Kuldeep Sharma
@nituk.ac.in
Assistant Professor (Grade-I)
National Institute of Technology Uttarakhand
I did my PhD from the Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand in the year 2012. My research interests lie primarily in the field of advanced computational techniques for solving partial differential equations with applications in solid mechanics problems such as FEM, XFEM, Meshfree Methods, Distributed Dislocation Method, Numerical Solution of Singular Integral Equations, Riemann-Hilbert Problems and Fracture in Smart Materials.
EDUCATION
PhD (Mathematics), Indian Institute of Technology Roorkee, Uttarakhand, India
RESEARCH INTERESTS
Applied Mathematics, Computational Mechanics
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Ashish Kumar, Kuldeep Sharma, and Tinh Quoc Bui
Elsevier BV
Ashish Kumar, Kuldeep Sharma, and Tinh Quoc Bui
Wiley
AbstractThis paper presents the analytical closed‐form solutions of moving two equal collinear semipermeable cracks in magneto‐electro‐elastic material considering the strip electric‐magnetic polarization saturation (EMPS) model. To simulate the dynamic/moving cracks problem, two equal collinear Yoffe type cracks moving with a constant subsonic velocity along the plane of the cracks is considered. The problem is solved by considering semipermeable crack face conditions and under the in‐plane electro‐magnetic‐mechanical loading. Applying distributed dislocation technique and symmetry of the collinear cracks, the problem is reduced into simultaneous singular integral equations which have been solved in closed form expressions using finite Hilbert approach. The explicit expressions for dynamic distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), and local stress intensity factors (LSIFs) are evaluated for both the cases of the EMPS model (magnetic zone is smaller or greater than electric zone). For evaluation of inner and outer electric and magnetic zone lengths (MZLs), an iterative approach is applied to solve the developed two non‐linear equations. Also, to implement the semipermeable crack‐face conditions, a bisection iterative method has been applied. Based on the developed closed form solutions, numerical studies are presented for standard fracture parameters with respect to crack propagation velocity, electrical loading and inter‐crack space distance. This study shows that electric displacement and magnetic induction defined over the crack‐surface for semipermeable conditions decrease whereas the numerical values of saturated zone lengths, COD, COP, COI, and LSIFs increase with increasing crack propagation velocity. Moreover, for both static and dynamic cracks problems, the significant crack‐interaction effects have been observed on all the studied fracture parameters except the crack‐face conditions.
Kuldeep Sharma, Sandeep Singh, and Tinh Quoc Bui
Wiley
AbstractIn this paper, we present the distributed dislocation technique (DDT) based numerical algorithms to study the generalized strip saturated (GSS) models for two equal collinear cracks in 2‐D finite and infinite piezoelectric media. Numerical studies for particular cases such as linear, quadratic and cubic strip saturated models are simulated by considering their equivalent forms based on the principle of superposition. Two equal collinear cracks problem and its particular case of coalesced zones are considered in 2‐D semipermeable piezoelectric media under arbitrary poling direction and in‐plane electromechanical loadings. The results of saturated zone lengths (inner and outer) and local stress intensity factors (at inner and outer tips) are evaluated numerically for infinite and finite domain problems. The results of infinite domain obtained using DDT are compared with the reference analytical solutions. A good agreement of the results shows the efficacy of the proposed algorithms based on DDT for solving GSS two equal collinear cracks problems in 2‐D finite/infinite piezoelectric media.
Rajalaxmi Rath and Kuldeep Sharma
Springer Nature Singapore
Sandeep Singh, Kuldeep Sharma, and Tinh Quoc Bui
Elsevier BV
Sandeep Singh and Kuldeep Sharma
IOP Publishing
Abstract Complex variable technique and extended Stroh formalism approach are applied to develop the closed-form solutions for mode-III quadratically varying polarization saturation (PS) model in an infinite piezoelectric media. A semipermeable centre crack problem is considered for study under the influence of out of plane far-field mechanical loading and in-plane electrical displacement loading. Similar to PS model, the electrical yielding zones or saturated zones are considered just infront of the crack-tips in the form of a strip. But in place of constant PS condition imposed on yielding zones, the quadratically varying PS condition is considered for study. Mathematically, this problem reduces into simultaneous non-homogeneous Riemann-Hilbert problems which are solved by finding the solutions of involved singular integrals. Hence, some standard fracture parameters are derived in explicit forms such as saturated zone lengths, crack sliding displacement, crack potential drop and local stress intensity factor. Also, the comparative studies for quadratically varying PS model and PS model are presented graphically.
Sandeep Singh and Kuldeep Sharma
IOS Press
The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters.
Kuldeep Sharma and Sandeep Singh
Springer Singapore
Sandeep Singh and Kuldeep Sharma
AIP Publishing
Analytical solution for mode-III linearly varying polarization saturation (PS) model in semipermeable piezoelectric me- dia is presented. An infinite arbitrary polarized piezoelectric domain weakened by a center crack is considered for the study based on linearly varying polarization saturation model. For the analysis, an out of plane mechanical and in-plane electric displacement loadings are applied on the boundaries of the infinite domain. After mathematical formulation using complex variable and ex- tended Stroh's formalism approach, the problem is reduced into simultaneous non-homogeneous Riemann-Hilbert (R-H) problems in terms of complex variable functions. Explicit solutions for fracture parameters such as saturated zone length, crack sliding dis- placement (CSD), crack opening potential (COP), local stress intensity factor (LSIF), electric displacement intensity factor (EDIF) and normalize energy release rate (G∗) are derived after obtaining the solution for the R-H problems.
Sandeep Singh, Kuldeep Sharma, and Tinh Quoc Bui
Springer Science and Business Media LLC
Sandeep Singh, Kuldeep Sharma, and R. R. Bhargava
Wiley
An analytical solution and study is presented for two equal collinear cracks in 2‐D semipermeable piezoelectric media based on modified strip saturation models. The constant saturated condition defined in strip saturation model is modified here by considering the symmetric and polynomial varying saturation conditions. These proposed saturated conditions are multiplicative of saturated electric displacement value and polynomial (constant to cubic order) of a variable defined as ratio of distance of a point on saturated zone length to the extended half‐crack length. Moreover, these are interpolated on the basis of possible saturated values near the crack‐tips and zone tips. To present the analytical study, a problem of two cracks of equal length situated in series is considered in 2‐D arbitrary polarized infinite piezoelectric domain subjected to semipermeable crack‐face and electromechanical loading conditions. Applying the extended Stroh formalism and complex variable approach, these problems are mathematically modeled into non‐homogeneous Riemann Hilbert problems in terms of unknown complex functions representing stress and electric displacement components at any point within the domain. Using Muskhelishvili [1] and Collin's [2] mathematical techniques, these complex functions are obtained from the developed non‐homogeneous Riemann Hilbert problems. Hence, the explicit expressions for saturated zone lengths (inner and outer), crack opening potentials (COPs), crack opening displacements (CODs) and local stress intensity factors (LSIFs) are obtained. Further, the impact of polynomial varying saturated conditions is highlighted on these fracture parameters with respect to inter crack space distance, crack‐face conditions, polarization angle by presenting the numerical applications in infinite 2‐D PZT‐4 media.
S. Singh, K. Sharma, and R. R. Bhargava
Springer Science and Business Media LLC
A. Jha, V. Kukshal, A. Sharma, and K. Sharma
Author(s)
This Paper combines the Dugdale’s Approach with Extended finite element method (XFEM) in order to estimate the Plastic zone length (PZL) for a straight edge cracked plate (SECP) under uniaxial tensile loading condition. Dugdale utilized a different approach to evaluate the PZL by nullifying the effect of singularity at the tip of the virtually extended crack by the applying a uniform pressure which is equal to the yielding stress. XFEM is utilized for analyzing SECP as it is more efficient and accurate as compared to other conventional numerical tools. In XFEM, crack can be extended without any re-meshing because elements near crack interface need not to conform the crack geometry.PZL for SECP is evaluated for crack length, a, varying in the range of 0.01 to 0.05 (m) in steps of 0.01 and load intensity (σ0/Y) ranging from 0.1 to 0.5 in steps of 0.1. Crack Position (h/H) is also varied ranging from 0 to 0.8 in step of 0.2 in order to analyse its effect on PZL. MATLAB is employed for Extended Finite element analysis of SECP under Plane stress condition. Four node Quadrilateral elementsare used for extended finite element analysis. The numerical results are validated by the experimental results from the available literature.This Paper combines the Dugdale’s Approach with Extended finite element method (XFEM) in order to estimate the Plastic zone length (PZL) for a straight edge cracked plate (SECP) under uniaxial tensile loading condition. Dugdale utilized a different approach to evaluate the PZL by nullifying the effect of singularity at the tip of the virtually extended crack by the applying a uniform pressure which is equal to the yielding stress. XFEM is utilized for analyzing SECP as it is more efficient and accurate as compared to other conventional numerical tools. In XFEM, crack can be extended without any re-meshing because elements near crack interface need not to conform the crack geometry.PZL for SECP is evaluated for crack length, a, varying in the range of 0.01 to 0.05 (m) in steps of 0.01 and load intensity (σ0/Y) ranging from 0.1 to 0.5 in steps of 0.1. Crack Position (h/H) is also varied ranging from 0 to 0.8 in step of 0.2 in order to analyse its effect on PZL. MATLAB is employed for Extended Finite element...
Kuldeep Sharma and Sandeep Singh
Springer Singapore
S. Singh, K. Sharma, and R. R. Bhargava
Springer Science and Business Media LLC
K. Sharma, T.Q. Bui, and Sandeep Singh
IOS Press
Kuldeep Sharma, Tinh Quoc Bui, R.R. Bhargava, Tiantang Yu, Jun Lei, and Sohichi Hirose
Elsevier BV
S. Bhattacharya, G. Pamnani, S. Sanyal, and K. Sharma
World Scientific Pub Co Pte Lt
Piezoelectric materials due to their electromechanical coupling characteristics are being widely used in actuators, sensor, transducers, etc. Considering wide application it is essential to accurately predict their fatigue and fracture under applied loading conditions. The present study deals with analysis of fatigue crack growth in piezoelectric material using the extended finite element method (XFEM). A pre-cracked rectangular plate with crack at its edge and center impermeable crack-face boundary conditions is considered for simulation. Fatigue crack growth is simulated using extended finite element method under plane strain condition and mechanical, combined (mechanical and electrical) cyclic loading. Stress intensity factors for mechanical and combined (mechanical and electrical cyclic loadings) have been evaluated by interaction integral approach using the asymptotic crack tip fields. Crack propagation criteria have been applied to predict propagation and finally the failure.
R.R. Bhargava and Kuldeep Sharma
IOS Press
The analytic solution for Griffith's crack in an infinite 2-D piezoelectric domain is obtained for arbitrary polarization direction. The analytical approach considered here is simple and different from the existing methodology (where the solutions are firstly obtained for an elliptical void and then degenerated to Griffith's crack solution). The obtained results have shown that intensity factors (IFs) are independent of the polarization direction for Griffith's crack in an infinite 2-D piezoelectric domain. The solution for a polarization perpendicular to the crack is also obtained and validated with existing results. The results of IFs are also obtained numerically using extended finite element method (X-FEM). It is observed that IFs for a finite specimen is polarization direction dependent.
K. Sharma, T.Q. Bui, Ch. Zhang, and R.R. Bhargava
Elsevier BV
R.R. Bhargava and Kuldeep Sharma
Elsevier BV
R. R. Bhargava and Kuldeep Sharma
Springer Science and Business Media LLC
R. R. Bhargava and Kuldeep Sharma
Springer Berlin Heidelberg
Rama R. Bhargava and Kuldeep Sharma
Trans Tech Publications, Ltd.
The numerical solution for an edge crack problem in a two-dimensional (2-D) finite piezoelectric media has been discussed using extended finite element method. The four-fold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors (IFs). The intensity factors as well as the mechanical energy release rate and the total energy release rate has been analyzed for different electro-mechanical boundary conditions. It is observed that the IFs results are coupled and contrary to analytic solution which shows uncoupled behaviour.
R.R. Bhargava and Kuldeep Sharma
Elsevier BV