Abstract Accurate numerical modeling of multifield piezoelectric materials is challenging because of the inherent electro-mechanical coupling effect and material anisotropic behaviors. The modeling becomes even more difficult especially for problems with non-smooth solutions like crack under dynamic loading. We present in this paper an extension of the extended isogeometric analysis (XIGA) for simulation of two-dimensional fracture mechanics problems in piezoelectric materials under dynamic and static coupled electromechanical loads. The discretization of problem domain is based on basis functions generated from NURBS, which are used for both geometric description and approximation of solution field variables. To capture the discontinuity across the crack-faces and the singularity at the crack-tip, the isogeometric approximation is locally enriched by discontinuous Heaviside function and asymptotic crack-tip branch functions. The sixfold enrichment functions particularly suitable for electromechanical crack-tip singularity of piezoelectric materials are used. To evaluate the generalized fracture parameters, a domain-form of electromechanical interaction integral is employed. For dynamic analysis, the implicit time integration scheme considering inertial effect is taken. Five numerical examples for single and mixed-modes of impermeable cracks are considered and the generalized fracture parameters under dynamic and static loads are analyzed. The accuracy and effectiveness of the proposed XIGA are illustrated through numerical investigations of the generalized dynamic and static fracture parameters. Numerical results are validated against the reference solutions derived from the boundary element methods. The effects of some numerical aspect ratios on generalized fracture parameters are also investigated. Additionally, we present some numerical results of quasi-static crack propagation in piezoelectric solids using the developed XIGA, taking fracture toughness anisotropy of polarized electroelastic materials into account, and employing the maximum modified hoop stress intensity factor criterion for predicting the growing direction of crack.
#2Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
Last. Sohichi Hirose(TITech: Tokyo Institute of Technology)H-Index: 15
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In this work, a new approach in the framework of the local partition of unity finite element method (XFEM) to significantly improve the accuracy of natural frequency in free vibration analysis of cracked Reissner–Mindlin plates is presented. Different from previous approaches, the present formulation is expected to be more accurate and effective in modeling cracked plates by integrating the stabilized discrete shear gap (DSG) into the XFEM setting. Intensive numerical results at low frequency de...
#2Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
Last. Sohichi Hirose(TITech: Tokyo Institute of Technology)H-Index: 15
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Interfacial dynamic impermeable cracks analysis of dissimilar piezoelectric solids under coupled electromechanical impact loadings by the extended finite element method (X-FEM) is presented. The dynamic X-FEM approach recently developed by the authors is further extended to analyze transient responses of interfacial impermeable cracks in dissimilar piezoelectric structures. The mechanical displacements and electrical potential are approximated by appropriate enrichment functions that are not onl...
#1G. Bhardwaj(IITR: Indian Institute of Technology Roorkee)H-Index: 12
#2Indra Vir Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 31
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract In this paper, extended isogeometric analysis (XIGA) is performed to simulate the cracked functionally graded material (FGM) plates using first order shear deformation theory (FSDT) under different types of loading and boundary conditions. The gradation in material properties of the plate vary exponentially along thickness direction. The top and bottom surfaces of the plate are composed of ceramic and metal respectively. The properties of the equivalent composite are evaluated by rule o...
#1G. Bhardwaj(IITR: Indian Institute of Technology Roorkee)H-Index: 12
#2Indra Vir Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 31
In this work, extended Isogeometric analysis (XIGA) is successfully extended to evaluate the fatigue life of a homogenous finite plate in the presence of multiple defects (cracks, holes and inclusions) under cyclic loading condition. In isogeometric analysis, same basis functions, i.e. non uniform rational B-splines are used for defining the geometry and solution. In XIGA, the crack faces are modeled by discontinuous Heaviside jump functions, whereas the singularity in stress field at the crack ...
Last. Timon Rabczuk(KU: Korea University)H-Index: 101
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We propose an approach to extend the isogeometric analysis (IGA) method to solve material interface problems. The development is carried out through incorporating the advantages of the extended finite element method into the standard IGA approach for solving problems with discontinuities. By applying both the XIGA and IGA methods to solve Poisson's equation problem containing weak discontinuities, we demonstrate that the XIGA achieves the optimal convergence rate, whereas the IGA only converges ...
#2Arman Afshar(UT: University of Tehran)H-Index: 6
Last. S. Mohammdi(UT: University of Tehran)H-Index: 1
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Abstract The extended isogeometric analysis method (XIGA) is further developed to study fracture of homogeneous and inhomogeneous materials under mechanical and thermo-mechanical loadings. The domain of the problem is discretized by the knot spans of the isogeometric analysis (IGA) and the same basis functions used for constructing the geometry are employed to discretize the solution. In addition, crack face discontinuity and tip enrichment functions of the extended finite element method (XFEM) ...
Last. Sohichi Hirose(TITech: Tokyo Institute of Technology)H-Index: 15
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Abstract This paper presents a novel approach based on isogeometric analysis (IGA) and a simple first-order shear deformation plate theory (S-FSDT) for geometrically nonlinear analysis of homogeneous and non-homogeneous functionally graded plates. Owing to many advantages such as (a) the S-FSDT is free of shear-locking, (b) less one unknown for the S-FSDT as compared with the conventional FSDT, (c) the awkward C 1 continuity required for the generalized displacements is treated straightforwardly...
#1Indra Vir Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 31
#2G. Bhardwaj(IITR: Indian Institute of Technology Roorkee)H-Index: 12
Last. B.K. Mishra(IITR: Indian Institute of Technology Roorkee)H-Index: 27
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In this paper, a new criterion is proposed for the modeling multiple discontinuities i.e. crack, hole and inclusion passing through an element by XIGA. The modeling of multiple discontinuities passing through an element is done by imposing the additional degrees of freedom at the control points lying inside the influence of elements intersected by the discontinuities. In XIGA, the crack faces are modeled by discontinuous Heaviside jump functions, whereas the singularity in stress field at the cr...
#1G. Bhardwaj(IITR: Indian Institute of Technology Roorkee)H-Index: 12
#2Indra Vir Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 31
Last. B.K. Mishra(IITR: Indian Institute of Technology Roorkee)H-Index: 27
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Abstract In this work, extended isogeometric analysis (XIGA) is employed to compute the fatigue life of interfacial edge cracked functionally graded materials (FGMs). The effect of multiple defects (holes, inclusions and minor cracks) on the fatigue life of the interfacial cracked FGM plate is evaluated by XIGA. The bottom layer of the bi-layered plate is made of aluminum alloy while the upper one is made of FGM. The gradation in FGM layer is taken from left to right with 100% aluminum alloy on ...
Last. Timon Rabczuk(Bauhaus University, Weimar)H-Index: 101
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Fracture analysis of orthotropic cracked media is investigated by applying the recently developed extended isogeometric analysis (XIGA) (Ghorashi et al., 2012) using the T-spline basis functions. The signed distance function and orthotropic crack tip enrichment functions are adopted for extrinsically enriching the conventional isogeometric analysis approximation for representation of strong discontinuity and reproducing the stress singular field around a crack tip, respectively. Moreover, by app...
#1S.Z. Feng(HEBUT: Hebei University of Technology)H-Index: 2
#2Xu Han(HEBUT: Hebei University of Technology)H-Index: 61
Last. Atilla Incecik(University of Strathclyde)H-Index: 28
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Abstract null null An effective approach is proposed to predict the remaining fatigue life (RFL) of structures with stochastic parameters. The extended finite element method (XFEM) was firstly used to produce a large amount of datasets associated with structural responses and RFL. Then, a RFL prediction model was developed using the ensemble learning algorithm, which employed multiple machine-learning algorithms to learn useful degradation patterns of the structures from the XFEM datasets. Sever...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract null null Limit analysis can be used to directly calculate the ultimate load of structures without considering cumbersome elastic–plastic analysis. We present an adaptive mesh refinement strategy by mean of extended isogeometric analysis (XIGA) in association with second-order cone programming (SOCP) for kinematic limit analysis of hole and inclusion problems. The location of hole and inclusion can be captured by level set function without regard for its interfaces. The local refined no...
This paper presents the numerical simulation of permeable, semi-permeable and impermeable crack interaction study in 2D piezoelectric domains using an element-free Galerkin method (EFGM). The elect...
Last. Atilla Incecik(University of Strathclyde)H-Index: 28
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Abstract In this work, we proposed a novel approach for the prediction of residual useful life (RUL) of structures through appropriately combining the phase field method and deep-learning. In this new approach, the phase field method is firstly utilized to obtain the structural responses of crack growth, which are further preserved as images. Then, the convolutional neural network (CNN) is constructed to establish a predictive model . The proposed approach is a hybrid model of both physical and ...
Abstract The thermo-elastic analysis of thermally induced crack in functionally graded materials (FGMs) is performed using extended isogeometric analysis (XIGA). For the study, two types of cracks, i.e., adiabatic and isothermal, are considered in the FGM body. The suitable enrichment functions are employed to capture the discontinuity (i.e., displacements and temperature) along the crack face and singular fields around the crack tip. The material property gradation in FGM (composed of aluminum ...
Last. Saeid Ghouli(IUST: Iran University of Science and Technology)H-Index: 5
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This paper reviews crack tip asymptotic fields in generic plane anisotropic media, rigorously categorising about 400 studies devoted to the determination of the asymptote coefficients, also referred to as crack tip parameters. These studies cover a broad spectrum of methodologies focused on determining crack tip parameters in anisotropic materials, from analytical, numerical and experimental perspectives, conducted over the last six decades. Brief descriptions are given for a selected number of ...
#1Hongjun Yu(HIT: Harbin Institute of Technology)H-Index: 15
#2Meinhard Kuna(Freiberg University of Mining and Technology)H-Index: 31
Abstract A critical overview of past research on the interaction integral (I-integral) method is presented. The I-integral is the two-state mutual energy release rate decided by a designable auxiliary field and the actual field. Due to the designability of the auxiliary field, the I-integral has been used extensively in extracting the individual stress intensity factors (SIFs) and the T-stress of a crack in single materials or at a bi-material interface. The practical implementation of the I-int...
Last. Sachin D. Daxini(Gujarat Technological University)H-Index: 4
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Abstract This review presents developments in structural shape optimization post 2000 from perspective of numerical analysis techniques. Traditional shape optimization with FEM has undergone considerable transformation as developments in CAD, numerical analysis techniques and optimization algorithms have contributed significantly in improving it. Mesh dependency and inconsistent description of the geometry for design and analysis models remained major challenges in traditional FEM based shape op...
#1S.K. Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 6
#2Indra Vir Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 31
Abstract In this work, we present an extended isogeometric analysis (XIGA) for cracked functionally graded magneto-electro-elastic (FGMEE) material. The material properties inside the FGMEE domain vary exponentially. An electrically and magnetically impermeable crack in the FGMEE domain is modeled by adding appropriate enrichment functions into the isogeometric analysis (IGA) approximation. Heaviside function is utilized to model the displacement, electric, and magnetic potential along the crack...
