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Showing papers by "J. N. Reddy published in 2018"


Journal ArticleDOI
TL;DR: In this article, a non-local nonlinear analysis of functionally graded plates subjected to static loads is studied, and the nonlinear displacement finite element model of the resulting governing equations is developed, and Newton's iterative procedure is used for the solution of nonlinear algebraic equations.

79 citations


Journal ArticleDOI
TL;DR: In this paper, the wave propagation in magneto-electro-elastic (MEE) nanoshells is investigated via two nonlocal strain gradient shell theories, namely, the Kirchhoff-love shell theory and the first-order shear deformation (FSD) shell theory.

57 citations


Journal ArticleDOI
TL;DR: In this article, the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with different boundary conditions is investigated, which consists of combining the nonlocal theory with the strain and velocity gradient theory to capture both softening and stiffening sizedependent behavior of the nanorod.

52 citations


Journal ArticleDOI
TL;DR: In this paper, the non-local nonlinear finite element formulations for the case of nonuniform rotating laminated nano cantilever beams using the Timoshenko beam theory were presented.
Abstract: In this paper, we present the non-local 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. Non-local stress resultants are obtained by employing Eringen's nonlocal differential model. Geometric nonlinearity is taken into account by using the Green Lagrange strain tensor. Numerical solutions of nonlinear bending and free vibration are presented. Parametric studies have been carried out to understand the effect of non-local parameter and surface stresses on bending and vibration behavior of cantilever beams. Also, the effects of angular velocity and hub radius on the vibration behavior of the cantilever beam are studied.

40 citations


Journal ArticleDOI
TL;DR: In this article, a micropolar Timoshenko beam formulation is developed and used to model web-core sandwich beams, where the split of the shear forces into symmetric and antisymmetric parts plays a pivotal role.

36 citations


Journal ArticleDOI
TL;DR: In this paper, a non-local nonlinear finite element analysis of laminated composite plates using Reddy's third-order shear deformation theory (TSDT) and Eringen's non-locality EINGEN and (Edelen, 1972) is presented.

26 citations


Journal ArticleDOI
TL;DR: In this article, a phase-field damage model for orthotropic materials is proposed and used to simulate delamination of orthotropic laminated composites using the deviatoric and hydrostatic tensile components.
Abstract: A phase-field damage model for orthotropic materials is proposed and used to simulate delamination of orthotropic laminated composites. Using the deviatoric and hydrostatic tensile components of the stress tensor for elastic orthotropic materials, a degraded elastic free energy that can accommodate damage is derived. The governing equations follow from the principle of virtual power and the resulting damage model, by its construction, conforms with the physical relevant condition of no matter interpenetration along the crack faces. The model also dispenses with the traction separation law, an extraneous hypothesis conventionally brought in to model the interlaminar zones. The model is assessed through numerical simulations on delaminations in mode I, mode II, and another such problem with multiple initial notches. The present method is able to reproduce nearly all the features of the experimental load displacement curves, allowing only for small deviations in the softening regime. Numerical results also show forth a superior performance of the proposed method over existing approaches based on a cohesive law.

26 citations


Journal ArticleDOI
TL;DR: In this paper, a topology optimization formulation for multilayer piezoelectric energy harvesters is developed for designing LAPEHs that consider a combination of harmonic and transient optimization problems with the aim of designing the so-called "multi-entry" devices in which the power generated is the same for different types of excitation.
Abstract: Summary Laminated piezocomposite energy harvesters (LAPEHs) are multilayer arrangements of piezoelectric and non-piezoelectric materials. Multiple materials and physics, and dynamic analysis need to be considered in their design. Usually these devices are designed for harmonic excitation, however, they are subjected to other types of excitations. Thus, a novel topology optimization formulation is developed for designing LAPEHs that considers a combination of harmonic and transient optimization problems with the aim of designing the so-called “multi-entry" devices in which the power generated is the same for different types of excitation. LAPEHs are modeled by the finite element method (FEM) and the material model used for the piezoelectric layer is based on penalization and polarization model (PEMAP-P) who controls material distribution and corresponding polarization. To optimize the RLC circuit, a novel linear interpolation model of coupled electrical impedance (LIMCEI) is also introduced to consider different magnitudes of the coupled impedance. The topology optimization problem seeks to maximize the active power generated by the LAPEH at its RLC circuit, to minimize its response time measured as the slope of the power versus time curve, and to maximize its stiffness. Numerical examples are shown in order to illustrate the potential of the method. This article is protected by copyright. All rights reserved.

25 citations


Journal ArticleDOI
TL;DR: A methodology is proposed here to design LAPA with TOM using the classical SIMP and PEMAP-P models and a novel self-penalizable interpolation model to optimize the fiber orientation angles in the composite material.

24 citations


Journal ArticleDOI
TL;DR: Hard biological materials such as nacre, bone, and teeth exhibit high values of toughness although it is meanly made of a ceramic material as mentioned in this paper, however, they are brittle and fail in a catas...
Abstract: Hard biological materials such as nacre, bone, and teeth exhibit high values of toughness although it is meanly made of a ceramic material. Ceramic materials are brittle and fail in a catas...

24 citations


Journal ArticleDOI
TL;DR: In this article, a novel computational approach using the moving element method (MEM) for simulating the dynamic response of Mindlin plate resting on a viscoelastic foundation and subjected to m...
Abstract: Presented herein is a novel computational approach using the moving element method (MEM) for simulating the dynamic response of Mindlin plate resting on a viscoelastic foundation and subjected to m...

Journal ArticleDOI
TL;DR: The availability of the analytical model and solutions presented in this paper may be useful to estimate diagnostically relevant poroelastic parameters such as interstitial permeability and fluid pressure, and, in general, for a better interpretation of clinically-relevant ultrasound elastography results.
Abstract: The mechanical behavior of biological tissues has been studied using a number of mechanical models. Due to the relatively high fluid content and mobility, many biological tissues have been modeled as poroelastic materials. Diseases such as cancers are known to alter the poroelastic response of a tissue. Tissue poroelastic properties such as compressibility, interstitial permeability and fluid pressure also play a key role for the assessment of cancer treatments and for improved therapies. At the present time, however, a limited number of poroelastic models for soft tissues are retrievable in the literature, and the ones available are not directly applicable to tumors as they typically refer to uniform tissues. In this paper, we report the analytical poroelastic model for a non-uniform tissue under stress relaxation. Displacement, strain and fluid pressure fields in a cylindrical poroelastic sample containing a cylindrical inclusion during stress relaxation are computed. Finite element simulations are then used to validate the proposed theoretical model. Statistical analysis demonstrates that the proposed analytical model matches the finite element results with less than 0.5% error. The availability of the analytical model and solutions presented in this paper may be useful to estimate diagnostically relevant poroelastic parameters such as interstitial permeability and fluid pressure, and, in general, for a better interpretation of clinically-relevant ultrasound elastography results.

Journal ArticleDOI
TL;DR: The moving element method is extended to establish the coupling formulations of the mass, damping, and stiffness matrices in vertical and lateral directions, where the element matrices are formulated based on a convected coordinate system attached to the moving vehicle.
Abstract: In this article, the dynamic analysis of three-dimensional high-speed train-track model is carried out using moving element method. The train comprises a car-body supported by a secondary suspensio...

Journal ArticleDOI
TL;DR: In this paper, a generalized model is formulated with the hope to unify local and non-local continuum frameworks, and a compact mapping matrix which converts surface-based forces (stresses) to the nonlocal body based forces is found.

Journal ArticleDOI
TL;DR: In this paper, a theoretical framework for the stress analysis of material-tailored adhesively bonded multilayers is presented, which can be readily extended to study effect of anisotropic tailoring of adherends.

Journal ArticleDOI
TL;DR: In this article, it was shown that the Cauchy moment tensor is not symmetric and the antisymmetric components of the Couchy stress tensor are not balanced by the gradient of the angular momenta balance law.
Abstract: In the non-classical continuum theories for solid continua the presence of internal rotations and their gradients arising due to Jacobian of deformation and/or consideration of Cosserat rotations as additional unknown degrees of freedom at a material point necessitate existence of moment tensor. For small deformation, small strains theories, in Lagrangian description the Cauchy moment tensor and the rates of rotation gradients are rate of work conjugate pair in addition to the rate of work conjugate Cauchy stress tensor and the strain rate tensor. It is well established that in such non-classical theories the Cauchy stress tensor is non-symmetric and the antisymmetric components of the Cauchy stress tensor are balanced by gradients of the Cauchy moment tensor, the balance of angular momenta balance law. In the non-classical continuum theories incorporating internal rotations and conjugate moment tensor that are absent in the classical continuum theories, the fundamental question is “are the conservation and balance laws used in classical continuum mechanics sufficient to ensure dynamic equilibrium of the deforming volume of matter”. At this stage the Cauchy moment tensor remains non-symmetric if we only consider standard balance laws that are used in classical continuum theories. Thus, requiring constitutive theories for the symmetric as well as anti-symmetric Cauchy moment tensors. The work presented in this paper shows that when the thermodynamically consistent constitutive theories are used for symmetric as well as antisymmetric Cauchy moment tensor non physical and spurious solutions result even in simple model problems. This suggests that perhaps the additional conjugate tensors resulting due to presence of internal rotations, namely the Cauchy moment tensor and the antisymmetric part of the Cauchy stress stress tensor must obey some additional law or restriction so that the spurious behavior is precluded. This paper demonstrates that in the non-classical theory with internal rotations considered here the law of balance of moment of moments and the consideration of the equilibrium of moment of moments are in fact identical. When this balance law is considered the Cauchy moment tensor becomes symmetric, hence eliminating the constitutive theory for the antisymmetric Cauchy moment tensor and thereby eliminating spurious and non physical solutions. The necessity of this balance law is established theoretically and is also demonstrated through model problems using thermoelastic solids with small strain small deformation as an example. The findings reported in this paper hold for thermoviscoelastic solids with and without memory as well as when deformation and strains are small. Extensions of the concepts presented here for finite deformation and finite strain will be presented in a follow up paper.

Journal ArticleDOI
TL;DR: In this article, the effect of the material homogenization scheme on the flexural response of a thin to moderately thick FGM plate is studied, where the plate is subjected to different loading and boundary conditions.
Abstract: Functionally graded materials (FGM) are an 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 effect of the material homogenization scheme on the flexural response of a thin to moderately thick FGM plate is studied. The plate is subjected to different loading and boundary conditions. The formulation is developed based on the first-order shear deformation theory. The mechanical properties are assumed to vary continuously through the thickness of the plate and obey a power-law distribution of the volume fraction of the constituents. The variation of volume fraction through the thickness is computed using two different homogenization techniques, namely rule of mixtures and Mori–Tanaka scheme. Comparative studies have been carried out to demonstrate the efficiency of the present formulation. The results obtained from the two techniques have been compared with the analytical solutions available in the literature. In addition to the above a parametric study bringing out the effect of boundary conditions, loads, and power-law index has also been presented.

Journal ArticleDOI
TL;DR: In this paper, the feasibility and performance of standard and boundary layer perturbation techniques in nonlinear analyses of cylindrical shells are investigated. And the uncoupled governing equations of shell theory with first-order approximation and the von Karman nonlinearity are decoupled.

Journal ArticleDOI
TL;DR: In this article, it was shown that the Cauchy moment tensor is not symmetric in the non-classical theory with internal rotation rates and the gradient of the rate of total rotations is a rate of work conjugate pair.
Abstract: In the non-classical theories for fluent continua, the presence of internal rotation rates and their gradients arising due to the velocity gradient tensor necessitate existence of moment tensor. The Cauchy moment tensor acting on the faces of the deformed tetrahedron (derived using Cauchy principle) and the gradients of the rates of total rotations are a rate of work conjugate pair in addition to the rate of work conjugate Cauchy stress tensor and rate of strain tensor. It is well established that in such non-classical continuum theories the Cauchy stress tensor is non-symmetric and the antisymmetric components of the Cauchy stress tensor are balanced by the gradients of the Cauchy moment tensor, balance of angular momenta balance law. In the non-classical continuum theories incorporating internal rotation rates and conjugate Cauchy moment tensor that are absent in classical continuum theories, the fundamental question is “are the conservation and balance laws used in classical continuum mechanics sufficient to ensure dynamic equilibrium of the deforming volume of matter?" If one only considers conservation and balance laws used in classical continuum theories, then the Cauchy moment tensor is non-symmetric. Thus, requiring constitutive theories for the symmetric as well as non-symmetric Cauchy moment tensors. The work presented in this paper shows that when the thermodynamically consistent constitutive theories are used for the symmetric as well as antisymmetric Cauchy moment tensors, non-physical and spurious solutions result even in simple flows. This suggests that perhaps the additional conjugate tensors resulting due to the presence of internal rotation rates, namely the Cauchy moment tensor and the antisymmetric part of Cauchy stress tensor, must obey some additional law or restriction so that the spurious behavior is precluded. The paper demonstrates that in the non-classical theory with internal rotation rates considered here the balance of moment of moments balance law and the equilibrium of moment of moments are in fact identical. When this balance law is considered, the Cauchy moment tensor becomes symmetric, hence eliminating the constitutive theory for the antisymmetric Cauchy moment tensor and thereby eliminating spurious and non-physical solutions. The necessity of this balance/equilibrium law is established theoretically, its derivation is presented using rate considerations, and its necessity is also demonstrated by a model problem using thermoviscous incompressible fluid as an example. The findings reported in this paper hold for all fluent continua, compressible as well as incompressible.

Journal ArticleDOI
TL;DR: In this paper, it is shown that it is possible to model the elasto-plastic behavior of an inextensible beam undergoing finite bending by using a novel implicit rate type response relation directly between the bending moment, curvature, and their rates.
Abstract: The aim of this paper is to show that it is possible to model the elasto-plastic behavior of an inextensible beam undergoing finite bending by using a novel implicit rate type response relation directly between the bending moment, curvature, and their rates. This is in contrast to conventional approaches that require the integration of elasto-plastic stress–strain relations across the thickness of the beam at each time step. The model proposed here (a) is rate independent and exhibits hysteresis, (b) requires no notion of plastic strain and no integration across the thickness, and (c) does not have a sharp yield point and instead transits smoothly between nominally elastic and inelastic response. The governing equations are solved numerically as a set of first order differential equations with very low order interpolation functions for quasi-static response and are capable of modeling both hardening and softening behavior as well as the formation of plastic hinges, etc. Since there is no yield function, there is no necessity to use a return mapping algorithm that was developed specifically for use in elasto-plasticity with sharp yield functions. This simplifies the numerical algorithm also. The simulations for an elastic perfectly plastic beam are compared with elasto-plastic models in ABAQUS TM , and they show good agreement at a fraction of the computational time. Moreover we have compared simulations of large deformations of an aluminum alloy bar subject to three point bending experiments. The simulations also match the experimental results very well. We demonstrate that it is possible to incorporate frictionless sliding contact (which is needed for the three point bending comparison) in a relatively straightforward manner without the complexity that arises when it is handled in a full three-dimensional (3D) model.

Journal ArticleDOI
01 Aug 2018
TL;DR: In this paper, a poroelastic mathematical model of a tumor tissue in cylindrical coordinate system, where the permeability of the tumor tissue is assumed to be higher than the surrounding normal tissue, is presented.
Abstract: Cancerous tissues are known to possess different poroelastic properties with respect to normal tissues. Interstitial permeability is one of these properties, and it has been shown to be of diagnostic relevance for the detection of soft tissue cancers and for assessment of their treatment. In some cases, interstitial permeability of cancers has been reported to be lower than the surrounding tissue, while in other cases interstitial permeability of cancers has been reported to be higher than the surrounding tissue. We have previously reported an analytical model of a cylindrical tumor embedded in a more permeable background. In this paper, we present and analyze a poroelastic mathematical model of a tumor tissue in cylindrical coordinate system, where the permeability of the tumor tissue is assumed to be higher than the surrounding normal tissue. A full set of analytical expressions are obtained for radial displacement, strain, and fluid pressure under stress relaxation testing conditions. The results obtained with the proposed analytical model are compared with corresponding finite element analysis results for a broad range of mechanical parameters of the tumor. The results indicate that the proposed model is accurate and closely resembles the finite element analysis. The availability of this model and its solutions can be helpful for ultrasound elastography applications such as for extracting the mechanical parameters of the tumor and normal tissue and, in general, to study the impact of poroelastic material properties in the assessment of tumors.

Journal ArticleDOI
TL;DR: A realistic FE model of the mechanical behavior of a cancer embedded in a normal tissue under ultrasound elastography testing conditions is designed and implemented and it is demonstrated that the presence of the elevated interstitial fluid pressure affects both the temporal and spatial distributions of the axial, lateral, volumetric strains and related elastographic parameters.
Abstract: Finite element (FE) modeling provides a useful tool to understand the mechanical behavior of complex tissues, such as cancers, in a variety of testing conditions. Although a number of numerical and analytical models for cancerous tumors are retrievable in the literature, none of these models is capable of completely describing the behavior of a cancer embedded in a normal tissue in the conditions typical for an ultrasound elastography experiment. In this paper, we first design and implement a realistic FE model of the mechanical behavior of a cancer embedded in a normal tissue under ultrasound elastography testing conditions. In addition to the commonly used tissue mechanical properties, for the cancer, elevated interstitial fluid pressure (IFP) is incorporated in the model. IFP is a parameter of great clinical significance, but it is not typically considered in elastographic models of tumors. The developed model is then used to thoroughly study the effect of IFP on the axial, lateral and volumetric strains inside the tumor. The results of this study demonstrate that the presence of the IFP affects both the temporal and spatial distributions of the axial, lateral, volumetric strains and related elastographic parameters. Thus, these results lead to two important considerations: (1) that a correct interpretation of experimental elastographic data need a clear understanding of the effect of the IFP on the obtained elastograms and (2) that this IFP-dependent alteration of the elastographic parameters may provide an opportunity to non-invasively gain localized information about this clinically relevant parameter.

Journal ArticleDOI
TL;DR: In this paper, nonlinear analysis of ionic polymer-metal composite (IPMC) strips using the Euler-Bernoulli beam theory with the von Karman nonlinear strain is presented.
Abstract: In this study, nonlinear analysis of ionic polymer–metal composite (IPMC) strips using the Euler–Bernoulli beam theory with the von Karman nonlinear strain is presented. The governing equations are derived using a variational formulation based on a thermodynamic framework. The nonlinear extensions to the linear theory are made in such a way that the resulting form of the coupling between deformation and solvent concentration remains simple. A hybrid finite element–finite volume numerical solution and a operator-split time stepping scheme are formulated for obtaining numerical solutions of the transient electromechanical response. The model is phenomenological, but it is capable of simulating the transient response of IPMC strips under general loading conditions, and it would be useful in the design of mechanisms with IPMC strips as components. The results of the nonlinear analysis are compared with the corresponding linear results for a cantilever beam like IPMC strip. Significant differences in simulation results of tip deflection, solvent concentration, and beam configurations are observed between the linear and the nonlinear beam theory. The differences are due to coupling between the bending and the axial stiffness as properly formulated in the proposed nonlinear theory.

Journal ArticleDOI
TL;DR: In this paper, a generalized curvilinear cylindrical coordinate (CCC) system is introduced in the reference configuration of the rod and a new generalized frame that contains the well-known orthonormal moving frames of Frenet and Bishop (a hybrid frame) as special cases.
Abstract: In this study, the governing equation of motion for a general arbitrary higher-order theory of rods and tubes is presented for a general material response. The impetus for the study, in contrast to the classical Cosserat rod theories, comes from the need to study bulging and other deformation of tubes (such as arterial walls). While Cosserat rods are useful for rods whose centerline motion is of primary focus, here we consider cases where the lateral boundaries also undergo significant deformation. To tackle these problems, a generalized curvilinear cylindrical coordinate (CCC) system is introduced in the reference configuration of the rod. Furthermore, we show that this results in a new generalized frame that contains the well-known orthonormal moving frames of Frenet and Bishop (a hybrid frame) as special cases. Such a coordinate system can continuously map the geometry of any general curved three-dimensional (3D) structure with a reference curve (including general closed curves) having continuous tangent, and hence, the present formulation can be used for analyzing any general rod or pipe-like 3D structures with variable cross section (e.g., artery or vein). A key feature of the approach presented herein is that we utilize a non-coordinate “Cartan moving frame” or orthonormal basis vectors, to obtain the kinematic quantities, like displacement gradient, using the tools of exterior calculus. This dramatically simplifies the calculations. By the way of this paper, we also seek to highlight the elegance of the exterior calculus as a means for obtaining the various kinematic relations in terms of orthonormal bases and to advocate for its wider use in the applied mechanics community. Finally, the displacement field of the cross section of the structure is approximated by general basis functions in the polar coordinates in the normal plane which enables this rod theory to analyze the response to any general loading condition applied to the curved structure. The governing equation is obtained using the virtual work principle for a general material response, and presented in terms of generalized displacement variables and generalized moments over the cross section of the 3D structure. This results in a system of ordinary differential equations for quantities that are integrated across the cross section (as is to be expected for any rod theory).

Journal ArticleDOI
TL;DR: In this article, a model for thermoviscoplastic deformation in metals is proposed based on the two-temperature theory of non-equilibrium thermodynamics, where the dynamics of dislocation densities play the role of internal state variables in the formulation.
Abstract: Posed within the two-temperature theory of non-equilibrium thermodynamics, we propose a model for thermoviscoplastic deformation in metals. We incorporate the dynamics of dislocation densities–mobile and forest—that play the role of internal state variables in the formulation. The description based on two temperatures appears naturally when one recognizes that the thermodynamic system undergoing viscoplastic deformation is composed of two weakly interacting subsystems, viz. a kinetic-vibrational subsystem of the vibrating atomic lattices and a configurational subsystem of the slower degrees of freedom relating to defect motion, each with its own temperature. Starting with a basic model that involves only homogeneous deformation, a three-dimensional model for inhomogeneous viscoplasticity applicable to finite deformation is charted out in an overstress driven viscoplastic deformation framework. The model shows how the coupled evolutions of mobile and forest dislocation densities, which are critically influenced by the dynamics of configurational temperature, govern the strength and ductility of the metal. Unlike most contemporary models, the current proposal also affords a prediction of certain finer details as observed in the experimental data on stress–strain behaviour of metals and this in turn enhances the understanding of the evolving and interacting dislocation densities.

Journal ArticleDOI
TL;DR: In this article, the 2-D approximation functions based on a general exact 3-D plate solution are used to derive locking-free, rectangular, 4-node Mindlin, Levinson and Full Interior plate finite elements.

Journal ArticleDOI
TL;DR: In this article, a non-classical continuum theory in the Lagrangian description for thermoviscoelastic solids without memory is derived by incorporating internal rotations and Cosserat rotations at a material point.
Abstract: The work in this paper is based on a non-classical continuum theory in the Lagrangian description for thermoviscoelastic solids without memory in which the conservation and balance laws are derived by incorporating internal rotations ( $${}_i \pmb {\varvec{{\varTheta } }}$$ ) arising from the Jacobian of deformation ( $$ \pmb {\varvec{J }}$$ ), as well as Cosserat rotations ( $${}_e \pmb {\varvec{{\varTheta } }}$$ ) at a material point. Such non-classical solids have additional energy storage due to rotations and additional dissipation due to rotation rates compared to classical continuum theories. Rotations $${}_i \pmb {\varvec{{\varTheta } }}$$ are completely defined by $$ \pmb {\varvec{J }}$$ , whereas displacements $$ \pmb {\varvec{u }}$$ and Cosserat rotations $${}_e \pmb {\varvec{{\varTheta } }}$$ are degrees of freedom at each material point. When $${}_i \pmb {\varvec{{\varTheta } }}$$ and $${}_e \pmb {\varvec{{\varTheta } }}$$ are resisted by the deforming matter, conjugate moments arise, which together with ( $${}_i \pmb {\varvec{{\varTheta } }},{}_e \pmb {\varvec{{\varTheta } }}$$ ) and ( $${}_i\overset{\,\text{. }}{ \pmb {\varvec{{\varTheta } }}},{}_e\overset{\,\text{. }}{ \pmb {\varvec{{\varTheta } }}}$$ ) result in additional work and rate of work. This paper utilizes thermodynamic framework for non-classical solids derived based on internal as well as Cosserat rotations and presents a thermodynamically consistent derivation of the constitutive theories that incorporate the aforementioned deformation physics. The constitutive theories are derived using the conditions resulting from the entropy inequality in conjunction with the representation theorem.

Journal ArticleDOI
TL;DR: In this article, a mixed least-squares finite element model with spectral/hp approximations is developed for the analysis of steady, two-dimensional flows of generalized Newtonian fluids obeying the Carreau-Yasuda constitutive model.
Abstract: A mixed least-squares finite element model (LSFEM) with spectral/hp approximations is developed for the analysis of steady, two-dimensional flows of generalized Newtonian fluids obeying the Carreau–Yasuda constitutive model. The finite element model (FEM) is composed of velocity, pressure, and stress fields as independent variables (therefore, called a mixed model). FEMs based on least-squares formulations are considered an alternative variational setting to the conventional weak-form Galerkin models for the Navier–Stokes equations, and no compatibility conditions on the approximation spaces are needed for the velocity, pressure, and stress fields if the polynomial order (p) is sufficiently high (say, p > 3, as determined numerically). In addition, applying high-order spectral/hp approximation functions to the least-squares formulation avoids various forms of locking that often occur in low-order LSFEMs for incompressible viscous fluids, and accurate results can be obtained with exponential conver...

Journal ArticleDOI
TL;DR: It is concluded that elastography techniques can be used to accurately identify the presence and location of fractures in a long bone and the proposed model-based approach can be use to predict and analyze strains at a bone fracture site and to better interpret experimental elastographic data.
Abstract: The mechanical behavior of long bones and fractures has been under investigation for many decades due to its complexity and clinical relevance. In this paper, we report a new subject-specific methodology to predict and analyze the mechanical behavior of the soft tissue at a bone interface with the intent of identifying the presence and location of bone abnormalities with high accuracy, spatial resolution, and contrast. The proposed methodology was tested on both intact and fractured rabbit femur samples with finite element-based 3-D simulations, created from actual femur computed tomography data, and ultrasound elastography experiments. The results included in this study demonstrate that elastographic strains at the bone/soft tissue interface can be used to differentiate fractured femurs from the intact ones on a distribution level. These results also demonstrate that coronal plane axial shear strain creates a unique contrast mechanism that can be used to reliably detect fractures (both complete and incomplete) in long bones. Kruskal–Wallis test further demonstrates that the contrast measure for the fracture group (simulation: 2.1286±0.2206; experiment: 2.7034 ± 1.0672) is significantly different from that for the intact group (simulation: 0 ± 0; experiment: 1.1540±0.6909) when using coronal plane axial shear strain elastography ( $p$ < 0.01). We conclude that: 1) elastography techniques can be used to accurately identify the presence and location of fractures in a long bone and 2) the proposed model-based approach can be used to predict and analyze strains at a bone fracture site and to better interpret experimental elastographic data.

Journal ArticleDOI
TL;DR: In this article, a general higher-order one-dimensional model for large deformation analysis of 3-D solids is developed, where the displacement vector of the cross-section or slices of a 3D body are approximated in the reference frame using general basis functions in polar coordinates.