In this paper, we derive the second-order crack opening displacement tensor for an arbitrarily oriented elliptical crack in an elliptically orthotropic (EO) matrix. This result is obtained in explicit closed form. The approach is based on the Saint-Venant’s idea of linear transformation between boundary value problems for elliptically orthotropic and isotropic bodies. The solution utilizes the classical

The increasing applications of nanoporous materials in engineering structures call for robust strength criteria that are able to model the size effects of multiscale voids inherent to these materials. Many literature works have devoted to this line of research by either employing the classical homogenization approach or extending Gurson’s model to incorporate the nanovoid surface mechanics. However

This work provides a comparative analysis of the effect of nanovoids distribution associated with trigonometric functions on forced mechanical characteristics of functionally graded curved nanobeams. A geometrically exact model is developed for the simply-supported beam utilizing a higher-order beam theory including thickness stretching effect. In order to capture the small-scale effects, the governing

The extremely low thickness-to-length ratio (aspect ratio) of graphene nanofillers has long been considered beneficial to the overall thermal conductivity of graphene-polymer nanocomposites as it creates large surface area and extra channels for phonon transport. From time to time, however, a lower aspect ratio of the nanofillers did not yield a higher thermal conductivity as expected. To explain such

This paper derives a novel analytical model for stress dependent permeability of argillaceous porous media (APM) considering clay swelling using fractal theory. The model shows that the stress dependent permeability is a function of effective stress, clay content, clay expansion coefficient, initial irreducible water saturation and rock lithology. It is validated by the available test data from experimental

Size-dependent dynamic responses of small-size frames are modelled by stress-driven nonlocal elasticity and assessed by a consistent finite-element methodology. Starting from uncoupled axial and bending differential equations, the exact dynamic stiffness matrix of a two-node stress-driven nonlocal beam element is evaluated in a closed form. The relevant global dynamic stiffness matrix of an arbitrarily-shaped

The paper is focused on the dynamic homogenization of lattice-like materials with lumped mass at the nodes to obtain energetically consistent models providing accurate descriptions of the acoustic behavior of the discrete system. The equation of motion of the Lagrangian one-dimensional lattice is transformed according to a unitary approach aimed to identify equivalent non-local continuum models of

A thermodynamic framework has been developed for a class of amorphous polymers used in fused deposition modeling (FDM), in order to predict the residual stresses and the accompanying distortion of the geometry of the printed part (warping). When a polymeric melt is cooled, the inhomogeneous distribution of temperature causes spatially varying volumetric shrinkage resulting in the generation of residual

Recently, among other smart and multifunctional materials, magneto-electric soft materials are expected to open a new horizon with myriad of potential applications such as wireless energy harvesting, spintronics and nonvolatile memories, magneto-electric random access memory, to mention a few. Magneto-electric coupling can be defined as the ability of a material to electrically polarize upon the application

A weakly nonlinear analysis is conducted for localized necking of a hyperelastic solid cylinder under axial stretching based on the exact theory of nonlinear elasticity. The amplitude equation derived is shown to be consistent with the one-dimensional model recently proposed by Audoly and Hutchinson (J. Mech. Phys. Solids 97, 2016, 68–91). It is shown that results based on the infinite-length approximation

This paper investigates the Mode-I crack problem that a three-dimensional infinite space of transversely isotropic multi-ferroic composite medium is weakened by multiple coplanar penny-shaped cracks under uniform mechanical, electric and magnetic loadings. These cracks are arbitrarily distributed in an isotropic plane of the material. Four kinds of idealized electro-magnetic crack boundary conditions

This work provides comparative analysis of the effect of manufacturing processes and process parameters on mechanical and thermal properties of stainless steel 316L. The properties are compared for the parts produced by additive manufacturing (Selected Laser Melting), thermal spraying, casting, hot/cold rolling, hot-isostatic pressing, and forging technologies. Each of these manufacturing processes

We discuss the propagation of localized surface waves in the framework of the linear Gurtin–Murdoch surface elasticity and taking into account a roughness of a free boundary. We derive a boundary-value problem for anti-plane motions with curvilinear boundary and surface stresses. Using the asymptotic technique developed earlier, we obtain the form of a localized wave and analyze its amplitude evolution

The resonance phenomenon is for the first time investigated in anisotropic and functionally graded anisotropic nano-size structure. The structure is considered as a doubly curved shell which is modeled exploiting a quasi-three-dimensional model and nonlocal strain gradient theory in order to predict the small-size effects. The doubly-curved nanoshell is made from aragonite with an orthorhombic crystal

It is developed and derived that the ductile/brittle transition is located at ν*=2/3 where ν*is the renormalized form of the standard Poisson's ratio. This is for homogeneous and isotropic materials in the state of uniaxial tension. This then converts to the ductile/brittle transition as being established at μ/k =1/2 where μ and k are the shear and bulk moduli. The consequences of these results for

Three-dimensional exact solutions for temperature and thermoelastic stresses in multilayered anisotropic plates are derived for advanced boundary-value problems with general boundary conditions. The extended Stroh formalism is formulated to include the thermal coupling with the Eringen nonlocal elasticity theory that captures small scale effects. The simply supported structures are subjected to time-harmonic

In this paper, we derive an exact closed-form solution of three-dimensional transient Green's functions (GFs) at the free surface of a constrained transversely isotropic (TI) half-space due to an arbitrarily oriented surface point force of Heaviside time variation. The solution clearly delineates the distinct features of body waves (P-, SV- and SH- waves) as well as Rayleigh surface wave in displacement

We analyse a problem of a hydraulic fracture driven by a non-Newtonian shear-thinning fluid. Fluid viscosity is described by the four-parameter truncated power-law model. By varying the parameters of the rheological model we investigate spatial and temporal evolution of fluid flow inside the crack and the resulting fracture geometry. A detailed quantitative and qualitative analysis of the underlying

A homogeneous anisotropic conductive medium with a set of anisotropic heterogeneities of arbitrary shapes is considered. Calculation of local fields in the medium subjected to arbitrary external fields is reduced to systems of volume integral equations. For numerical solution, these equations are discretized using Gaussian approximating functions concentrated at the nodes of a regular grid. The elements

The current article presents a thorough investigation into the natural frequencies and mode shapes of thin doubly curved shallow microshells by taking into account the influence of material length scale parameter. The mathematical model of system is obtained by applying the Hamilton's principle along with the modified couple stress theory and the Kirchhoff-Love's shell theory. In order to extract the

A new methodology of the evaluation of the thermal/electrical properties of the skeleton of a porous material from measurements of the overall properties of this material saturated with various conductive fluids is proposed and numerically verified. The approach is based on the concept of equivalent microstructure and solution of the inverse homogenization problem in the framework of Mori-Tanaka-Benveniste

A nonlocal theory is presented for the bending in large deformations under applied loads of an initially straight rod. This has similarities with the classical Euler’s elastica in the sense that the bending stiffness remains homogeneously constant, but it depends on an integral average of the entire curvature field. The discretized form of the equilibrium equations is identical to those governing the

Several recent experiments have shown that the glass-transition temperature and temperature-dependent storage modulus of graphene-polymer nanocomposites are dependent on the graphene loading, but at present no theory exists to explain these observations. In this paper, we take the view that both issues are closely tied to the principle of irreversible thermodynamics, and that, by considering the phase

The effective piezoelectric properties of heterogeneous materials are evaluated in the context of periodic homogenization, whereby a variational formulation is developed, articulated with the extended Hill macrohomogeneity condition. The entire set of homogenized piezoelectric moduli is obtained as the volumetric averages of the microscopic properties of the individual constituents weighted by the

A new mechanical and analytical models of the human eye is presented in order to study Glaucoma disease and its complications. Mechanical modeling of the human eye is performed with a hollow sphere under internal pressure. The first-order shear deformation theory is used to obtain the governing equations of the model, which are the set of partial differential equations. The nonlinear von Kármán assumption

We investigate the microscopic and long-wave (or macroscopic) instabilities in fiber composites (FCs) with hyperelastic phases. To study the influence of the phase stiffening behavior, we employ the phase constitutive models that are developed based on the non-Gaussian statistics of polymeric molecular chains. These non-Gaussian models accurately predict the non-linear behavior of soft materials. Moreover

The thickness-extensional mode in layered piezoelectric plates can be inevitably interfered by some undesirable eigen-modes due to the lateral edge effect. A reported theoretical method to predict high-frequency coupled vibrations is the 2D high-order plate theory derived based on approximate dispersion relations. In this paper, based on accurate dispersion relations a novel approach called Frequency

By using the variational-asymptotic method, a universal asymptotic model for composite sandwich plates is established to achieve a great compromise between efficiency and accuracy through the synthesis of two competing theories: equivalent single-layer theories and layer-wise theories. When each layer of a sandwich structure can be individually considered as an elastic plate, and all material constitutive

Payne effect is the complex nonlinear response of filled elastomers to oscillatory loading. Although usually characterized by the decrease in the storage modulus with strain amplitude, and by the bell-shaped curve of loss modulus with strain amplitude, the response has many other peculiar features. The manner of decrease in storage modulus with strain amplitude does not change when the frequency of

We present a new methodology to derive imperfect interface models for the problems with interphase layers. The test case is potential problems, e.g., thermal conductivity, antiplane elasticity, etc. The methodology combines classical asymptotic analysis with concepts from the theory of complex-valued functions. Its major advantage over existing asymptotic approaches is the straightforward derivation

Property contribution tensors constitute basic building blocks for evaluation of effective properties of heterogeneous materials. Most of the existing results, however, are obtained for inhomogeneities of simple shapes, like ellipsoidal. With this paper we introduce open access software that allows one to calculate the components of compliance and stiffness contribution tensors of inhomogeneities of

Recently developed hard-magnetic soft (HMS) materials/structures are very attractive for applications in the fields of soft robots, biomedical devices and stretchable electronics, etc. In general, the mechanical responses of HMS structures strongly depend on the volume fraction of the embedded magnetic particles in the HMS materials. In this work, we focus on the mechanics of functionally graded hard-magnetic

Anisotropic core-shell model of a nano-grained polycrystal is extended to estimate the effective elastic stiffness of several metals of hexagonal crystal lattice symmetry. In the approach the bulk nanocrystalline material is described as a two-phase medium with different properties for a grain boundary zone and a grain core. While the grain core is anisotropic, the boundary zone is isotropic and has

This study provides a multi-step analytical model to investigate the synergistic effects of carbon black nanoparticles and micro-scale carbon fibers on the electrical conductivity of the polymer matrix multi-scale nanocomposites. In the first step, the homogenized electrical conductivity of the nanoparticle-polymer nanocomposites containing the nanoparticle agglomeration is calculated using the percolation

We focus on the mechanical strength of piezomagnetic beam-like nanosize sensors during post-buckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected to be a Euler-Bernoulli type beam. Long-range interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations

A nonlocal linear elastic fracture formulation is presented based on a discrete layer approach and an interface model to study cracked nanobeams. The formulation uses the stress-driven nonlocal theory of elasticity to account for the size-dependency in the constitutive equations, and the Bernoulli-Euler beam theory to define the kinematic field. Two fundamental mode I and mode II fracture nanospecimens

This work compares the transition and competitive mechanism between three types of instabilities of an incompressible dielectric tube: wrinkling, pull-in instability and electric breakdown. We also see how to select one type of instability mode on demand. First, we investigate the finite response and the wrinkling of a tube subject to a combination of applied radial voltage, torsion and axial force

We address the calculation of the effective properties of non-aging linear viscoelastic composite materials. This is done by solving the microscale periodic local problems obtained via the Asymptotic Homogenization Method (AHM) by means of finite element three-dimensional simulations. The work comprises the investigation of the effective creep and relaxation behavior for a variety of fiber and inclusion

The results of analytical and numerical studies of the internal structure of random packed beds of metal micro-particles are presented. To construct packed beds from mono- and polydisperse solid spheres, an algorithm for their random generation based on the discrete element method is used. Analysis of the structure of the packed bed includes the determination of porosity, specific surface area and

With recent ground-breaking advances, machine learning (ML) has been applied widely in numerous fields in this day and age. However, because of the application of backpropagation algorithms based on gradient descent (GD) techniques, the network of ML may be trapped in local minima, especially if its starting point is not on the same side of the global best or the network contains too many local minima

Interfacial behavior within fibrous piezoelectric composites (PZCs) may dramatically degrade the overall electromechanical performance and simultaneously vary the effective coupling moduli of these intelligent materials. In the present paper, we first recapitulate a physics-based general interfacial relation, which is rigorously derived from an ideal three-phase configuration and thus owns explicit

Traumatic brain injury (TBI) is an important cause of mortality and morbidity worldwide. Finite element models of the human head are used widely to simulate TBI loading scenarios, to improve the understanding of the mechanical pathogenesis of head trauma. The reliability of such computational models depends strongly on the accuracy of the mechanical properties of the different components of the brain

Based on the Ginzburg-Landau's theory, the free energy function of polycrystalline system was modified by introducing an extra grain boundary energy, and a new two-dimensional phase field model considering the continuous variation of temperature was proposed to investigate the grain size dependent super-elasticity (SE) and shape memory effect (SME) of nanocrystalline NiTi shape memory alloys (SMAs)

Rayleigh waves are analysed in elastic lattices incorporating inertial devices that couple in-plane displacements. The vector problems of elasticity for a triangular lattice and its long-wavelength/low-frequency continuum approximation are considered. The analytical procedure for the derivation of the Rayleigh dispersion relation is fully detailed and, remarkably, explicit solutions for the Rayleigh

In this study, the non-linear dynamic analysis of torus-shaped and cylindrical shell-like structures has been studied. The applied material is assumed as the functionally graded material (FGM). The structures are considered to be used for important machines such as wind turbines. The effects of some environmental factors on the analysis like temperature and humidity have been considered. The strain

Due to its superior modelling capabilities, there is an increasing interest in distortion gradient plasticity theory, where the role of the plastic spin is accounted for in the free energy and the dissipation. In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity

In this paper, we consider the mechanism of misfit stress relaxation in lattice-mismatched core-shell nanowires (NWs) through the formation of a periodic array of misfit prismatic dislocation loops (PDLs). In doing so, we calculate and analyze the stress fields and strain energy of a PDL and the energy of pair elastic interaction between PDLs in an elastically isotropic cylinder with free surface.

Crack hitting a domain having the same elastic properties but different fracture toughness (due, for example, to thermal processing) is considered. The focus is on the choice between crack deflection by the domain and crack penetration into it. This choice is controlled by two factors: the angle at which the crack approaches the domain and the fracture toughness contrast. This problem is motivated

Experimental observation demonstrates that both negative and positive dispersion relations are possible for porous media, which classical Biot theory fails to predict and interpret. The present paper establishes a higher-order strain gradient nonlocal poroelasticity considering both the size effects and heterogeneity structure effects to describe the specific physical characteristics of material and

In this paper, a two-dimensional stress-driven nonlocal integral model is introduced for the bending and transverse vibration of rectangular nanoplates for the first time. An appropriate kernel function, which satisfies all essential properties, is proposed for two-dimensional problems in the Cartesian coordinate system. Using Leibniz integral rule and Hamilton's principle, the curvature-moment relations

A three-dimensional analysis is presented for the prediction of the behavior of periodic fiber-reinforced composites with numerous broken fibers and debonded fiber-matrix interfaces. The locations of these defects in the composite are randomly determined. The analysis is based on the representative cell method and the higher-order theory. In the framework of the representative cell method, the problem

This paper focuses on the modeling of the effect of saturation on the overall elastic properties of cortical bone. We first use micromechanical model of Salguero, Saadat & Sevostianov (2014) to model anisotropic effective elastic stiffness of drained cortical bone and then apply replacement relations (see review of Sevostianov, 2020) to evaluate effect of the saturation. The model is verified by comparison

In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven integral formulation of elasticity. The present research extends the treatment in Barretta, Čanađija, Luciano, and de Sciarra (2018b) confined to elastically homogeneous

The problems of quasi-static poroelasticity for stationary and extending cracks in an isotropic homogeneous medium are considered. The crack driving forces are caused by pressure of fluid injected inside the crack by external sources. Using simple and double layer potentials of poroelasticity, the problems are reduced to systems of 2D-integral equations on the crack surface. The integral equations

Aim of this work is to model a multiphasic porous material modified with a hydrogel made from a granulate of Superabsorbent Polymers (SAP). The void space of the material is simultaneously filled with two interacting phases, namely a chemically active hydrogel and a multi-component aqueous pore fluid. The hydrogel has the ability to absorb and retain large amounts of the pore fluid. Depending on the

Transverse wrinkles commonly occur in a uniaxially tensile elastic membrane and can vanish upon excess stretching. The wrinkling direction is usually perpendicular to the stretching direction under isotropic elasticity. Here, we show that wrinkles are orientable by material anisotropy, such as in fiber-reinforced or fibrous films, and the wrinkling orientation can be tuned by varying the stiffness

This paper is devoted to mathematical modelling of thermal processes in the polyp-colon system during electrosurgical polypectomy. This medical surgery (colonoscopy) is used to remove abnormal growths from the colon (the large intestine) in order to reduce the risk of the colon cancer development.In the electrosurgical polypectomy procedure, a polypectomy snare is passed over the polyp and tightened

Based on the variational three-point correlation results for the conductivity (thermal, electrical,...) of the multi-coated sphere assemblages, limiting procedures have been developed to construct the explicit expressions of the macroscopic conductivity and the respective microscopic gradient and flux fields for spherically-symmetric inclusion composites with anisotropic coating in d dimensions (d=2

In this review, we discuss replacement (or substitution) relations that quantify changes in various physical properties of heterogeneous materials, produced by variation in the properties of one (or several) of the constituents while keeping the microstructure unmodified. The latter may be formed by interconnected pores, isolated inhomogeneities (cracks, pores, inclusions), or represent the combination

We investigate theoretically the effects of capillarity and gravity on interfacial Marangoni waves (M-waves). Previous studies which neglected these effects have shown the decay rate of M-waves to vary monotonically. In this work, we disprove it by deriving a new dispersion relation (accounting for these effects) for the M-waves, and show that their decay rate passes through a minimum, rather than