Showing papers by "J. N. Reddy published in 2013"
TL;DR: In this article, a non-classical microbeam model incorporating the material length scale parameter was proposed to capture the size effect of the FG microbeams and the governing equations and the related boundary conditions were derived using Hamilton's principle.
424 citations
TL;DR: Based on the modified couple stress theory (MCST), a unified higher order beam theory which contains various beam theories as special cases is proposed for buckling of a functionally graded (FG) microbeam embedded in elastic Pasternak medium as mentioned in this paper.
194 citations
TL;DR: In this article, an analytical solution of a general third-order plate theory that accounts for the power-law distribution of two materials through thickness and microstructure-dependent size effects is presented.
151 citations
TL;DR: In this article, a modified couple stress theory and a meshless method are used to study the bending of simply supported laminated composite beams subjected to transverse loads, and the results show that the present model can capture the effects of the microstructure.
145 citations
01 Jan 2013
TL;DR: In this paper, the authors present a model of linearized elasticity and linearized viscoelasticity for heat transfer and stress measures, and show that linearised elasticity is equivalent to heat transfer.
Abstract: 1. Introduction 2. Vectors and tensors 3. Kinematics of continua 4. Stress measures 5. Conservation and balance laws 6. Constitutive equations 7. Linearized elasticity 8. Fluid mechanics and heat transfer 9. Linearized viscoelasticity.
126 citations
Journal Article•
TL;DR: In this article, the static analysis of functionally graded (FGM) and laminated doubly-curved shells and panels resting on nonlinear and linear elastic foundations using the Generalized Differential Quadrature (GDQ) method is considered.
Abstract: This work focuses on the static analysis of functionally graded (FGM) and laminated doubly-curved shells and panels resting on nonlinear and linear elastic foundations using the Generalized Differential Quadrature (GDQ) method. The First-order Shear Deformation Theory (FSDT) for the aforementioned moderately thick structural elements is considered. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Several types of shell structures such as doubly-curved shells (elliptic and hyperbolic hyperboloids), singly-curved (spherical, cylindrical and conical shells), and degenerate panels (rectangular plates) are considered in this paper. The main contribution of this paper is the application of the differential geometry within GDQ method to solve doubly-curved FGM shells resting on nonlinear elastic foundations. The linear Winkler-Pasternak elastic foundation has been considered as a special case of the nonlinear elastic foundation proposed herein. The discretization of the differential system by means of the GDQ technique leads to a standard nonlinear problem, and the Newton-Raphson scheme is used to obtain the solution. Two different four-parameter power-law distributions are considered for the ceramic volume fraction of each lamina. In order to show the accuracy of this methodology, numerical comparisons between the present formulation and finite element solutions are presented. Very good agreement is observed. Finally, new results are presented to show effects of various parameters of the nonlinear elastic foundation on the behavior of functionally graded and laminated doubly-curved shells and panels.
117 citations
TL;DR: In this article, the effect of nonlinearity, shear deformation, power-law index, microstructural length scale, and boundary conditions on the bending response of beams under mechanical loads are investigated.
113 citations
TL;DR: In this article, a non-classical third-order shear deformation plate model was developed using a modified couple stress theory and Hamilton's principle, which can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction.
Abstract: A non-classical third-order shear deformation plate model is developed using a modified couple stress theory and Hamilton’s principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation. This newly developed plate model contains one material length scale parameter and can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction. It is shown that the new third-order shear deformation plate model recovers the non-classical Reddy-Levinson beam model and Mindlin plate model based on the modified couple stress theory as special cases. Also, the current non-classical plate model reduces to the classical elasticity-based third-order shear deformation plate model when the material length scale parameter is taken to be zero. To illustrate the new model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new plate model are smaller than those predicted by its classical elasticity-based counterpart, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significant when the plate thickness is small, but they are diminishing with increasing plate thickness.
93 citations
TL;DR: A modified couple stress theory and a meshless method are used to study the bending of simply supported micro isotropic plates according to the first-order shear deformation plate theory, also known as the Mindlin plate theory.
85 citations
TL;DR: In this paper, a modified creep ductility exhaustion approach is employed to calculate the creep damage and stress state from micromechanics viewpoint, and numerical analyses of creep crack growth are conducted with a failure simulation technique.
81 citations
TL;DR: In this article, the authors developed the governing equations for a fully constrained finitely deforming hyperelastic Cosserat continuum where the directors are constrained to rotate with the body rotation.
Abstract: The aim of this paper is to develop the governing equations for a fully constrained finitely deforming hyperelastic Cosserat continuum where the directors are constrained to rotate with the body rotation. This is the generalization of small deformation couple stress theories and would be useful for developing mathematical models for an elastic material with embedded stiff short fibers or inclusions (e.g., materials with carbon nanotubes or nematic elastomers, cellular materials with oriented hard phases, open cell foams, and other similar materials), that account for certain longer range interactions. The theory is developed as a limiting case of a regular Cosserat elastic material where the directors are allowed to rotate freely by considering the case of a high “rotational mismatch energy”. The theory is developed using the formalism of Lagrangian mechanics, with the static case being based on Castigliano's first theorem. By considering the stretch U and the rotation R as additional independent variables and using the polar decomposition theorem as an additional constraint equation, we obtain the governing and as well as the boundary conditions for finite deformations. The resulting equations are further specialized for plane strain and axisymmetric finite deformations, deformations of beams and plates with small strain and moderate rotation, and for small deformation theories. We also show that the boundary conditions for this theory involve “surface tension” like terms due to the higher gradients in the strain energy function. For beams and plates, the rotational gradient dependent strain energy does not require additional variables (unlike Cosserat theories) and additional differential equations; nor do they raise the order of the differential equations, thus allowing us to include a material length scale dependent response at no extra “computational cost” even for finite deformation beam/plate theories
TL;DR: In this article, the authors studied the dynamic thermal postbuckling behavior of functionally graded cylindrical shells with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and applied actuator voltage.
Abstract: Dynamic thermal postbuckling behavior of functionally graded cylindrical shells with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and applied actuator voltage is studied. The shell material is graded across the thickness according to a power law. The material properties of the functionally graded cylindrical shells are considered to be temperature dependent. The theoretical formulations are based on the Sanders nonlinear kinematic relations, which account for the transverse shear strains, and the third-order shear deformation shell theory is employed. Hamilton's principle is used to derive the equations of motion governing piezoelectric FGM cylindrical shells. A finite difference approximation combined with the Runge-Kutta method is employed to predict the postbuckling equilibrium paths, and the dynamic buckling temperature difference is detected according to Budiansky's stability criterion. Numerical results are presented to demonstrate the effects of the applie...
TL;DR: In this article, the performance of the active constrained layer damping (ACLD) treatment for active control of thin laminated cylindrical shells conveying fluid has been investigated, and the constraining layer of the ACLD treatment has been considered to be made of vertically or obliquely reinforced 1-3 piezoelectric composite (PZC) materials.
01 Apr 2013
TL;DR: In this article, a beam theory for a small strain continuum model of thermoviscoelastic shape memory polymers (SMPs) is developed, where the elastic predictor is based on the solution to a beam-based boundary value problem while the dissipative corrector is entirely local (and hence can be parallelized) and is applied by considering the beam as a two or three dimensional body.
TL;DR: In this article, a locking-free curved beam finite element model was developed using coupled polynomial displacement field interpolations to eliminate curvature related locking effects in the out-of-plane deformation of Timoshenko and Euler-Bernoulli curved beam elements.
TL;DR: The results of this study indicate that the presence of an underlying permeability contrast may create a new contrast mechanism in the spatial and temporal distributions of the axial strains and the effective Poisson's ratios experienced by the tissue and as imaged by the corresponding elastograms.
Abstract: Elastography is a well-established imaging modality. While a number of studies aimed at evaluating the performance of elastographic techniques are retrievable in the literature, very little information is available on the effects that the presence of an underlying permeability contrast in the tissue may have on the resulting elastograms. Permeability is a fundamental tissue parameter, which characterizes the ease with which fluid can move within a tissue. This parameter plays a central role both biomechanically in the description of the temporal behavior of fluid-filled tissues and clinically in the development of a number of diagnostic and therapeutic modalities. In this paper, we present a simulation study that investigates selected elastographic image quality factors in nonhomogeneous materials, modeled as poroelastic media with different geometries and permeability contrasts. The results of this study indicate that the presence of an underlying permeability contrast may create a new contrast mechanism in the spatial and temporal distributions of the axial strains and the effective Poisson's ratios experienced by the tissue and as imaged by the corresponding elastograms. The effect of permeability on the elastographic image quality factors analyzed in this study was found to be a nonsymmetric function of the underlying mechanical contrast between background and target, the geometry of the material and the boundary conditions.
TL;DR: In this paper, the authors consider the development of constitutive theories in Eulerian description for compressible and incompressible ordered homogeneous and isotropic thermofluids in which the deviatoric Cauchy stress tensor and the heat vector are functions of density, temperature, temperature gradient, and the convected time derivatives of the strain tensors of up to a desired order.
Abstract: The paper considers developments of constitutive theories in Eulerian description for compressible as well as incompressible ordered homogeneous and isotropic thermofluids in which the deviatoric Cauchy stress tensor and the heat vector are functions of density, temperature, temperature gradient, and the convected time derivatives of the strain tensors of up to a desired order. The fluids described by these constitutive theories are called ordered thermofluids due to the fact that the constitutive theories for the deviatoric Cauchy stress tensor and heat vector are dependent on the convected time derivatives of the strain tensor up to a desired order, the highest order of the convected time derivative of the strain tensor in the argument tensors defines the ‘order of the fluid’. The admissibility requirement necessitates that the constitutive theories for the stress tensor and heat vector satisfy conservation laws, hence, in addition to conservation of mass, balance of momenta, and conservation of energy, the second law of thermodynamics, that is, Clausius–Duhem inequality must also be satisfied by the constitutive theories or be used in their derivations. If we decompose the total Cauchy stress tensor into equilibrium and deviatoric components, then Clausius–Duhem inequality and Helmholtz free energy density can be used to determine the equilibrium stress in terms of thermodynamic pressure for compressible fluids and in terms of mechanical pressure for incompressible fluids, but the second law of thermodynamics provides no mechanism for deriving the constitutive theories for the deviatoric Cauchy stress tensor. In the development of the constitutive theories in Eulerian description, the covariant and contravariant convected coordinate systems, and Jaumann measures are natural choices. Furthermore, the mathematical models for fluids require Eulerian description in which material point displacements are not measurable. This precludes the use of displacement gradients, that is, strain measures, in the development of the constitutive theories. It is shown that compatible conjugate pairs of convected time derivatives of the deviatoric Cauchy stress and strain measures in co-, contravariant, and Jaumann bases in conjunction with the theory of generators and invariants provide a general mathematical framework for the development of constitutive theories for ordered thermofluids in Eulerian description. This framework has a foundation based on the basic principles and axioms of continuum mechanics but the resulting constitutive theories for the deviatoric Cauchy stress tensor must satisfy the condition of positive work expanded, a requirement resulting from the entropy inequality. The paper presents a general theory of constitutive equations for ordered thermofluids which is then specialized, assuming first-order thermofluids, to obtain the commonly used constitutive theories for compressible and incompressible generalized Newtonian and Newtonian fluids. It is demonstrated that the constitutive theories for ordered thermofluids of all orders are indeed rate constitutive theories. We have intentionally used the term ‘thermofluids’ as opposed to ‘thermoviscous fluids’ due to the fact that the constitutive theories presented here describe a broader group of fluids than Newtonian and generalized Newtonian fluids that are commonly referred as thermoviscous fluids.
TL;DR: In this paper, the authors presented a general framework for rate constitutive theories for thermoviscoelastic solids with memory based on the physics and derivations that are consistent within the framework of continuum mechanics and thermodynamics.
Abstract: This paper presents ordered rate constitutive theories in Lagrangian description for compressible as well as incompressible homogeneous, isotropic thermoviscoelastic solid matter with memory in which the material derivative of order m of the deviatoric stress tensor and heat vector are functions of temperature, temperature gradient, time derivatives of the conjugate strain tensor up to any desired order n, and the material derivatives of up to order m−1 of the stress tensor. The thermoviscoelastic solids described by these theories are called ordered thermoviscoelastic solids with memory due to the fact that the constitutive theories are dependent on orders m and n of the material derivatives of the conjugate stress and strain tensors. The highest orders of the material derivative of the conjugate stress and strain tensors define the order of the thermoviscoelastic solid. The constitutive theories derived here show that the material for which these theories are applicable have fading memory. As is well known, the second law of thermodynamics must form the basis for deriving constitutive theories for all deforming matter (to ensure thermodynamic equilibrium during evolution), since the other conservation and balance laws are independent of the constitution of the matter. The entropy inequality expressed in terms of Helmholtz free energy density \({\Phi}\) does not provide a mechanism to derive a constitutive theory for the stress tensor when its argument tensors are stress and strain rates in addition to others. With the decomposition of the stress tensor into equilibrium and deviatoric stress tensors, the constitutive theory for the equilibrium stress tensor is deterministic from the entropy inequality. However, for the deviatoric stress tensor, the entropy inequality requires a set of inequalities to be satisfied but does not provide a mechanism for deriving a constitutive theory. In the present work, we utilize the theory of generators and invariants to derive rate constitutive theories for thermoviscoelastic solids with memory. This is based on axioms and principles of continuum mechanics. However, we keep in mind that these constitutive theories must satisfy the inequalities resulting from the second law of thermodynamics. The constitutive theories for heat vector q are derived: (i) strictly using conditions resulting from the entropy inequality; (ii) using the theory of generators and invariants with admissible argument tensors that are consistent with the stress tensor as well as the theories in which simplifying assumptions are employed which yield much simplified theories. It is shown that the rate theories presented here describe thermoviscoelastic solids with memory. Mechanisms of dissipation and memory are demonstrated and discussed, and the derivation of memory modulus is presented. It is shown that simplified forms of the general theories presented here result in constitutive models that may resemble currently used constitutive models but are not the same. The work presented here is not to be viewed as extension of the current constitutive models; rather, it is a general framework for rate constitutive theories for thermoviscoelastic solids with memory based on the physics and derivations that are consistent within the framework of continuum mechanics and thermodynamics. The purpose of the simplified theories presented in the paper is to illustrate possible simplest theories within the consistent framework presented here.
TL;DR: In this article, the thermal buckling behavior of two-layer shear-deformable beams with partial interaction between the layers was studied. And the stability equations were obtained on the basis of the adjacent equilibrium criterion.
Abstract: This study deals with the thermal buckling behavior of two-layer shear-deformable beams with partial interaction between the layers. The Timoshenko kinematics are considered for both layers and the shear connection is represented by a continuous relationship between the interface shear flow and the corresponding slip. Geometrically nonlinear behavior based on the von Karman simplification of the Green strain tensor is accounted in the formulation. A set of differential equations is obtained from a general 2D bifurcation analysis using the aforementioned assumptions. The stability equations are obtained on the basis of the adjacent equilibrium criterion. It is shown that, due to the existence of the stretching–bending coupling effect in the composite beams, the bifurcation state occurs only for beams with both edges clamped.
TL;DR: In this article, a weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory.
Abstract: A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive equations are efficiently discretized using the trapezoidal rule in conjunction with a two-point recurrence formula. Locking is avoided through the use of standard low-order reduced integration elements as well through the employment of a family of elements constructed using high-polynomial order Lagrange and Hermite interpolation functions.
Journal Article•
TL;DR: In this article, the authors derived the Giesekus constitutive model in Eulerian description based on ordered rate constitutive theories for thermoviscoelastic fluids for compressible and incompressible cases in contra-, co-variant and Jaumann bases.
Abstract: This paper presents derivation of Giesekus constitutive model in Eulerian description based on ordered rate constitutive theories for thermoviscoelastic fluids for compressible and incompressible cases in contra-, co-variant and Jaumann bases. The ordered rate constitutive theories for thermoviscoelastic fluids of orders ( m , n ) consider convected time derivative of order m of the deviatoric Cauchy stress tensor in a chosen basis (i.e. co-, contra-variant or Jaumann) as dependent variable in the development of constitutive theories for the stress tensor. Its argument tensors consist of density, temperature, convected time derivatives of the deviatoric Cauchy stress tensor of up to order m -1 and convected time derivative of up to order n of the conjugate strain tensor. In addition, constitutive theory for the heat vector compatible with the constitutive theory for the deviatoric stress tensor is also presented in co-, contra-variant and Jaumann bases. It is shown that the Giesekus constitutive model is a subset of the rate constitutive theory of orders m = n = 1. It is also shown that the deviatoric Cauchy stress tensor (contra-, co-variant or Jaumann basis) naturally results as dependent variable in the constitutive theory, and that currently used Giesekus constitutive model in deviatoric polymer Cauchy stress tensor is not derivable based on axioms and principles of the constitutive theory in continuum mechanics. Numerical studies are presented for fully developed flow between parallel plates for a dense polymeric liquid using the Giesekus constitutive model derived in this paper as well as currently used model.
TL;DR: In this paper, two nonlinear elasticity theories that account for geometric nonlinearity and microstructure-dependent size effects are revisited to establish the connection betweenthe two theories.
Abstract: In this paper two different nonlinear elasticity theories that account for (a) geometric nonlinearityand (b) microstructure-dependent size effects are revisited to establish the connection betweenthe two theories. The first theory is based on modified couple stress theory of Yang et al. [1]and the second one is based on Srinivasa–Reddy gradient elasticity theory [2]. The modified couplestress theory includes a material length scale parameter that can capture the size effect in a material.The gradient elasticity theory was developed for finitely deforming hyperelastic cosserat continuum,and it is a generalization of small deformation couple stress theories. The Srinivasa–Reddy theorycontains, as a special case, the first one. These two theories are used to derive the governing equationsof beams and plates. In addition, a discrete peridynamics idea as an alternative to the conventionalperidynamics is also presented.
TL;DR: In this article, a multiscale homogenization-based analysis of the constituent properties of soft tissues and underlying endoskeleton are developed for impact mitigation using nanotube-reinforced composite shields.
Abstract: Kinetic energy of an inert projectile or its fragment can cause considerable damage to soft tissues and cause debilitating injuries or fatalities. The primary aim of threat mitigation due to kinetic energy dissipation is to provide adequate protection against projectiles or fragments in the form of body shields. Recently, novel nanocomposite materials reinforced with nanotubes are used as shields to protect the soft-tissues during impact. Soft tissues constitute an important part of human body performing various mechanical functions and a deep understanding of the behavior of soft tissue is required to characterize its response to external mechanical forces. Soft tissues are non-homogenous anisotropic materials, and their properties are dependent on the the physiological structure. In this paper, a multiscale homogenization-based analysis of the constituent properties of soft tissues and underlying endoskeleton are developed for impact mitigation using nanotube-reinforced composite shields.
TL;DR: In this paper, the authors present constitutive theories for finite deformation of homogeneous, isotropic thermoelastic solids in Lagrangian description using Gibbs potential.
Abstract: This paper presents constitutive theories for finite deformation of homogeneous, isotropic thermoelastic solids in Lagrangian description using Gibbs potential. Since conservation of mass, balance of momenta and the energy equation are independent of the constitution of the matter, the second law of thermodynamics, that is, entropy inequality, must form the basis for all constitutive theories of the deforming matter to ensure thermodynamic equilibrium during the evolution (Surana and Reddy in Continuum mechanics, 2012; Eringen in Nonlinear theory of continuous media. McGraw-Hill, New York, 1962). The entropy inequality expressed in terms of Helmholtz free energy is recast in terms of Gibbs potential. The conditions resulting from the entropy inequality expressed in terms of Gibbs potential permit the derivation of the constitutive theory for the strain tensor in terms of the conjugate stress tensor and the constitutive theory for the heat vector. In the work presented here, it is shown that using the conditions resulting from the entropy inequality, the constitutive theory for the strain tensor can be derived using three different approaches: (i) assuming the Gibbs potential to be a function of the invariants of the conjugate stress tensor and then using the conditions resulting from the entropy inequality, (ii) using theory of generators and invariants and (iii) expanding Gibbs potential in the conjugate stress tensor using Taylor series about a known configuration and then using the conditions resulting from the entropy inequality. The constitutive theories resulting from these three approaches are compared for equivalence between them as well as their merits and shortcomings. The constitutive theory for the heat vector can also be derived either directly using the conditions resulting from the entropy inequality or using the theory of generators and invariants. The derivation of the constitutive theory for the heat vector using the theory of generators and invariants with the complete set of argument tensors yields a more comprehensive constitutive theory for the heat vector. In the work, we consider both approaches. Summaries of the constitutive theories using parallel approaches (as described above) resulting from the entropy inequality expressed in terms of Helmholtz free-energy density are also presented and compared for equivalence with the constitutive theories derived using Gibbs potential.
TL;DR: In this paper, the transient electromechanical response of an ionic polymer-metal composite (IPMC) is modeled within a thermodynamic framework using the Euler-Bernoulli beam theory coupled with electrostatically driven diffusion to account for the flow of the ionic fluid phase.
19 Jul 2013
TL;DR: In this article, a study on viscoelastic behavior of the adhesive and damage analysis of adhesive-adherend interfaces in adhesively bonded joints is presented, where a finite element model is proposed for bond failure analysis at the visco-elastic adhesive and adherend interface for a mixed-mode fracture problem.
Abstract: : This paper presents a study on viscoelastic behavior of the adhesive and damage analysis of adhesive-adherend interfaces in adhesively bonded joints. First, viscoelastic finite element analysis of a model joint with viscoelastic adhesive has been conducted while considering geometric nonlinearity as well as thermal expansion. Then a finite element model for bond failure analysis at the viscoelastic adhesive-elastic adherend interface for a mixed-mode fracture problem is proposed. In the framework of cohesive zone model, traction-separation law is used to define the constitutive response of the cohesive elements at the interface. Quadratic nominal stress criterion and mixed-mode energy criterion are used to determine the damage initiation and evolution at the interface, respectively.
05 Sep 2013
TL;DR: In this paper, a theory of mixture-based finite element model for nutrient flow in a hollow fiber membrane bioreactor and the use of computational tools to improve the efficiency of the bioreactors was discussed.
Abstract: Abstract Conventional experimental or computational techniques are often inadequate for the analysis and development of nanocomposite-based materials as they are tedious (e.g., experimental methods) or are unsuitable to capture the properties of these novel materials (e.g., conventional computational techniques), thereby requiring multiscale computational strategies. During the last 5 years, major developments were made by the authors on the formulation and implementation of multiscale computational models, using atomistic simulation and micro-mechanics-based techniques, to study the mechanical and thermal behavior of nanocomposite-based materials. In this article, the advances made in the computational analysis of nanocomposites for tissue engineering applications (e.g., scaffolds and bioreactors) would be discussed. The material properties of the nanocomposites in the lower scales were determined using molecular dynamics, and were then transferred to the macroscale using various homogenization techniques. Also in this article, the authors discuss the development of a theory of mixture-based finite element model for nutrient flow in a hollow fiber membrane bioreactor and the use of computational tools to improve the efficiency of the bioreactor.
01 Jan 2013
TL;DR: In this paper, the use of high-order spectral/hp approximation functions in finite element models of various of nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids is discussed.
Abstract: This study deals with the use of high-order spectral/hp approximation functions in finite element models of various of nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. For many of these classes of problems, the high-order (typically, polynomial order 4 p