Journal of Elasticity最新文献

Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this purpose, we solve the governing elasticity equations for linearly elastic, potentially compressible solids, as well as the low-Reynolds-number flow equations for incompressible fluids. Technically speaking, we derive the associated Green’s functions under confinement by two planar boundaries that meet at a straight edge. The two boundaries both feature no-slip or free-slip conditions, or one of these two conditions per boundary. Previously, we solved the simpler case of the force being oriented parallel to the straight edge. Here, we complement this solution by the more challenging case of the force pointing into a direction perpendicular to the edge. Together, these two cases provide the general solution. Specific situations in which our analysis may find application in terms of quantitative theoretical descriptions are particle motion in confined colloidal suspensions, dynamics of active microswimmers near edges, or actuated distortions of elastic materials due to activated contained functionalized particles.

This study presents an analytical solution for an exponentially-graded transversely isotropic half-space reinforced by a thin plate, subjected to frictionless contact conditions and buried static point loads. The adopted material model captures the behavior of anisotropic and functionally graded media with improved accuracy compared to the assumption of transverse isotropy. Expressions for displacement field are derived, integrating material anisotropy, functional gradation, and interface conditions. The results show that increasing the thin plate stiffness significantly reduces the normal displacement of the half-space, with displacement nearly vanishing under extreme conditions. Additionally, variations in material gradation initially lead to a substantial reduction in displacement, while specific reinforcement conditions may result in localized increases. These findings provide insights into the mechanical behavior of surface-reinforced anisotropic media and multi-layered structures in applications such as protective coatings, pavements, and ground reinforcements.

This study investigates the dispersion of Rayleigh waves propagating in fiber-reinforced medium over a compressible porous semi-infinite medium under the influence of micropolar elasticity. Perfect and slip boundary conditions are applied on the interface of stratum and substrate to yield the dispersion relation. The model incorporates one of the most effective scheme, the Finite Difference Scheme (FDS) to compute the phase velocities and group velocities of Rayleigh waves. Stability condition of FDS has been derived for the phase velocity and group velocity. The effects of porosity, reinforcement, and micropolarity on Rayleigh waves propagation are studied graphically. A higher mode of the dispersion curve is also analyzed with respect to welded (perfect) and slip boundary conditions.

This paper presents solutions for a transversely isotropic unsaturated half-space subjected to axisymmetric time-harmonic vertical and fluid pressure loading. The Biot’s coupled poroelastodynamic equations are modified to include the unsaturated case by adding the air phase into the balance equations. The resulting fully coupled field equations of the three-phase medium are analytically solved to obtain the frequency-domain general solutions by using Hankel integral transforms in the radial direction. A boundary value problem is then formulated to obtain explicit expressions for the solutions of a half-space subjected to internally applied time-harmonic vertical loading and applied fluid pressure. To validate the accuracy of the proposed formulation, a comparison is made with existing solutions for surface loading on an unsaturated half-space. Numerical results are presented to illustrate the influence of the degree of saturation and the frequency of excitation on the dynamic response of the unsaturated half-space under internal excitations. The analysis reveals significant differences in profiles of displacement, stress, and pore pressure for the unsaturated soils compared to fully saturated cases, highlighting the importance of incorporating partial saturation in dynamic poroelastic modelling for geotechnical and earthquake engineering applications.

It is well-known that analytic solutions for problems in nonlinear elasticity for incompressible isotropic hyperelastic materials can be obtained either by using constitutive models in terms of classical invariants of the right Cauchy-Green tensor or alternatively by using the principal stretches directly. In this paper, we describe an efficient procedure for transforming strain-energy densities expressed in terms of the principal stretches into their counterparts in terms of the invariants. To illustrate the results, applications to the problems of simple shear and pure torsion are described. It is demonstrated that the stretch formulation has some advantages in the former case while the principal invariant approach seems preferable for the torsion problem.

This study provides an example demonstrating that a universal deformation does not constrain the shape of a body. We show that bending, inflation, azimuthal shearing, and expansion or contraction of the major radius of a toroidal sector belong to the class of Family 5 deformations. Therefore, this family of universal deformations for incompressible isotropic solids is not restricted to an annular wedge. The proposed example is shown to be a family of inhomogeneous deformations in which the Cauchy deformation tensor has constant principal invariants — a property which is found only in the Family 5 class of deformations.

Curved nanobeams are fundamental components of nanoscale systems, such as nano and microelectromechanical systems, where accurate modeling of small-scale effects is essential for achieving high precision. This study introduces a novel framework for analyzing the in-plane static behavior of curved nanobeams resting on an elastic foundation, particularly for small displacements. Nonlocal constitutive equations are derived based on nonlocal elasticity theory and solved using the initial value method and the approximate transfer matrix approach to address the challenges arising from the high degree of statical indeterminacy. A convergence analysis is conducted, showing that the proposed method provides a systematic and computationally efficient solution. A parametric analysis reveals that the nonlocal parameter, elastic foundation, and opening angle significantly influence the displacements in the tangential and normal directions, the rotation and bending moment in the binormal direction, the shear force in the normal direction, and the axial force in the tangential direction. These findings further elucidate the mechanics of curved nanostructures, contributing to the design and optimization of nanoscale devices.

Liquid crystal elastomers (LCEs) are actuating soft solids that exhibit large and reversible contractions along the liquid crystal director on heating through the nematic-isotropic transition. Recently, mechanical programming was used to fabricate LCEs that can actuate into arbitrarily complex shapes such as a face. Here, we combine theoretical and experimental observations to explain how such complex mechanical programming works. Crucially, we identify the intermediate pre-programmed state as an isotropic genesis polydomain, which, during programming, can accommodate the imposed strains via a pure soft-mode response enabled by director rotation and laminar microstructures. Second cross-linking fixes these microstructures as preferred but, since they were achieved softly, they do not involve any reconfiguration of the isotropic state, allowing it to be restored on heating. Experimental observations of programmed LCEs reveal both single and double laminate structures, as anticipated by the theory, and also a quantitative match between the 3D deformations that can and cannot be programmed. The set of programmable deformations includes all modest isochoric deformations, explaining why arbitrary shape programming works. Finally, we demonstrate theoretically and experimentally that programming also allows one to engineer samples with desired extents of softness in different directions.

This Note focuses on kinematics in continuum mechanics and suggests the need for distinguishing between a mapping and a deformation process. As an example, it is shown that the standard discussion of isochoric bending of a cube into sectors of circular tubes is actually an isochoric deformation process that continuously deforms only members of the set of sectors of circular tubes. Specifically, this mapping cannot continuously deform a cube into sectors of circular tubes.

Motivated by the recent experimental and analytical developments enabling high-fidelity material characterization of (heterogeneous) sheet-like solid specimens, we seek to elucidate the constitutive behavior of linear viscoelastic solids under the plane stress condition. More specifically, our goal is to expose the relationship between the plane-stress viscoelastic constitutive parameters and their (native) “bulk” counterparts. To facilitate the sought reduction of the three-dimensional (3D) constitutive behavior, we deploy the concept of projection operators and focus on the frequency-domain behavior by resorting to the Fourier transform and the mathematical framework of tempered distributions, which extends the Fourier analysis to functions (common in linear viscoelasticity) for which Fourier integrals are not convergent. In the analysis, our primary focus is the on class of linear viscoelastic solids whose 3D rheological behavior is described by a set of constant-coefficient ordinary differential equations, each corresponding to a generic arrangement of “springs” and “dashpots”. On reducing the general formulation to the isotropic case, we proceed with an in-depth investigation of viscoelastic solids whose bulk and shear modulus each derive from a suite of classical “spring and dashpot” configurations. To enable faithful reconstruction of the 3D constitutive parameters of natural and engineered solids via (i) thin-sheet testing and (ii) applications of the error-in-constitutive-relation approach to the inversion of (kinematic) sensory data, we also examine the reduction of thermodynamic potentials describing linear viscoelasticity under the plane stress condition. The analysis is complemented by a set of analytical and numerical examples, illustrating the effect on the plane stress condition on the behavior of isotropic and anisotropic viscoelastic solids.