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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 literature. [ABSTRACT FROM AUTHOR]

Artificial Intelligence (AI) is a broad discipline that uses powerful algorithms to emulate important aspects of human intelligence. Provided by the Industry 4.0 revolution, AI is increasingly applied in different fields from research to production. One of these fields is Materials Science and Engineering (MSE) which studies the relationships between processing, structure, properties, and performance of materials. The application of AI to MSE has triggered the invention of new materials to satisfy the demanding requirements in myriad sectors through the years. In this context, the "MSE paradigm" emerged as a framework to define these relationships supported by the available technologies at the corresponding time. This is how Polymer Matrix Composites (PMC) were synthesized. During the last years, they have turned from a futuristic solution to a necessity due to the wide range of advantages they offer concerning other conventional materials. The present work presents a modified approach to the MSE paradigm with the application of AI algorithms. An overview of the research advances from 2003 to 2019 in each fundamental link of the proposed MSE paradigm for PMC is exhibited in an organized fashion. This article must serve engineers and scientists working at the intersection of mechanical engineering, materials science and computer science to identify trendy topics in these fields. It aims to represent a starting point for developing innovative methods and proposing new research topics in the framework of the MSE paradigm powered by AI for PMC. [ABSTRACT FROM AUTHOR]

In this paper the authors develop the governing equations for a finite element model of micro-cracking based on a novel approach, eschewing differential equations and continuum mechanics. Instead of first stating the continuum balance laws and constitutive relations followed by discretization, the body is discretized first and then the equations of equilibrium are directly stated for the discretized body. It is shown that, as a result, the balance laws and constitutive relations can be entirely stated in terms of edge forces and lengths rather than strains. Furthermore, by ensuring that microcracks always propagate along the dual mesh which represents the possible fracture microplanes in the element, the need for creating additional nodes, gap elements or cohesive zones is avoided. Finally, the notion of the survival probability of a fracture microplane is introduced and the transition probability evolution is described by using probabilistic notions from population models. Thus the resulting governing equations can be solved by a conventional elastic predictor, followed by a nonlocal fracture corrector, making this convenient to augment conventional elements with fracture abilities. [ABSTRACT FROM AUTHOR]

Geometrically nonlinear and elastoplastic behavior of a circular FGM (functionally graded material) plate under mechanical loading–unloading condition is investigated employing three-dimensional finite element method (FEM) modeling. The through-thickness material distribution of the FGM plate is defined by a power-law variation. The elastic mechanical properties and the elastoplastic material behavior of the FGM plate described respectively by the Mori–Tanaka scheme and the TTO (Tamura–Tomota–Ozawa) model are implemented in the FEM model. The FEM model is validated presenting a very good agreement with the studies from the literature. The influences of nonlinearity, especially the elastoplastic and elastoplastic with geometrically nonlinear behavior, load parameter and thickness-to-radius ratio in terms of nonlinearity, and material composition on the mechanical behavior of the FGM plate are examined. The FEM results are evaluated in terms of the permanent central deflection and the plastic equivalent stress distributions of the FGM plate. The results indicate that a considerable difference occurs between the elastoplastic and elastoplastic with geometrically nonlinear behavior of the FGM plate in terms of both the permanent central deflection and the plastic equivalent stress distributions except ceramic-rich composition that has almost a linear–elastic material behavior, and the geometrical nonlinearity becomes an important parameter with increasing load parameter and decreasing thickness-to-radius ratio. The combination of geometrical and material nonlinearities exhibits a significant influence on the nonlinear mechanical behavior of the FGM plate under plastic deformation. [ABSTRACT FROM AUTHOR]

This paper presents a numerical model to determine the ballistic performance of functionally graded plates under normal and oblique impact. Functionally graded plates consist of metal (Al 6061) and ceramic (SiC) components. The volume fraction of the two components varying throughout the thickness of the functionally graded plates were tailored according to a power-law. The Mori-Tanaka micro-mechanics model was used for determining the local material properties in the graded region of the plates. In the ballistic analyses, the deformation and damage conditions of the functionally graded plates having metal-rich (n = 0.1), linear (n = 1.0) and ceramic-rich (n = 10.0) material compositions were investigated at five different projectile impact angles such as 0°, 15°, 30°, 45°, 60°. In addition, ballistic limit velocity, which is an important parameter in armor design, has been determined at different projectile impact angles of functionally graded plates. It was found that the material composition gradient as well as projectile impact angle played a significant role on the ballistic performance of the plates. [ABSTRACT FROM AUTHOR]

Nacre is an inner layer of seashells that has a remarkable combination of stiffness, strength, and toughness. Engineers are inspired to mimic it to create engineering composites with properties not available in current materials. Toward designing and realizing a bioinspired nacre, a search for some best combination of tablets material, matrix material, and system geometry is needed to obtain optimal mechanical properties. In this work, a multiobjective optimization model is developed based on a genetic algorithm optimization method. The multi-objective optimization problem solved results in a set of optimal solutions that the designers can select according to their preferences. [ABSTRACT FROM AUTHOR]

This article presents an investigation on the postbuckling behavior of doubly curved graphene-reinforced composite (GRC) laminated panels supported by an elastic foundation and subjected to lateral pressure and in thermal environments. The piece-wise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the panels. The overall mechanical properties of the FG-GRCs are assumed to be temperature dependent and are estimated through the extended Halpin-Tsai micromechanical model. The governing differential equations for the doubly curved panels are based on a higher order shear deformation shell theory with von Kármán strain-displacement relationships and the panel-foundation interaction. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The governing equations are first deduced to a boundary layer type that includes nonlinear prebuckling deformations and initial geometric imperfections of the panel. The postbuckling equilibrium path for the perfect and geometrically imperfect GRC laminated doubly curved panels are obtained by applying a singular perturbation technique along with a two-step perturbation approach. The impacts of material property gradient, temperature variation, panel curvature ratio, as well as foundation stiffness on the postbuckling behavior of FG-GRC laminated doubly curved panels are investigated. [ABSTRACT FROM AUTHOR]

We studied the characteristics of a phononic crystal which consists of hollow pillars mounted on the surface of semi-infinite substrate. In this study, the existence of surface waves whispering gallery modes referred as localized cavity modes of the hollow pillars at the subwavelength frequency spectrum is reported. The interaction of the hollow pillars with the surface waves induce localized cavity modes and by tuning the inner radius of the hollow pillars these confined modes can be adjusted/tuned inside the bandgap region, thus introducing new applications for the surface waves based phononic crystals and acoustic metamaterial devices. These subwavelength confined cavity modes possess high-q narrow passband characteristics induced by the interaction of cavity modes with the surface waves propagating at the surface of semi-infinite substrate. We demonstrate the subwavelength waveguiding and other functionalities of these localized cavity modes by tuning the inner radius of the hollow pillars and allowing the specific wavelength frequencies to pass through the monochannel, multichannel, and linear cavity based compact waveguides. To make the study more general, we demonstrate the wave multiplexing phenomena for the identical frequencies (diameters of the hollow pillars are kept constant) for all types of waveguides. However, by varying the inner radii of the hollow pillars, the high-q localized frequencies can be tuned. All the physical phenomena presented shows excellent agreement and it indicates promising applications for the manipulation of surface waves in the surface acoustic waves devices, surface waves sensor and actuator technology, and other photonic/phononic and metamaterial applications. [ABSTRACT FROM AUTHOR]

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 models are developed using a four-noded rectangular conforming element with 8 degrees of freedom per node. Numerical examples are presented to illustrate the effects of nonlocality on the transient dynamic behavior of laminated composite plates. [ABSTRACT FROM AUTHOR]

We present a recently developed three-dimensional-finite-deformation-rate form-based constitutive theory to describe the deformation and fracture of viscoelastic solids. The constitutive theory was also implemented into a commercial finite-element program. Damage and fracture in viscoelastic solids is simulated using the element failure method coupled with a Gibbs free energy-based nonlocal fracture criterion. By numerically simulating selected boundary value problems, we show that our newly developed computational framework is able to reproduce the correct stress-strain response, force–displacement response and crack propagation characteristics in viscoelastic solids undergoing fracture, when compared to the response obtained using the extended finite-element method implementation in a commercially available finite element program. [ABSTRACT FROM AUTHOR]

In this paper, a finite element formulation, using eight independent parameters and high‐order spectral/hp functions, for nonlinear analysis is presented. This formulation allows the use of a third‐order thickness stretch kinematics, which also avoids Poisson's locking. Full nonlinear terms up to quadratic in the Green–Lagrange strain tensorare retained. Several nontrivial problems are solved using the presented formulation. A comparison between this formulation and others found in the literature,and with shell and solid elements in commercial codes ABAQUS and ANSYS are presented and the differences are brought out. [ABSTRACT FROM AUTHOR]

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 catastrophic manner therefore they have low values of toughness. Researchers have been curious in examining the reasons behind such performance. It has been found that the staggered structure of these materials, that is brittle tablets embedded into a soft matrix, is the main reason that allows for multiple toughening mechanisms to operate at different length scales. In addition, it has been shown that the tablets are not flat. There is some waviness that generates hardening and spreading of nonlinear deformation leading to high values of toughness. The effect of waviness was not included in previous analytical toughness models. In the present work, a toughness model based on J-integral approach is developed that considers the waviness. Crack resistance curve, denoted by R-curve, is obtained that agrees with the experimental results. The developed toughness model aids in the design and optimization of nacre-like materials. [ABSTRACT FROM AUTHOR]

A nonclassical internal polar continuum theory for finite deformation and finite strain for isotropic, homogeneous compressible and incompressible solids is presented in this paper. Since the Jacobian of deformation is a fundamental measure of deformation in solid continua, in its entirety must be incorporated in the thermodynamic framework. Polar decomposition of into right stretch tensor and pure rotation tensor shows that the entirety of implies the entirety of and. The classical continuum theories for isotropic and homogeneous solid continua are based only on. The influence of on the thermodynamic framework is ignored altogether. The purpose of this research is to present a thermodynamic framework for finite deformation and finite strain of solids that incorporates complete deformation physics described by. This can be accomplished by incorporating the additional physics due to in the current theories as these theories already contain the physics due to. We note that the rotation tensor results due to deformation of solid continua, hence arises in all deforming solids. Thus, this theory can be referred to as internal polar nonclassical theory for solid continua. The use of internal polar nonclassical is appropriate as the theory considers internal rotations. When the varying internal rotations and the rotation rates are resisted by the solid continua, conjugate internal moments, which together with rotations and rotation rates can result in additional energy storage, dissipation and memory. The objective of the nonclassical continuum theory presented here is to present a new thermodynamic framework for solid continua with finite deformation and finite strain that is consistent with the complete deformation physics in isotropic, homogeneous continua, which necessitates that in its entirety must form the basis for derivation of conservation and balance laws and constitutive theories. [ABSTRACT FROM AUTHOR]

In the present work, the close similarity that exists between Mindlin's strain gradient elasticity and Eringens nonlocal integro-differential model is explored. A relation between length scales of nonlocal-differential model and gradient elasticity model has been arrived. Further, a relation has also been arrived between the standard and nonstandard boundary conditions in both the cases. C0-based finite element methods (FEMs) are extensively used for the implementation of integro-differential equations. This results in standard diagonally dominant global stiffness matrix with off diagonal elements occupied largely by the kernel values evaluated at various locations. The global stiffness matrix is enriched in this process by nonzero off diagonal terms and helps in incorporation of the nonlocal effect, there by accounting the long-range interactions. In this case, the diagonally dominant stiffness matrix has a band width equal to influence domain of basis function. In such cases, a very fine discretization with larger number of degrees of freedom is required to predict nonlocal effect, thereby making it computationally expensive. In the numerical examples, both nonlocal-differential and gradient elasticity model are considered to predict the size effect of tensile bar example. The solutions to integro-differential equations obtained by using various higher-order approximations are compared. Lagrangian, Bèzier and B-Spline approximations are considered for the analysis. It has been shown that such higher-order approximations have higher inter-element continuity there by increasing the band width and the nonlocal character of the stiffness matrix. The effect of considering the higher-order and higher-continuous approximation on computational effort is made. In conclusion, both the models predict size effect for one-dimensional example. Further, the higher-continuous approximation results in less computational effort for nonlocal-differential model. [ABSTRACT FROM AUTHOR]

For thermoelastic solids, rate of mechanical work equilibrates with the rate of kinetic energy and rate of strain energy. In this article, this aspect of the physics is utilized to: (i) derive an alternate form of the energy equation based on the first law of thermodynamics and (ii) derive an alternate form of entropy inequality based on the second law of thermodynamics, both free of rate of strain energy. This alternate form of entropy inequality strictly contains physics related to the rates of entropy. This form of entropy inequality is essential to show that the constitutive theories for stress tensor for thermoelastic solids are free of any thermodynamic restrictions and thus can be derived independently of the entropy inequality. In this article, we explore both forms of entropy inequality, one containing rate of strain energy and the alternate form that is free of rate of strain energy in deriving the constitutive theories for the stress tensor. It is shown that the alternate for entropy inequality free of rate of strain energy provides greater flexibility in deriving the constitutive theories for the stress tensor as it places no thermodynamic restrictions on the constitutive theories for the stress tensor. Both forms of the entropy inequality are examined for establishing dependent variables and their arguments for deriving constitutive theories for such solids in Lagrangian description. The solid matter is assumed to be homogeneous, isotropic, compressible, aswell as incompressible, but the deformation and the strains can be finite. [ABSTRACT FROM AUTHOR]

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 convergence. The benchmark problem of the flow past a circular cylinder is solved to verify and validate the model. Then, a parametric study is performed to examine the effect of change in parameters of the Carreau-Yasuda model on the flow past a circular cylinder. [ABSTRACT FROM AUTHOR]

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 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 nonlocal 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. [ABSTRACT FROM AUTHOR]

In this article, the equations of motion for functionally graded plates with surface-mounted piezoelectric layers, while accounting for the gradient elasticity through the modified couple stress model and linear piezoelectricity, are derived using Hamilton’s principle. The formulation includes the coupling between mechanical deformations and the charge equations of electrostatics. The mathematical model developed herein is an equivalent single layer theory for mechanical displacement field and the potential functions. The in-plane displacements are assumed to vary as cubic functions of the thickness coordinate while the transverse displacement is assumed to vary as a quadratic function of the thickness coordinate through plate thickness. The potential function is assumed as the combination of half cosine variation of electric potential and linear variation of applied voltage on outer surfaces. The approach described here is that standard plate models can be enhanced to include the coupling between the charge equations and the mechanical deformations as well as the size dependent effect of micro- and nano-scale structures. An analytical solution of the developed model is presented using the Navier solution technique. A parametric study is performed to study the effect of material variation through thickness of plates, length scale parameters to capture the size-dependent effects, and thickness ratio between piezoelectric layers and the whole plate. [ABSTRACT FROM AUTHOR]

This article presents constitutive theories for the stress tensor and the heat vector for homogeneous, isotropic thermoelastic solids in Lagrangian description for finite deformation. The deforming solid is assumed to be in thermodynamic equilibrium during the evolution. Since conservation of mass, balance of momenta, and balance of energy are independent of the constitution of the matter, the second law of thermodynamics must form the basis for deriving the constitutive theories. We introduce the concept of rate constitutive theory and show that for thermoelastic solids the constitutive theories are, in fact, rate theories of order zero. These theories for stress tensor consider material derivative of order zero of the conjugate strain tensor as one of the argument tensors of the stress tensor established as a dependent variable in the constitutive theory. Generalization of this concept leading to higher order rate theories in Lagrangian description are considered in followup works [1, 2]. The conditions resulting from the entropy inequality in Helmholtz free energy density permit the derivation of constitutive theory for stress tensor in terms of conjugate strain tensor or material derivative of order zero of the conjugate strain tensor. In the work presented here, it is shown that, using the conditions resulting from the entropy inequality, the constitutive theory for the stress tensor can be derived using three approaches: (i) assuming Helmholtz free energy density to be a function of the invariants of the material derivative of order zero of the conjugate strain tensor and temperature θ and then using the conditions resulting from the entropy inequality; (ii) using the theory of generators and invariants; and (iii) expanding Helmholtz free energy density in the material derivative of order zero of the conjugate strain tensor using Taylor series about a known configuration and then using the condition resulting from entropy inequality. The constitutive theories resulting from these three approaches are compared for equivalence as well as their merits and shortcomings. It is shown that the constitutive theory for heat vector can be derived: (i) using the conditions resulting from the entropy inequality; and (ii) using the theory of generators and invariants. In this approach, the argument tensors of the heat vector determine the specific form of the resulting constitutive theory. In this article, we use second Piola–Kirchhoff stress tensor and Green’s strain tensor (material derivative of the Green’s strain tensor of order zero) as a conjugate pair. [ABSTRACT FROM PUBLISHER]