Micro-to-macro transitions for continua with surface structure at the microscale

An improved technique for characterizing the fracture toughness via scratch test experiments

A novel constitutive model for surface elasticity at finite strains suitable across compressibility spectrum

The presence of connective tissue as well as interstitial clefts forms a natural barrier to the electrical propagation in the heart. At a microscopic scale, such uncoupling structures change the pattern of the electrical conduction from uniform towards complex and may play a role in the genesis of cardiac arrhythmias. The anatomical diversity of conduction structures and their topology at a microscopic size scale is overwhelming for experimental techniques. Mathematical models have been often employed to study the behavior of the electrical propagation at a sub-cellular level. However, very fine and computationally expensive meshes are required to capture all microscopic details found in the cardiac tissue. In this work, we present a numerical technique based on the finite element method which allows to reproduce the effects of microscopic conduction barriers caused by the presence of uncoupling structures without actually resolving these structures in a high resolution mesh, thereby reducing the computational costs significantly.

Surface layers with microstructures are widely used in many engineering fields. The mechanical behavior of microstructures in solids can be described by gradient elasticity theories. [One of them is the couple stress theory (Mindlin and Tiersten in Arch. Ration. Mech. Anal. 11:415–448, 1962).] In the present paper, we study the in-plane surface wave propagating in a classical elastic half-space covered by a surface layer described by the couple stress theory. We firstly develop the full solution for the above configuration. Since our primary objective is to introduce the couple stress theory (or strain-gradient elasticity theory) into the surface elasticity model (Gurtin and Murdoch in Arch. Ration. Mech. Anal. 57:291–323, 1975), we are particularly interested in the case that the surface layer is very thin. Therefore, as our second step, by employing the Kirchhoff thin plate model, we establish the surface elasticity model considering couple stresses and derive the isotropic surface elasticity solution of the present problem. Thirdly, by employing the second-order strain-gradient model (Aifantis in Int. J. Eng. Sci. 30:1279–1299, 1992), we derive the dispersion equation of the surface wave for the case that the microstructure length scale is larger than the layer thickness. The last two solutions are compared with the full solution numerically for the lowest mode of the surface wave. It should be pointed out that the present study involves multi-field knowledge of surface waves, couple stress theory, and surface elasticity theory.

This paper is focused to investigate the effects of nonlinear sources, including viscoelastic foundation and geometrical nonlinearity along with the surface elasticity and residual surface stress effects on the primary frequency response of a harmonically excited nanoscale Bernoulli-Euler beam. Due to large surface-area-to-volume ratio, the theory of surface elasticity as well as residual surface stress effects are taken into account within the beam models. The Galerkin approach accompanied by trigonometric shape functions is utilized to reduce the governing PDEs of the system to ODEs. The multiple scales perturbation method theory is applied to compute the nonlinear frequency response of nanobeam. The effects of linear and nonlinear viscoelastic damping coefficient of the medium, crystallographic directions of [100] and [111] of anodic alumina, geometrical nonlinear term and geometrical property on the nonlinear primary frequency response of nanoscale beam are investigated. The results show that theses parameters have a significant effect on the nonlinear frequency response of nanobeams in the case of primary resonance.

In micro/nanoresonators, thermoelastic damping (TED) serves as a principal energy dissipation mechanism that critically determines device performance. The mechanical and thermal responses of these small‐scale structures cannot be captured by traditional formulations and demand scale‐dependent simulations. This research outlines a fresh modeling approach addressing the role of surface effect in TED for rectangular nanoplate resonators subjected to nonlocal dual‐phase‐lag (NDPL) heat conduction. The analysis initiates by developing the governing equations for displacement and temperature in Kirchhoff plates through the application of the surface elasticity theory (SET) and the NDPL heat transfer model. The frequency‐based technique, combined with the derived equations, yields an explicit TED formulation for nanoscale rectangular plates, accounting for the surface effect. The results section, after confirming model accuracy, delivers various numerical evaluations aimed at assessing the impact of scale effects, plate dimensions, boundary types, vibration modes, and material selections. The analysis implies that TED is attenuated under the influence of non‐classical parameters introduced by the SET, in contrast to the higher damping levels predicted by classical elasticity.

Here we report quasi-isentropic dynamic compression and thermodynamic characterization of solid, precompressed deuterium over an ultra fast time scale (< 100 ps) and a microscopic length scale (< 1 ìm). We further report a fast transition in dynamically compressed solid deuterium that is consistent with the ramp to shock transition, with a time scale of less than 10 ps. These results suggest that high density dynamic compression of hydrogen may be possible on microscopic length scales.

Using surface elasticity theory, this article first analyzes the surface effect on the elastohydrodynamic lubrication (EHL) line contact between an elastic half-plane and a rigid cylindrical punch. In this theory, the surface effect is characterized with two parameters: surface elastic modulus and residual surface stress. The density and viscosity of the lubricant, considered as Newtonian fluid, vary with the fluid pressure. A numerical iterative method is proposed to simultaneously deal with the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Then, the fluid pressure and film thickness are numerically determined at the lubricant contact region. Influences of surface elastic modulus, residual surface stress, punch radius, resultant normal load, and entraining velocity on the lubricant film thickness and fluid pressure are discussed. It is found that the surface effect has remarkable influences on the micro-/nano-scale EHL contact of elastic materials.

Low velocity impact of a nanoparticle on a rectangular nanoplate: A theoretical study

The multiple scattering of elastic waves by uniformly arranged nanopores and the equivalent properties of nanoporous materials are studied in this paper. By using displacement potential function method, the stress fileds and strain fields around nanopores and the matrix are solved in accordance with the classical elasticity theory and surface elasticity theory. The equivalent bulk moduli and shear moduli of nanoporous materials are studied using the Mori-Tanaka method. Results show that the equivalent properties of nanoporous materials not only depend on the surface parameters but are also affected by the volume percentage of the holes.

Macroscopic mechanical responses of alloy steels dispersed with fine vanadium carbide particles [1] were analyzed by crystal plasticity finite element method. Average distance of dispersed particles was used as a microscopic length scale and introduced to the models of the critical resolved shear stress and the mean free path of dislocations. Numerical result of yield stress agreed well with that of experimental result [1], but that of the work hardening rate was slightly higher than that of experimental one. When the dislocation mean free path was set to be 2 to 3 times the average spacing of dispersed particles, the work hardening rate fit better with the experimental one.

A new non-classical model for circular Kirchhoff plates subjected to axisymmetric loading is developed using a modified couple stress theory, a surface elasticity theory and Hamilton’s principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation. The new plate model contains a material length scale parameter to capture the microstructure effect and three surface elasticity constants to describe the surface energy effect. The current non-classical plate model includes the plate models considering the microstructure influence or the surface energy effect alone as special cases and recovers the classical elasticity-based Kirchhoff plate model when both the microstructure and surface energy effects are suppressed. To demonstrate the new model, the static bending problem of a clamped solid circular Kirchhoff plate subjected to a uniform normal load is analytically solved by directly applying the general formulas derived. The numerical results reveal that the deflection of the clamped circular plate predicted by the current Kirchhoff plate model is smaller than that predicted by the classical elasticity-based model, but the former approaches the latter with the increase of the plate thickness. It is also found that the difference between the plate deflection predicted by the model incorporating the surface energy effect and that predicted by the classical model is significant when the plate thickness is sufficiently small. However, the difference is diminishing as the plate thickness increases. These predicted size effects at the micron scale agree with the general trends observed in experiments.

Solvent Effect on the Unfolding Force of a Single Hydrophobic Polymer

With the extensive applications of the micro/nano-electro-mechanical systems, a great deal of attention has been paid to explore the influences of the arising size-dependent effect and surface effect on their performance. Along with these effects, the nonlocal elasticity, strain gradient theory, and surface elasticity theory were successively proposed. Moreover, it is inevitable for MEMS/NEMS to work in a variable temperature environment, correspondingly, the thermal-induced stress or deformation becomes another issue that needs serious concern. Thermoelastic damping (TED), as a main energy dissipation source, is a major challenge in designing higher-quality factor resonators. However, considering the thermoelastic coupling effect, the aforementioned theories are not capable enough to depict the thermoelastic performance of micro/nano-resonators. To amend this deficiency, based on nonlocal strain gradient theory, a new model for assessing the TED of nanobeam resonators by incorporating the thermal relaxation effect and the surface effect is developed. The corresponding governing equations for the Euler–Bernoulli microbeam resonator model are formulated, and then, solved by means of a complex frequency method. The influences of the nonlocal parameter, strain gradient coefficients, aspect ratio, surface stress and surface elasticity on the TED are examined and discussed in detail.

This work addresses the scattering of time‐harmonic waves by a finite, blunt nano‐crack in a graded isotropic bulk material with a free surface. The mechanical model is based on classical elastodynamic theory and describes the elastic, isotropic, graded half‐plane with quadratically varying material parameters along the depth coordinate. This model is extended to nano‐mechanics by using non‐classical boundary conditions and localized constitutive equations at the interface between crack and matrix material following the Gurtin‐Murdoch surface elasticity theory. The computational technique employed is based on the non‐hypersingular traction boundary integral equation method (BIEM) using a closed form Green's function for a half‐plane consisting of a functionally graded material (FGM). The dependences of the diffracted and scattered waves and of the local stress concentration fields on key problem parameters such as size and depth of the embedded crack, surface elasticity effects, type and characteristics of the incident wave, and the dynamic interaction phenomenon between the crack and the free‐surface boundary are all examined through parametric studies.