures under quasi-static assumption. The extended finite element method (X-FEM) is utilized to solve the fracture parameters and simulate the growth paths, in which the suitable enrichment functions are chosen according to different singular properties of the crack tip. Based on the crack-tip fields of interfacial crack in PE-PM bimaterials, the mechanical energy rel...
Finite element analysis is developed to simulate the breakage of capsule in capsule-based self-healing concrete. A 2D circular capsule with different core-shell thickness ratios embedded in the mortar matrix is analyzed numerically along with their interfacial transition zone. Zero-thickness cohesive elements are pre-inserted into solid elements to represent potential cracks. This study focuses on the effects of mismatch fracture properties, namely fracture strength and energy, between capsule a...
Abstract This study was aimed to computationally investigate the thermal load combining the mechanical load effect on dynamic characteristics of intelligent composite structures. For this purpose, the cell-based smoothed finite element method (CS-FEM) was applied to the multi-physic coupling problem, and the coupled multi-physic CS-FEM (CPCS-FEM) integrating the magneto-electro-thermo-elastic (METE) coupling effect was put forward. Compared with standard FEM, this method with higher accuracy, lo...
#2Jeong-Hoon Song(CU: University of Colorado Boulder)H-Index: 21
Last. Cosmin Anitescu(Bauhaus University, Weimar)H-Index: 15
view all 4 authors...
Abstract The topic of Chapter 5 is extended meshfree methods. Firstly, the basic concept of meshfree methods is explained. Subsequently, we present several popular meshfree approximations including the Smoothed Particle Hydrodynamics (SPH) and improvements of it such as the Reproducing Kernel Particle Method (RKPM). The mostly rational shape functions and lack of the so-called Kronecker-delta property impose additional challenges on meshfree methods compared to FEM. In this context, we provide d...
In accord with the literature reviews, there is not a promising examination regarding the several straight and curved cracks interaction with arbitrary arrangement in the rectangular FGP plane. The purpose of this paper is to consider the effect of crack length, position of the point load, material non-homogeneity constant and also the arrangement of cracks on the resulting field intensity factors.,First of all, in order to obtain a set of Cauchy singular integral equations, both the dislocation...
#1Hai-Tao Liu(HEBUT: Hebei University of Technology)H-Index: 2
#2Jian-Guo Wu(HEBUT: Hebei University of Technology)H-Index: 1
Last. Tie-Jun Li(HEBUT: Hebei University of Technology)H-Index: 1
view all 3 authors...
Abstract This paper presents the dynamic non-local theory solution to a limited-permeable mode-I crack in piezoelectric materials (PMs) with the crack surfaces subjected to harmonic stress waves. The generalized Almansi’s theorem and the Schmidt method are used for this purpose. Based on the Fourier transform technique, this problem is formulated into coupled dual integral equations. The dynamic non-local stress and the dynamic non-local electric displacement fields at the crack tips are obtaine...
#1Michael Wünsche(SAV: Slovak Academy of Sciences)H-Index: 9
#2Jan Sladek(SAV: Slovak Academy of Sciences)H-Index: 53
Last. Miroslav Repka(SAV: Slovak Academy of Sciences)H-Index: 5
view all 5 authors...
This paper presents the transient dynamic analysis of micro-cracks of arbitrary shape in two-dimensional, linear piezoelectric fiber reinforced composite materials. Interface cracks between fiber a...
The effects of interfacial strength on fractured microcapsule are investigated numerically. The interaction between crack and microcapsule embedded in mortar matrix is modeled based on cohesive approach. The microcapsules are modelled with variation of core-shell thickness ratio and potential cracks are represented by pre-inserted cohesive elements along the element boundaries of the mortar matrix, microcapsules core, microcapsule shell, and at the interfaces between these phases. Special attent...
Abstract This article conducts an exact analysis of a thermal dielectric crack moving in piezoelectric materials. Self-generating thermal and electric loadings by the crack interior are exerted on the crack surfaces as well as various external loadings including a shearing force. Fundamental solutions of the thermal and electro-elastic coupling fields are given by determining a temperature function and a harmonic function with eigenvalues properties due to material properties considered. Analyti...