International Journal of Engineering Science最新文献

We introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are proposed. As an example we discuss propagation shear (anti-plane) waves in media with surface stresses taking into account viscoelastic effects. Here we analysed surface waves in an elastic half-space with viscoelastic coatings. Dispersion relations were derived.

Propagation of Rayleigh-like surface waves is studied in an isotropic elastic solid half-space coated with a thin isotropic elastic solid layer. The half-space and the thin coated layer are in welded contact with each other and contain a uniform distribution of small void pores. Effective boundary condition method is employed to derive an approximate secular equation of second-, third-, and fourth-orders in terms of dimensionless wavenumber. The corresponding secular equations are solved numerically to obtain the speed of propagating Rayleigh-like waves for a particular model. The computed results are presented graphically and compared with those obtained from exact secular equation. The fourth-order approximate secular equation is found to have high accuracy as it provides solutions that are in close vicinity of those obtained from the exact secular equation in the considered model. The presence of voids in the model is found to influence the speed of Rayleigh-like waves theoretically and verified numerically. By ignoring the presence of voids in the model, the secular equation is found to be in complete agreement to the earlier known results in the literature for the corresponding model.

The goal of the current investigation is to determine the dynamic behaviour of double-arch systems: the system is made of two arches reinforced by three different functionally graded patterns of carbon nanotubes and connected with an elastic layer of spring bed. The carbon-nanotube functionally graded patterns considered are uniformly distributed, FG-X and FG-O. Two different boundary conditions of movable and immovable simply supported (named SS1 and SS2) are studied for the reinforced double-arches, where the displacements along the curve-line are constrained for the ends of SS2 arches. Both the Hamilton principle and force-moment technique are utilised to formulate the coupled equations of motion. A series expansion technique is then used to solve the equations. A validation is performed and consistent agreement between the proposed methodology and simplified version of the double-arch system is achieved. One prominent observation arising from this study is that an increase in the opening angle of the double-arch system results in a decline in both the series for the transverse natural frequencies for SS1. Conversely, the systems with SS2 boundary conditions exhibit an initial rise in both the series of natural frequencies as the opening angle increases, followed by a gradual decrease. A thicker carbon-nanotube reinforced functionally graded double-arch system demonstrates an increased natural-frequency sensitivity to variation in opening angles. Lastly, increasing the elastic layer coefficient of stiffness causes an increment in the second series natural frequency of the system.

The paper is a review of Hashin–Shtrikman type bounds for effective moduli of conductivity and elasticity of polycrystals and composites written from the perspective of the variational principle for probabilistic measure. The results for such bounds are rederived in probabilistic terms. Remarkably, in probabilistic terms the Hashin–Shtrikman approach gets especially simple form. Besides, a clear distinction arises between the basic assumption, the choice of the trial field, and the simplifying assumptions, like geometrical isotropy, physical isotropy, texture isotropy, etc. We filled out several gaps. First, we derive an integral equation to be solved to get the bounds when the simplifying assumptions do not hold. Second, we extend the bounds for polycrystals with the cubic symmetry of crystallites to all thermodynamically possible crystallites; previously such bounds were found for crystallites with special elastic properties. One practical outcome considered is the derivation of approximate formulae for the temperature dependence of effective elastic moduli. Third, for crystallites with non-cubic symmetries, we formulated algebraic variational problems to be solved numerically to obtain the bounds, and solved these problems for several materials.

The path-independent M-integral plays an important role in analysis of solids with inhomogeneities. However, the available applications are almost limited to linear-elastic or physically non-linear power law type materials under the assumption of infinitesimal strains. In this paper we formulate the M-integral for a class of hyperelastic solids undergoing finite anti-plane shear deformation. As an application we consider the problem of rigid inclusions embedded in a Mooney–Rivlin matrix material. With the derived M-integral we compute weighted averages of the shear stress acting on the inclusion surface. Furthermore, we prove that a system of rigid inclusions can be replaced by one effective inclusion.

Chemical reactions in solids can induce chemical expansion of the solid that causes the emergence of the mechanical stresses, which, in turn, can affect the rate of the reaction. A typical example of this is the reaction of Si lithiation, where the stresses can inhibit the reaction up to the reaction locking. The reactions in solids can take place within some volume (bulk reactions) or localise at a chemical reaction front (localised reactions). These cases are typically described by different thermo-chemo-mechanical theories that contain the source/sink terms either in the bulk or at the propagating infinitely-thin interface, respectively. However, there are reactions that can reveal both regimes; hence, there is a need to link the theories describing the bulk and the localised (sharp-interface) reactions. The present paper bridges this gap and shows that when a certain structure of the Helmholtz free energy density is adopted (based on the ideas from the phase-field methods), it is possible to obtain (in the limit) the same driving force for the chemical reaction (hence, the same reaction kinetics) as derived within the theory of the sharp-interface chemical reactions based on the chemical affinity tensor.

Wave propagation in Rayleigh nanobeams resting on nonlocal media is investigated in this paper. Small-scale structure-foundation problems are formulated according to a novel consistent nonlocal approach extending the special elastostatic analysis in Barretta et al. (2022). Nonlocal effects of the nanostructure are modelled according to a stress-driven integral law. External elasticity of the nano-foundation is instead described by a displacement-driven spatial convolution. The developed methodology leads to well-posed continuum problems, thus circumventing issues and applicative difficulties of the Eringen–Wieghardt nonlocal approach. Wave propagation in Rayleigh nanobeams interacting with nano-foundations is then analysed and dispersive features are analytically detected exploiting the novel consistent strategy. Closed form expressions of size-dependent dispersion relations are established and connection with outcomes available in literature is contributed. A general and well-posed methodology is thus provided to address wave propagation nanomechanical problems. Parametric studies are finally accomplished and discussed to show effects of length scale parameters on wave dispersion characteristics of small-scale systems of current interest in Nano-Engineering.

The effect of applying different surface elasticity models related to the Gurtin–Murdoch and Steigmann–Ogden theories to the problem on an interaction of a dislocation row with a flat surface of a semi-infinite three-dimensional body is analyzed in the paper. The boundary conditions in the case of an arbitrary shape of a cylindrical surface under the plane strain are derived within the framework of the Steigmann–Ogden model involving all simplified versions of the Gurtin–Murdoch model and the Gurtin–Murdoch model itself. The boundary condition used in the paper for the flat surface is a particular case of the general one. The analytical solution of the corresponding boundary value problem is obtained in the paper in a closed form for the elastic field. Based on this solution, some numerical examples of the stress distribution at the surface and the image force acting on each dislocation are presented. It is shown that incorporating the bending resistance of the surface in the Steigmann–Ogden model leads to the decrease of some stresses and increase the other ones at the surface and to the decrease of the image force, as compared with those obtained by the Gurtin–Murdoch membrane theory of the surface.

Under the influence of the nonlinear fluid-solid coupling, hydraulic fracture exhibits various propagation modes (such as toughness- or viscosity-dominated), which stem from the competition between the solid deformation and fluid flow. Based on the homogeneous assumption, the basic theoretical analysis has divided toughness and viscosity scales in the tip region. However, regarding more realistic and complex geological conditions, like layered heterogeneity, knowledge of fluid-driven fracture propagation is still unclear. This work establishes a theoretical model and solving approach to reveal the multiscale asymptotic behavior during hydraulic fracture passing through the heterogeneous interface (i.e., discontinuous elastic properties). The influence of material discontinuity, regarded as the remote force, in the near-tip, intermediate, and far-field scales is analyzed by the asymptotic analysis and validated by the numerical solutions. Notably, solutions at the intermediate scale manifest as individual feature owing to the heterogeneity: as the crack in front of the interface, just a specific transition solution governed by the property and position of the interface appears; once the crack tip passes the interface, the interface-governed transition solution and interface solution occur simultaneously and interact as the crack tip moves away from the interface. Such multiscale property results in the interface-governed fluid-solid interaction in the tip region, and finally leads to changes in interface failure and propagation mode. On the one hand, the criterion for interface failure should be modified by simultaneously incorporating the heterogeneity of solid domain and multiscale nature of tip solution, especially for viscosity- or interface-dominated propagation regimes. On the other hand, the propagation mode in a heterogeneous domain is controlled by two characteristics: traditional l/l_mk for toughness-viscosity competition associated with c/L_μ for material discontinuity effect proposed in the present work. These insights provide the theoretical foundation for modeling hydraulic fracture propagation in layered heterogeneous domains.

This work investigates the electromechanical response and pull-in instability of an electrostatically-actuated CNT tweezer taking into consideration a TPNL constitutive behavior of the CNTs as well as the intermolecular forces, both of which provide a significant contribution at the nanoscale. The nonlocal response of the material introduces two additional parameters in the formulation, which are effective in capturing the size effects observed at the nanoscale. The problem is governed by a nonlinear integrodifferential equation, which can be reduced to a sixth-order nonlinear ODE with two additional boundary conditions accounting for the nonlocal effects near to the CNT edges. A simplified model of the device is proposed based on the assumption of a linear or parabolic distribution of the loading acting on the CNTs. This assumption allows us to formulate the problem in terms of a linear ODE subject to two-point boundary conditions, which can be solved analytically. The results are interesting for MEMS and NEMS design. They show that strong coupling occurs between the intermolecular forces and the characteristic material lengths as smaller structure sizes are considered. Considering the influence of the nonlocal constitutive behavior and intermolecular forces in CNT tweezers will equip these devices with reliability and functional sensitivity, as required for modern engineering applications.