International Journal of Engineering Science最新文献

Implicit elasticity presents the general response of materials without imposing assumptions at the fundamental level. A popular implausible assumption of continuum mechanics is that the reference configuration is stress-free, since residual stress is ubiquitous in Nature. This paper develops large and small deformation implicit elasticity frameworks using residually stressed reference configurations. The general forms of constitutive relations, in finite deformations, are obtained by pull-back or push-forward of all the associated tensors to the same (Eulerian or Lagrangian) configuration. These general forms are used to study the relationship between “residual stress and material symmetry” for implicit elasticity. Further, we use a virtual stress-free body, which is implicit elastic, to exactly determine the response of an initially stressed reference configuration. A number of such exact implicit relations are presented for residually stressed reference configurations, which are further simplified through interesting tensor analysis. The simplified implicit relations directly evaluates strain from a given Cauchy stress and residual stress tensor. One of these constitutive relations are employed for investigating the finite inflation of a residually-stressed, thick sphere. Finally, a small deformation implicit theory is attained by linearizing the developed relations for small strain and small rotation. To represent the small strain from a stressed reference, we need to invert a fourth order tensor. The closed-form inverse is determined in a new approach presented in the paper.

Quasi-static sliding contact of an axisymmetric convex rigid solid with an adhesive incompressible polymer layer bonded to a rigid base is considered. As generalizations of the state-of-the-art theories of interplay between adhesion and friction, the JKR (Johnson–Kendall–Roberts)-type so-called peeling and sliding models are developed and applied for analyzing a set of experimental data for spherical indenters of various radii, which is available in the literature. A special focus is placed on the acquisition of the model parameters from experimental data in the case of a nominal point contact. The postpredictive analysis of the obtained scaled results indicates the existence of a three-stage adhesive attachment-stick/peeling/sliding periodic instability.

If an elastic body is defined as one that does not dissipate energy into heat, the classes of elastic bodies not only include the Green elastic solid, but also some types of implicit constitutive relations recently presented in the literature. In this paper one of such new implicit relations is studied in detail, wherein the energy function depend on the second Piola–Kirchhoff stress tensor and the Green Saint-Venant strain tensor. It is assumed that the function is anisotropic having two directions of anisotropy, thus the case of a transversely isotropic body and an isotropic body are special cases of the above function. Spectral invariants are used and explicit expressions for some second derivatives of the energy function are found. Such second derivatives appear in the implicit constitutive relation.

The force method and displacement method on the basis of the reciprocal theorem play an important role in the field of structural mechanics and have been successfully applied in structural mechanics. However, it is interestingly found that the unexpected paradox exists when the authors attempt to apply it to problems of deformations of strain gradient beams. The reciprocal relation between higher order stresses and higher order strains within the framework of linear elastic strain gradient elasticity is proposed with a view toward studying the physical nature of this paradoxical phenomenon, and it is then used to prove the updated reciprocal theorem. At the same time, the reciprocal theorem of any gradients of any second-order symmetric stress tensors and their corresponding gradients of displacements are derived according to the proposed reciprocal relation. The results show that the essential reason for the failure of the conventional reciprocal theorem is that the effect of higher order surface forces and surface stresses that are produced by strain gradients contributes to the reciprocal work. When the strain gradients work-conjugating to stress gradients are considered, they satisfy the local reciprocal relation that cannot be degenerated to the conventional reciprocal theorem in the form of body forces and inertial forces. The theory developed in this paper may have an increasingly profound effect on continuum mechanics and is expected to be a helpful tool for the mechanics of cellular structures homogenized by strain gradient elasticity.

Radially transverse isotropic inclusions in homogeneous isotropic elastic host media are considered. Mellin transform method is used for solution of the volume integral equation of the problem for an isolated inclusion subjected to a constant external stress (strain) field. The tensor structure of the solution is revealed with precision to three scalar functions of the radial coordinate, and the system of ordinary differential equations for these functions is derived. For multilayered radially transverse isotropic inclusions with constant elastic coefficients inside layers, explicit solution of these equations is obtained. An efficient numerical algorithm of solution for inclusions with an arbitrary number of the layers is proposed. Neutral inclusions that do not disturb homogeneous external fields applied to the medium are considered. It is shown that an inclusion with an isotropic core and radially transverse isotropic external layer can be weak neutral by appropriate choice of the layer elastic constants. The effective field method is used for determination of the effective elastic stiffness tensor of a homogeneous isotropic medium containing a random set of radially transverse isotropic inclusions.

Investigation of the geometrical nonlinear action of doubly curved shell panels (DCSPs) in micro scale is the main target of this paper. The proposed microshell panels (MSPs) are assumed to be made of an auxetic honeycomb core (AHOC), leading to negative magnitudes of Poisson's ratio, covered by two nanocomposite enriched coating layers (NCECLs). To conduct the size-dependent nonlinear analysis and achieve the corresponding nonlinear equilibrium path (EQP) of the proposed MSPs, the nonlocal strain gradient theory (NLSGT) is utilized. The governing equations containing the equilibrium and compatibility nonlinear partial differential equations in terms of the deformation components are analytically solved based on the Galerkin technique for different types of simply-supported panels. The achieved results of the present solution exhibit the fact that nonlocal and material length scale parameters significantly affect the EQP of the proposed MSPs especially at their post-buckling stage during their snap-through instability. By solving several numerical examples, the effects of various parameters on the size-dependent EQP of the proposed MSPs are investigated. The results indicate that the influences of size-dependency are significantly affected by the curvature and also boundary conditions of the microshells.

A large electric field is typically present in anodic or passive oxide films. Stresses induced by such a large electric field are critical in understanding the breakdown mechanism of thin oxide films and improving their corrosion resistance. In this work, we consider electromechanical coupling through the electrostrictive effect. A continuum model incorporating lattice misfit and electric field-induced stresses is developed. We perform a linear stability analysis of the full coupled model and show that, for typical oxides, neglecting electrostriction underestimates the film’s instability, especially in systems with a large electric field. Moreover, a region where electrostriction can potentially provide a stabilizing effect is identified, allowing electrostriction to enhance corrosion resistance. We identified an equilibrium electric field intrinsic to the system and the corresponding equilibrium film thickness. The film’s stability is very sensitive to the electric field: a 40 percent deviation from the equilibrium electric field can change the maximum growth rate by nearly an order of magnitude. Moreover, our model reduces to classical morphological instability models in the limit of misfit-only, electrostatic-only, and no-electrostriction cases. Finally, the effect of various parameters on the film’s stability is studied.

We investigate the two-dimensional flows of a viscoplastic fluid in symmetric channels with impermeable walls under no-slip boundary conditions. To characterise the mechanical response of the viscoplastic fluid we consider both the celebrated Bingham model and a very general class of its regularisations. In order to make the problem amenable to analysis, we assume that the aspect ratio of the channel is small so that the lubrication approximation can be used. This allows us to obtain analytical solutions, perform an asymptotic analysis of the regularised solutions and compare the results predicted by the Bingham model and its regularisations. We find that in the limit as the regularisation parameter tends to zero, the regularised flow tends to those predicted by the Bingham model only in plane channels. In channels with curved walls, the results are instead markedly different.

The effect of a nanoplate buckling at a circular nanohole under the remote uniaxial tension is studied incorporating the surface energy in accordance with the Gurtin–Murdoch surface elasticity model. The hole surface within the framework of the plane problem and the faces of the plate within the framework of the Kirchhoff theory of the plate bending are characterized by both the surface elasticity properties and the residual surface tension. The full potential energy of the plate containing the surface tension with non-strain terms of the surface displacement gradient is derived. Based on the principle of virtual displacements, critical values of the load, corresponding symmetrical and asymmetrical forms of the buckling are found by the Ritz method. Numerical investigations reveal that allowing for the non-strain terms of the surface displacement gradient in the Gurtin–Murdoch constitutive relation leads to the essential increasing the rigidity of the plate and the critical Euler load. Two types of the size effect are detected. The nanoplate thickness and the ratio of the hole radius to the thickness influence independently the value of the critical load.

We investigate the impact of fluid drainage on the stress–strain state of a fluid–saturated reservoir. Our focus is on the transition from an elastic to an elastoplastic state of the rock mass and the appearance of constitutive instability during plastic yield. We determine the onset of inelastic deformations using the Drucker–Prager yield criterion and Eaton’s solution for an elastic medium. Our findings illustrate that the transition to an elastoplastic state occurs with increasing depth and decreasing pore fluid pressure at a fixed depth. When dealing with inelastic rock deformation, we analytically solve the Prandtl–Reuss equations under uniaxial strain conditions to obtain the distribution of minimum horizontal stress within the reservoir characterized by both hydrostatic and abnormally high pore fluid pressure. Furthermore, for a formation undergoing inelastic deformations, we identify the critical value of the plastic hardening modulus at which material instability emerges. The applied analytical approach relies on the Prandtl–Reuss equations, Darcy’s law, and continuity equation for an incompressible fluid.