Abstract In this paper, an extended isogeometric analysis (XIGA) is presented to model the crack in functionally graded piezoelectric materials (FGPMs). The material properties of functionally graded piezoelectric material (FGPM) vary in an exponential manner along the length of the domain. To model a crack in the FGPM, the isogeometric analysis (IGA) approximation is enriched with the Heaviside and crack tip enrichment functions. Conventional four-fold enrichment functions of isotropic materials are employed to capture the crack tip singularity. To determine the fracture parameters, the domain form of electromechanical interaction integral is used. The accuracy of the proposed XIGA approach is highlighted by validating the several cracked homogeneous and functionally graded piezoelectric material against the analytical/reference solution available in the literature. Several example problems of cracked FGPM domain are solved by XIGA. The influence of material non-homogeneity parameter, loading combination parameter and crack length are examined on the stress intensity factors (SIFs) and electrical displacement intensity factor (EDIF).
#1Subrato Sarkar(IITR: Indian Institute of Technology Roorkee)H-Index: 3
#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 the present work, adaptive h-refinement schemes are developed for the localizing gradient damage method. In general, the existing adaptive refinement schemes have been developed using the bilinear quadrilateral (Q4) elements for the weakly coupled systems such as XFEM and Phase field method. In contrast to this, the presently developed refinement schemes are designed for simultaneous refinement of the strongly coupled biquadratic serendipity (Q8) and Q4 elements, which is a typical r...
Abstract A generalized higher-order shear deformation theory (GHSDT) along with extended isogeometric analysis (XIGA) is presented for the analysis of cracked functionally graded material (FGM) plates. The material properties of the FGM vary exponentially along the thickness of the plate. The GHSDT ensures a traction-free boundary conditions at the surfaces of the plate without a need of shear correction factor (SCF). To model a crack, the isogeometric analysis (IGA) approximation is enriched wi...
Abstract In this work, we demonstrate the application of PHT-splines for time-harmonic acoustic problems, modeled by the Helmholtz equation. Solutions of the Helmholtz equation have two features: global oscillations associated with the wave number and local gradients caused by geometrical irregularities. We show that after a sufficient number of degrees of freedom is used to approximate global oscillations, adaptive refinement can capture local features of the solution. We compare residual-based...
#1Atul Kumar Sharma(IITR: Indian Institute of Technology Roorkee)H-Index: 7
#2M. M. Joglekar(IITR: Indian Institute of Technology Roorkee)H-Index: 13
Abstract This paper reports a finite element based numerical framework for simulating the electromechanical behavior of nonlinear anisotropic dielectric elastomer actuators at finite strains. Based on the existing models for incompressible anisotropic neo-Hookean hyperelastic solids and ideal dielectric elastomers, a theory of anisotropic dielectric elastomers is outlined. The analytical expressions are derived for the tangent moduli of the anisotropic materials. A computationally efficient stag...
#1V.B. Pandey(IITR: Indian Institute of Technology Roorkee)H-Index: 4
#2Indra Vir Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 31
Last. Vikas Kumar(DMRL: Defence Metallurgical Research Laboratory)H-Index: 14
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Abstract In this paper, we have developed a continuum damage mechanics (CDM) based methodology for high cycle fatigue crack growth simulations. A fatigue damage law is proposed and implemented in the framework of extended finite element method (XFEM). A new criterion is proposed based on damage evolution to identify the appropriate definition of stress triaxiality for acquiring the constraint effect on the stress state correctly. Few mesh regularization schemes are also employed for reducing the...
#1Manish Kumar(IITR: Indian Institute of Technology Roorkee)H-Index: 5
#2V.B. Pandey(IITR: Indian Institute of Technology Roorkee)H-Index: 4
Last. Vikas Kumar(DMRL: Defence Metallurgical Research Laboratory)H-Index: 14
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Abstract In this paper, a turbine disc of an aero-engine having a macro crack under creep loading is studied to predict the creep crack growth. Extended finite element method (XFEM) is used as it does not require conformal meshing and remeshing due to change in the topology during crack growth. The elasto-plastic behavior of the material is modelled by Ramberg-Osgood model and von-Mises yield criterion. The creep behavior is modelled by coupling of spatial and temporal dimensions to capture the ...
Abstract The stress intensity factors and the electrical displacement intensity factor for functionally graded piezoelectric materials (FGPMs) are influenced by: (a) the spatial variation of the mechanical property and (b) the electrical and mechanical boundary conditions. In this work, a semi-analytical technique is proposed to study the fracture parameters of FGPMs subjected to far field traction and electrical boundary conditions. A scaled boundary finite element formulation for the analysis ...
Abstract This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner–Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field approximaTion (GIFT) framework, which may be seen as a generalization of the Iso-Geometric Analysis (IGA). Within the GIFT framework, we describe the geometry of the structure exactly with NURBS (Non-Uniform Rational B-Splines), whilst independently employing P...
#1S.K. Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 6
#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, Bezier extraction based extended isogeometric analysis (XIGA) has been performed for three-dimensional (3-D) crack simulations in linear elastic materials. The Bezier extraction represent the original NURBS basis functions in terms of Bernstein shape functions defined over C 0 continuous isogeometric Bezier elements, and provides an element wise data structure of NURBS which makes the implementation similar to extended finite element method (XFEM). A crack in the domain is...
Abstract In this work, an extended isogeometric analysis (XIGA) is used for the analysis of through-thickness crack in a homogeneous and isotropic plate. In isogeometric analysis (IGA), non-uniform rational B-splines (NURBS) are used as a basis function. The plate kinematics is modelled by Reddy’s higher-order shear deformation theory (HSDT). The C 1 continuity requirement of HSDT can be easily fulfilled by the NURBS basis functions. In order to obtain the plate fracture parameters (moment inten...
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...
#1Srinivasu Chadaram(Institute of Infrastructure Technology Research and Management)H-Index: 1
#2Saurabh Yadav(Institute of Infrastructure Technology Research and Management)H-Index: 18
Abstract null null The effect of poling direction and thermal fracture analysis of penny-shaped crack (PSC) in piezoelectric material (PM) exposed to a uniform temperature and steady-state heat flow is presented using the XFEM approach. The intrinsic coupling, thermo-electro-mechanical under thermal shocks are studied and thermal stress intensity factors (TSIFs), and electrical displacement intensity factors (EDIF) are evaluated using the strain energy-based thermal interaction integral. The dis...
CNT/Graphene reinforced composites due to their exceptional mechanical, electrical, thermal, and optical characteristics that have attracted the scientific community working in the area of material development. In protraction, this review work on fracture analysis of CNT/Graphene reinforced composites is summarized from an exponentially growing literature inclusive of fabrication methods and present and potential applications. Owing to these composites' enormous structural applications, the numb...
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 ...
#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...
#1S. S. Durga Rao(Indian Institute of Technology Madras)H-Index: 1
#2Sethuraman Raju(Indian Institute of Technology Madras)H-Index: 2
Abstract Ill conditioning of system matrices is one of the drawbacks of Generalized/eXtended IsoGeometric Analysis (GIGA/XIGA), which results in increase in computational cost in the case of iterative solvers or erroneous results in the case of direct solvers. Linear dependency between the basis functions which can be measured in terms of smallest angle among all the bases is one of the attributes of ill conditioning in XIGA. In the present study, a simplified method to find the smallest angle a...
In this work, the extended isogeometric analysis (XIGA) is presented for the analysis of cracks in elastic material subjected to thermal, mechanical, and thermo-mechanical loading. The comparative ...
#1V.B. Pandey(IITR: Indian Institute of Technology Roorkee)H-Index: 4
#2S. S. Samant(IITR: Indian Institute of Technology Roorkee)H-Index: 4
Last. B.K. Mishra(IITR: Indian Institute of Technology Roorkee)H-Index: 27
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Abstract An improved continuum damage mechanics (CDM) and extended finite element method (XFEM) methodology is proposed to consider the effect of crack tip constraints on the fatigue crack growth (FCG) behavior. Several FCG experiments are conducted on compact tension (CT), single edge notch bending (SENB) and middle tension (MT) specimens prepared from modified 9Cr-1Mo steel. Combined CDM-XFEM methodology is improved to capture the crack tip constraints effect. Experimental and simulated FCG li...
