Amirtham Rajagopal

• Ph.D. (Structural Mechanics)
• Professor (Associate) at Indian Institute of Technology Hyderabad

Zirconium (Zr) and its alloys are being used in nuclear reactor components because of their low neutron capture cross-section and good mechanical and corrosion properties. But hydrogen was identified as an embrittling agent, and the source of embrittlement was found to be hydride precipitate. The precipitation of hydrides affects the ductility and...

In this work, a phase-field modeling approach for hydrogen-induced brittle fracture is presented. The phase-field model for fracture is coupled with hydrogen diffusion. The diffusion of hydrogen depends on the concentration gradient and hydrostatic stress gradient. The reduction of fracture resistance (fracture toughness) is governed by the enhance...

Contrary to the second-order Phase field model (PFM) of fracture, fourth-order PFM provides a more precise representation of the crack surface by incorporating higher-order derivatives (curvature) of the phase-field order parameter in the so-called crack density functional. As a result, in a finite element setting, the weak form of the phase-field...

Materials such as elastomeric composites, and soft biological tissues are heterogeneous and anisotropic in nature due to the presence of reinforcements like, fibers, axons, and they undergo large deformations and exhibit nonlinear elastic behavior. To understand the load carrying capacity and fracture phenomena in such materials, a nonlocal phase f...

In this manuscript, a rate-sensitive plasticity-based damage model for concrete subjected to dynamic loads is presented. The developed rate-sensitive damage model incorporates the key experimental evidence related to strain rate and damage rate. With increasing strain rates, the model is able to predict a decrease in the rate of damage evolution du...

In this work, a nonlocal strain gradient model is developed for the buckling analysis of laminated nanocomposite plates. The nonlocal and strain gradient constitutive equations are invoked to reformulate the governing equations of classical plate theory and third-order shear deformation plate theory. The resulting governing equations are solved usi...

The main aim of the current study is to explore direction-dependent fracture initiation and propagation within an arbitrary anisotropic solid. In particular, the specific objective is to develop an anisotropic cohesive phase-field (PF) fracture model. In this model, weak and strong anisotropy is considered both in the strain energy and fracture ene...

Purpose This study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C ¹ basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance...

In the present work, flexural analysis of a thin to moderately thick FGM plate subjected to transverse loads have been studied using finite element method. The formulation is developed based on the First order Shear Deformation Theory (FSDT). The mechanical properties are assumed to vary continuously through the thickness of the plate and obey a po...

The main purpose of this work is to understand the structural characterization of reinforced concrete slabs under near-field and contact explosions using the developed rate-sensitive damage model. The model is developed based on the experimental observation to include the effects of strain rate and damage rate. It is observed that with increasing s...

Elastomers and composites made thereof have wide applications, e.g., in automobile, aerospace, and civil engineering. Predicting fracture in such materials is crucial for efficient design and optimum utilization. These materials are oftentimes hyperelastic and anisotropic in nature and in general subjected to mixed mode loading rather than merely p...

A two-dimensional constitutive model, which is based on micromechanical rotation of domains, is presented in this work to demonstrate the non-linear behavior of ferroelectric materials under different loading conditions. A temperature-dependent combined material model that incorporates both phases i.e., tetragonal and rhombohedral phases is embedde...

Confinement of reinforced concrete (RC) columns through external bonding (EB) of fibre-reinforced polymer (FRP) composite becomes less effective in non-circular sections. The effectiveness of FRP confinement reduces with an increase in the size of the cross-section. Hence, it is essential to develop an effective FRP strengthening technique for larg...

The mechanical response and the fracture phenomena in a composite system not only depend on the elastic and fracture properties of individual constituents but also on additional parameters such as fiber alignment, fiber volume fraction, interface properties and laminate layup. Fiber alignment is one such parameter that governs the design of the com...

In this note, the use of Eringen’s nonlocal theory for the analysis of functionally graded beams, plates, and shells is discussed. The properties of the nonlocal modulus and its dependence on the internal length scale are brought out. The use of Eringen’s nonlocal model with different nonlocal approaches is discussed with an evidence from the liter...

In this work, buckling analysis of nanoplates considering both nonlocal and surface stress effects is presented. The potential application of nanoplates can be found in microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). An analytical solution based on Navier’s method for simply supported boundary conditions is presented...

In this work, an extension of Eringens model for analysis of functionally graded nano plates used in MEMS (micro-electromechanical systems) devices will be presented. Rule of mixtures and Mori-Tanaka methods are adopted for through thickness homogenization of material properties. The role of nonlocal parameter together with the choice of homogeniza...

Soft tissues display highly non linear behaviour under various mechanical loads. Due to various diseases, injury or when exposed to supra physiological loads, soft tissues demonstrate a softening behaviour or damage. Continuum damage models coupled with continuum material models have been successful in mathematically predicting the damage in tissue...

The dynamic structural behaviour and failure mechanisms of the reinforced concrete (RC) slabs under the combined blast and impact loading is numerically evaluated using the software LS-DYNA. The developed material model for concrete includes the plasticity behaviour under dynamic loading. The developed model includes the modified equation of state...

A comparison of the two different approaches for modelling damage in material in an infinitesimal strain setting is studied. The first approach is the nonlocal gradient enhanced damage model where the damage variable is taken as an independent variable which will be determined based on the local strain measure. Here, the nonlocal integral form is a...

The phase field method uses a length scale parameter to regularize the discrete crack to a diffuse crack, which removes the numerical tracking of the discontinuities in the displacement. The displacement field is coupled with the phase field and both are solved as a sequentially coupled systems using staggered method. The phase field ϕ varies betwe...

The problem on determining the effective properties of mixed composites consisting of a piezoceramic matrix with metal inclusions and pores is investigated. Composites with microporosity and mesoporosity are compared. For microporous composites, two-level models of two-phase structures are used. At the microlevel, the effective properties of a piez...

Analysis of tensors in oblique Cartesian coordinate systems always requires the definition of a set of orthogonal covariant basis vectors called the Reciprocal basis. This increases the complexity of the analysis and hence makes the method cumbersome. In this work a novel method is presented to effectively carry out the various transformations of t...

Damage in soft biological tissues are a major domain of study as tissues may either undergo degradation with time or may experience in vivo failure during invasive procedures leading to a multitude of medical complications. Continuum damage models have been very successful recently to predict damage that can take place either due to fatigue loading...

Hybrid structures consisting of metal and composites can be applied to specific requirements of different applications. The computational modeling of composites is quite complex compared to homogeneous and isotropic materials like metals because of the heterogeneity introduced due to the presence of different phases such as matrix, fiber and matrix...

Phase field method is used to study the dynamic crack propagation and branching in a brittle materials. The phase-field method uses a length scale parameter to regularise the discrete crack to a diffuse crack. The coupled system containing displacement field and the phase-field is solved as sequentially coupled system using the staggered method. Th...

A new phase field model considering the interfacial damage for different configurations of a fiber reinforced composite is proposed and formulated. Crack and non local interface are considered to be diffused. A coupled traction separation law based on a potential function is adopted to represent the behavior of the interface. Anisotropy is introduc...

Nacre, a composite layer present in sea-shells, exhibits a remarkable combination of toughness, strength, and stiffness through its brick–mortar micro-structure, acting as a template for novel materials. Strength, one of nacre’s important properties is highly variable due to distribution of underlying material’s properties as well as various defect...

Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibres embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modelled by incorporating the strains experienced by the fibres. From histological studies on soft ti...

A thermodynamically consistent phase field formulation for modeling the interactions between interfacial damage and bulk brittle fracture is presented. A regularization scheme is considered for both the interface and the crack phase field. A coupled exponential cohesive zone law is adopted to model the interface which has the contributions of both...

In the present work, vibroacoustic (VA) characteristics, namely sound transmission loss (STL), overall sound pressure levels (OASPLs) of aircraft panels made up of aluminum, composites and fiber metal laminates (FML) are studied. The investigation involves modeling of aircraft panels using finite element method (FEM) for low frequency, Boundary Ele...

In this work, we present a nonlocal phase field model for damage in brittle materials. We define a non-conservative order parameter for representing the damage. The Helmholtz free energy functional of the Ginzburg-Landau type that incorporates a new degradation function for the elastic strain energy is considered. The hypothesis of strain equivalen...

A plasticity-based approach has been proposed for reinforced concrete (RC) subjected to impact and blast loading. The proposed approach includes a new failure surface together with modified descriptions related to equation of state, strain rate effect and damage taken from literature. These selective descriptions in numerical analysis have been fou...

An explosion near a building can cause catastrophic damage to the building’s external and internal structural frames, causing the collapse of the walls and even loss of life. Due to the threat from such extreme loading conditions, efforts have been made during the past three decades to study the behaviour of structural concrete subjected to blast l...

In the present work, flexural response of functionally graded plates subjected to transverse loads have been investigated using the meshless natural neighbor Galerkin method (NNGM). The plate formulation has been developed based on the Reddy’s (Mechanics of laminated composite plates and shells: theory and analysis, 2nd edition, CRC Press, Boca Rat...

6 A plasticity based approach has been proposed for studying the dynamic performance 7 of reinforced concrete (RC) slabs subjected to impact and blast loading. The proposed 8 approach includes a new failure surface together with modified descriptions related to 9 equation of state, strain rate effect and damage taken from literature. These selectiv...

Purpose This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the...

In this work our objective is to understand the failure behaviour of unreinforced masonry under in-plane cyclic loading. For this purpose we proposed a plasticity based interface model consists of a single yield surface criteria which is a direct extension of Mohr-Coulomb criteria with a tension cut and compression cap and a back stress vector is i...

In this work, we propose a hybrid phase field model for the brittle fracture analysis of thick plates subjected to transient dynamic loads. Shear deformation effects which play important role on the behavior of thick plates are captured by using Reddy’s third-order shear deformation theory. The proposed model preserves the linearity of the elastic...

Hybrid phase field approach for thick plates

Recently developed phase field models of fracture require a diffusive crack representation based on an introduction of a crack phase field. We outline a thermodynamically consistent framework for phase field models of crack propagation in elastic solids, develop incremental variational principles. In this work, the numerical implementation of the p...

A new plasticity based material model has been proposed in the present work for concrete subjected to dynamic loads. The model has then been used for blast analysis of Reinforced Concrete slabs. The model has three parts; first the equation of state is described by a pressure versus volumetric strain relationship, second a method for defining damag...

In this work, nonlocal transient dynamic analysis of laminated composite plates using Reddy’s third-order shear deformation theory (TSDT) and Eringen’s nonlocality is presented. The nonlocal governing equations of TSDT are derived employing the Eringen’s stress-gradient constitutive model considering the dynamic effects. Displacement finite element...

In this work, we propose a thermodynamically consistent phase field model for the brittle fracture analysis of thick plates. A hybrid model, which is fast and accurate, is proposed for the phase field modeling of fracture in thick plates. Reddy's third-order shear deformation theory (TSDT) has been employed to capture the transverse shear deformati...

In this work nonlocal buckling analysis of laminated composite plates considering surface stress effects is presented. For computation of critical uniaxial and biaxial buckling loads, both approximate solutions and finite element solutions are presented. Approximate solutions based on Navier's method for simply supported boundary conditions and bas...

In this study, a locking‐free n‐sided C1 polygonal finite element is presented for nonlinear analysis of laminated plates. The plate kinematics is based on Reddy's third‐order shear deformation theory (TSDT) [1, 2]. The inplane displacements are approximated using barycentric form of Lagrange shape functions. The weak‐form Galerkin formulation base...

In this paper, natural neighbor Galerkin meshless method is employed for adaptive analysis of plates and laminates. The displacement field and strain field of plate are based on Reissner–Mindlin plate theory. The interpolation functions employed here were developed by Sibson and based on natural neighbor coordinates. An adaptive refinement strategy...

Functionally Graded Materials (FGM) are advanced class of engineering composites constituting of two or more distinct phase materials described by continuous and smooth varying composition of material properties in the required direction. In this work, the eect of material homogenization scheme on exural response of a thin to moderately thick FGM p...

Dynamic analysis of microbeams based on the modified strain gradient elasticity theory (MSGT) is carried out in this study. MSGT theory comprises additional material length scale parameters to effectively capture the size effect. Beams with fixed-fixed, simply supported and fixed-free boundary conditions are analysed. Additionally, frequency analys...

The chapter deals with the finite element modeling of the disk piezoelectric transducer with cymbal-shaped end-caps. Under radial oscillations of piezoceramic disk this transducer generates axial oscillations with large amplitude thanks to more flexible metal end-caps. One of the factors contributing to the efficiency of transformating radial displ...

The evolution of damage in laminated fiber reinforced composites is a complex phenomenon, which involves interaction of different modes of failure like fiber breakage, matrix cracking, fiber-matrix debonding and delamination. In the present work the effect of fiber volume fraction and different damage mechanisms such as fiber breakage, fiber-matrix...

In this work, we present the behaviour of laminated composite plates, subjected to a static bending load under the influence of varying value of material length scale parameters. Reddy’s (J Appl Mech 51:745, 1984 [1]) third order shear deformation theory (TSDT) is used, which describes the kinematics accurately. The geometric nonlinearity, which pr...

Functionally Graded Materials (FGM) are advanced class of engineering composites constituting of two or more distinct phase materials described by continuous and smooth varying composition of material properties in the required direction. In this work, the eect of material homogenization scheme on exural response of a thin to moderately thick FGM p...

In this work, nonlocal nonlinear analysis of functionally graded plates subjected to static loads is studied. The nonlocal nonlinear formulation is developed based on the third-order shear deformation theory (TSDT) of Reddy (1984, 2004). The von Kármán nonlinear strains are used and the governing equations of the TSDT are derived accounting for Eri...

In this paper, natural neighbor Galerkin meshless method is employed for adaptive analysis of plates and laminates. The displacement field and strain field of plate are based on Reissner–Mindlin plate theory. The interpolation functions employed here were developed by Sibson and based on natural neighbor coordinates. An adaptive refinement strategy...

In this work we present an implicit nonlocal gradient damage model. A scalar damage variable which is a function of monotonically increasing function of history parameter is introduced to account for damage. The nonlocal model accounts for spatial interaction of neighboring material element at different length scales. The history parameter accounti...

In this work, nonlocal nonlinear finite element analysis of laminated composite plates using Reddy's third-order shear deformation theory (TSDT) [1] and Eringen's nonlocality [2] is presented. The governing equations of third order shear deformation theory with the von Kármán strains are derived employing the Eringen's [2] stress-gradient constitu-...

Analytical and finite element studies on the behavior of Reinforced Concrete (RC) column elements strengthened using a hybrid Carbon Fiber Reinforced Polymer (CFRP) laminates and externally bonded fabric is explored in this study. The main objective of this study is to evaluate the effect of hybrid strengthening on the initial and post-cracking sti...

1 Abstract In the present work, the close similarity that exists between Mindlins strain gradient elasticity and Eringens nonlocal Integro differential model is explored. The methods are studied for one-dimensional examples. Through the proposed approach a relation between length scales of nonlocal-differential and gradient elasticity model is arri...

The study is devoted to the determination of the effective material properties of masonry based on its internal structure. Masonry is considered as a periodiccomposite consisting of bricks and mortar. According to the classical method of determining effective moduli for composites, in order to describe internal microstructure we consider a represen...

In this article, we present the nonlocal, nonlinear finite element formulations for the case of nonuniform rotating laminated nano cantilever beams using the Timoshenko beam theory. The surface stress effects are also taken into consideration. Nonlocal stress resultants are obtained by employing Eringen's nonlocal differential model. Geometric nonl...

In this work, we present an adaptive polygonal finite element method (Poly-FEM) for the analysis of two-dimensional plane elasticity problems. The generation of meshes consisting of n − sided polygonal finite elements is based on the generation of a centroidal Voronoi tessellation (CVT). An unstructured tessellation of a scattered point set, that m...

In this work an integrated approach has been proposed for the determination of the effective mechanical and temperature properties of thermoelastic periodic brick masonry wall with various porous structures. According to the classical method of determining effective moduli of composites, in order to describe internal micro- or macrostructure, we co...

In this contribution, we present a novel polygonal finite element method applied to hyperelastic analysis. For generating polygonal meshes in a bounded period of time we use the adaptive Delaunay tessellation (ADT) proposed by Constantinu et al \cite{Alexandru2008}. ADT is an unstructured hybrid tessellation of a scattered point set that minimally...

In this paper, we present the non-local nonlinear finite element formulations for the case of nonuni-form rotating laminated nano cantilever beams using the Timoshenko beam theory. The surface stress effects are also taken into consideration. Non-local stress resultants are obtained by employing Erin-gen's nonlocal differential model. Geometric non...

10 days GIAN course on FEM will be offered at IIT Hyderabad from 14-24 July 2016

Boundary value problems for a softening material suer from loss of uniqueness in the post-peak regime. Numerical solutions to such problems shows mesh dependency due to lack of internal length scale in the formulation. A regularization method which introduces a characteristic length is required to get mesh independent results. A second gradient mod...

In the present work, an r-h adaptive isogeometric analysis is proposed for plane elasticity problems. For performing the r-adaption, the control net is considered to be a network of springs with the individual spring stiffness values being proportional to the error estimated at the control points. While preserving the boundary control points, reloc...

Masonry is a heterogeneous anisotropic continuum, made up of the brick and mortar arranged in a periodic manner. Obtaining the effective elastic stiffness of the masonry structures has been a challenging task. In this study, the homogenization theory for periodic media is implemented in a very generic manner to derive the anisotropic global behavio...

In this paper, we present a non-local non-linear finite element formulation for the Timoshenko beam theory. The proposed formulation also takes into consideration the surface stress effects. Eringen׳s non-local differential model has been used to rewrite the non-local stress resultants in terms of non-local displacements. Geometric non-linearities...

In the present work, the numerical assesment of vibroacoustic (VA) performance of Fibre Metal Laminates (FML) with mid-plane center delamination is presented. A fluid structure interaction study has been done using Finite Element Method (FEM). Experimental validation is performed on aluminium panel for verifying the correctness of Finite Element id...

In this paper, we present a nonlocal nonlinear finite element formulation for the Timoshenko beam theory. The proposed formulation also takes into consideration the surface stress effects. Eringen's nonlocal differential model has been used to rewrite the nonlocal stress resultants in terms of nonlocal displacements. Geometric nonlinearities are ta...

In the present work, the geometrical nonlinear analysis of laminated composite plates is done using natural element method. The C1 natural neighbor interpolation function is implemented for geometric nonlinear analysis. The first order shear deformation plate theory is adopted for plate analysis. The geometric nonlinearity is based on the von Kármá...

In this work, a plasticity based composite interface model is proposed for failure analysis of unreinforced masonry. The hyperbolic composite interface model consists of a single surface yield criterion, which is a direct extension of Mohr-Coulomb criteria with cut in tension region and a cap in compression region. The inelastic behaviour includes...