Shantanu S. Mulay

Bio: Shantanu S. Mulay is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Finite element method & Damage mechanics. The author has an hindex of 8, co-authored 27 publications receiving 224 citations. Previous affiliations of Shantanu S. Mulay include Nanyang Technological University & University of Liège.

Meshless Methods and Their Numerical Properties

Abstract: Introduction Formulation of Classical Meshless Methods Introduction Fundamentals of Meshless Methods Common Steps of Meshless Method Classical Meshless Methods Summary Recent Development of Meshless Methods Introduction Hermite-Cloud Method Point Weighted Least-Squares Method Local Kriging (LoKriging) Method Variation of Local Point Interpolation Method (vLPIM) Random Differential Quadrature (RDQ) Method Summary Convergence and Consistency Analyses Introduction to Convergence Analysis Development of Superconvergence Condition Convergence Analysis Application of RDQ Method for Solving Fixed-Fixed and Cantilever Microswitches under Nonlinear Electrostatic Loading Introduction to Consistency Analysis of RDQ Method Consistency Analysis of Locally Applied DQ Method Effect of Uniform and Cosine Distributions of Virtual Nodes on Convergence of RDQ Method Summary Stability Analyses Introduction Stability Analysis of First Order Wave Equation by RDQ Method Stability Analysis of Transient Heat Conduction Equation Stability Analysis of the Transverse Beam Deflection Equation Summary Adaptive Analysis Introduction Error Recovery Technique in ARDQ Method Adaptive RDQ Method Convergence Analysis in ARDQ Method Summary Engineering Applications Introduction Application of Meshless Methods to Microelectromechanical System Problems Application of Meshless Method in Submarine Engineering Application of RDQ Method for 2-D Simulation of pH-Sensitive Hydrogel Summary Appendix A: Derivation of Characteristic Polynomial PHI(Z) Appendix B: Definition of Reduced Polynomial PHI1(Z) Appendix C: Derivation of Discretization Equation by Taylor Series Appendix D: Derivation of Ratio of Successive Amplitude Reduction Values for Fixed-Fixed Beam using Explicit and Implicit Approaches Appendix E: Source Code Development Index

2D simulation of the deformation of pH-sensitive hydrogel by novel strong-form meshless random differential quadrature method

Abstract: The objective of presented work is to simulate the response of 2D hydrogel when subjected to the varying pH of buffer solution and initial fixed-charge concentration inside the hydrogel. The novelty of the work is that this is the first attempt to perform the 2D simulation of pH-responsive hydrogel by novel strong-form meshless method, such as random differential quadrature (RDQ) method. The analytical equations, derived for the hydrogel deformation in the x and y directions, are numerically verified by the square shaped hydrogel disc. The jumps in the distributions of ionic concentrations and electrical potential, across the interface between solution and hydrogel, are effectively captured by the RDQ method. A novel approach is proposed to correctly impose natural boundary conditions for non-uniform boundary. The effects of solution pH and initial fixed-charge concentration on the hydrogel swelling are also successfully investigated.

Multi-scale damage framework for textile composites: Application to plain woven composite

Abstract: A damage mechanics-based progressive damage analysis (PDA) of plain woven textile composite (PWTC) is performed in this work. The primary objective is to identify the micro-scale and meso-scale failure modes, and compute the ultimate strength of PWTC under in-plane loadings. Multi-scale PDA is performed on an equivalent cross-ply laminate (ECPL) model by maximum stress theory to predict the meso-scale failure modes of PWTC. The damaged stiffness is computed by 3 different ways: 1) hypothesis of strain energy equivalence by proposed 4 t h order anisotropic damage tensor, 2) applying isotropic damage law, and 3) eliminating the stiffness terms. Novel multi-scale PDA approaches, applying Mori-Tanaka (MT) theory on ECPL model and on the quarter portion of representative volume element of PWTC, are performed to predict micro-scale failure modes. The macro-scale constitutive behaviour of PWTC is theoretically predicted and the corresponding strengths are computed. A user material (UMAT) subroutine is developed to validate the proposed constitutive behaviour of PWTC solving macro-scale boundary value problems in ABAQUS®. The PDA simulation results of 3D PWTC bar model are found to be reasonably matching with the in-house experiments.

Multiscale modelling framework for the fracture of thin brittle polycrystalline films: application to polysilicon

Abstract: Micro-electro-mechanical systems (MEMS) made of polycrystalline silicon are widely used in several engineering fields. The fracture properties of polycrystalline silicon directly affect their reliability. The effect of the orientation of grains on the fracture behaviour of polycrystalline silicon is investigated out of the several factors. This is achieved, firstly, by identifying the statistical variation of the fracture strength and critical strain energy release rate, at the nanoscopic scale, over a thin freestanding polycrystalline silicon film having mesoscopic scale dimensions. The fracture stress and strain at the mesoscopic level are found to be closely matching with uniaxial tension experimental results. Secondly, the polycrystalline silicon film is considered at the continuum MEMS scale, and its fracture behaviour is studied by incorporating the nanoscopic scale effect of grain orientation. The entire modelling and simulation of the thin film is achieved by combining the discontinuous Galerkin method and extrinsic cohesive law describing the fracture process.

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Mechanics of composite materials

Abstract: INTRODUCTION TO COMPOSITE MATERIALS Chapter Objectives Introduction Classi?cation Recycling Fiber-Reinforced Composites Mechanics Terminology Summary Key Terms Exercise Set References MACROMECHANICAL ANALYSIS OF A LAMINA Chapter Objectives Introduction Review of De?nitions Hooke's Law for Different Types of Materials Hooke's Law for a Two-Dimensional Unidirectional Lamina Hooke's Law for a Two-Dimensional Angle Lamina Engineering Constants of an Angle Lamina Invariant Form of Stiffness and Compliance Matrices for an Angle Lamina Strength Failure Theories of an Angle Lamina Hygrothermal Stresses and Strains in a Lamina Summary Key Terms Exercise Set References APPENDIX A: MATRIX ALGEBRA Key Terms APPENDIX B: TRANSFORMATION OF STRESSES AND STRAINS Transformation of Stress Transformation of Strains Key Terms MICROMECHANICAL ANALYSIS OF A LAMINA Chapter Objectives Introduction Volume and Mass Fractions, Density, and Void Content Evaluation of the Four Elastic Moduli Ultimate Strengths of a Unidirectional Lamina Coefficients of Thermal Expansion Coefficients of Moisture Expansion Summary Key Terms Exercise Set References MACROMECHANICAL ANALYSIS OF LAMINATES Chapter Objectives Introduction Laminate Code Stress-Strain Relations for a Laminate In-Plane and Flexural Modulus of a Laminate Hygrothermal Effects in a Laminate Summary Key Terms Exercise Set References FAILURE, ANALYSIS, AND DESIGN OF LAMINATES Chapter Objectives Introduction Special Cases of Laminates Failure Criterion for a Laminate Design of a Laminated Composite Other Mechanical Design Issues Summary Key Terms Exercise Set References BENDING OF BEAMS Chapter Objectives Introduction Symmetric Beams Nonsymmetric Beams Summary Key Terms Exercise Set References INDEX

Advances in Mechanics of Soft Materials: A Review of Large Deformation Behavior of Hydrogels

Abstract: Hydrogels possess magnificent properties which may be harnessed for novel applications. However, this is not achievable if the mechanical behaviors of hydrogels are not well understood. This paper aims to provide the reader with a bird's eye view of the mechanics of hydrogels, in particular the theories associated with deformation of hydrogels, the phenomena that are commonly observed, and recent developments in applications of hydrogels. Besides theoretical analyses and experimental observations, another feature of this paper is to provide an overview of how mechanics can be applied.

Dynamic pull-in of parallel plate and torsional electrostatic MEMS actuators.

Abstract: An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.