Shou-Wen Yu

Surface stress effect in mechanics of nanostructured materials

This review article summarizes the advances in the surface stress effect in mechanics of nanostructured elements, including nanoparticles, nanowires, nanobeams, and nanofilms, and heterogeneous materials containing nanoscale inhomogeneities. It begins with the fundamental formulations of surface mechanics of solids, including the definition of surface stress as a surface excess quantity, the surface constitutive relations, and the surface equilibrium equations. Then, it depicts some theoretical and experimental studies of the mechanical properties of nanostructured elements, as well as the static and dynamic behaviour of cantilever sensors caused by the surface stress which is influenced by adsorption. Afterwards, the article gives a summary of the analytical elasto-static and dynamic solutions of a single as well as multiple inhomogeneities embedded in a matrix with the interface stress prevailing. The effect of surface elasticity on the diffraction of elastic waves is elucidated. Due to the difficulties in the analytical solution of inhomogeneities of complex shapes and configurations, finite element approaches have been developed for heterogeneous materials with the surface stress. Surface stress and surface energy are inherently related to crack propagation and the stress field in the vicinity of crack tips. The solutions of crack problems taking into account surface stress effects are also included. Predicting the effective elastic and plastic responses of heterogeneous materials while taking into account surface and interface stresses has received much attention. The advances in this topic are inevitably delineated. Mechanics of rough surfaces appears to deserve special attention due to its theoretical and practical implications. Some most recent work is reviewed. Finally, some challenges are pointed out. They include the characterization of surfaces and interfaces of real nanomaterials, experimental measurements and verification of mechanical parameters of complex surfaces, and the effects of the physical and chemical processes on the surface properties, etc.

Mechanisms of superhydrophobicity on hydrophilic substrates

Surface microstructures of solids play a significant role in producing superhydrophobic surfaces. In the present paper, the Cassie?Baxter and Wenzel models on a rough substrate are examined from the viewpoints of geometry and energy. The result shows that if the air beneath a droplet on a sinusoidal substrate is open to the atmosphere, the superhydrophobic state can exist only when the substrate is hydrophobic, and that the geometric parameters of the microstructure have a great influence on the wetting behavior. Two mechanisms that may lead to a superhydrophobic property from a hydrophilic substrate are addressed. Firstly, for closed or airproof microstructures (e.g.?honeycomb structures), a negative Laplace pressure difference caused by the trapped air under the drop can keep the balance of the liquid/vapor interface. Secondly, some special topologies of surface structures satisfying a certain geometric condition may also lead to the formation of a Cassie?Baxter state even if the microstructures are open to the air. Therefore, some surface morphologies may be designed to obtain superhydrophobic properties on hydrophilic surfaces. The present study is also helpful to understand some superhydrophobic phenomena observed in experiments and in nature.

Possible giant magnetoelectric effect of ferromagnetic rare-earth–iron-alloys-filled ferroelectric polymers

Coupled magnetic–mechanical–electric effects in a composite with ferromagnetic rare-earth–iron alloys (e.g., Tb1−xDyxFe2) filled in ferroelectric polymers [e.g, poly(vinylidene-fluoride–trifluoroethylene) copolymer] are studied by using the Green’s function technique. Numerical results suggest a possible giant linear magnetoelectric effect in the ferroic polymer–matrix composite, which is markedly larger than that in the best-known magnetoelectric materials. In addition, the mechanically flexible composite exhibits large magnetostriction. The present results may stimulate further interest in the area of magnetoelectric materials for technological applications.

An arbitrarily-oriented plane crack terminating at the interface between dissimilar piezoelectric materials

Abstract The plane problem of a crack terminating at the interface of a bimaterial piezoelectric, and loaded on its faces, is treated. Emphasis is placed on how to transform this problem into a non-homogeneous Hilbert problem. To make the derivation tractable, the concept of the axial conjugate is introduced and related to the complex conjugate. The angle between the crack line and the interface may be arbitrary.

Griffith crack moving along the interface of two dissimilar piezoelectric materials

The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will reduce to the result for the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials.

Damage analysis of thermopiezoelectric properties: Part I — crack tip singularities

Abstract This is Part I of the work on a two-dimensional analysis of thermal and electric fields of a thermopiezoelectric solid damaged by cracks. It deals with finding the singular crack tip behavior for the temperature, heat flow, displacements, electric potential, stresses and electric displacements. By application of Fourier transformations and the extended Stroh formalism, the problem is reduced to a pair of dual integral equations for the temperature field with the aid of an auxiliary function. The electroelastic field is governed by another pair of dual integral equations. The inverse square root singularity is found for the heat flow field while the logarithmic singularity prevailed for the electroelastic field regardless of whether the crack lies in a homogeneous piezoelectric solid or at an interface of two dissimilar piezoelectric materials. Results are given for the energy release rate and a finite length crack oriented at an arbitrarily angle with reference to the external disturbances. Part II of this paper considers the modelling of a piezoelectric material containing microcracks. A representative cracked area element is used to obtain the effective conductivity and electroelastic modulus. Numerical results are given for a peizoelectric Bati O3 ceramic with cracks.

Interface effects on effective elastic moduli of nanocrystalline materials

Interfaces often play a significant role in many physical properties and phenomena of nanocrystalline materials (NcMs). In the present paper, the interface effects on the effective elastic property of NcMs are investigated. First, an atomic potential method is suggested for estimating the effective elastic modulus of an interface phase. Then, the Mori–Tanaka effective field method is employed to determine the overall effective elastic moduli of a nanocrystalline material, which is regarded as a binary composite consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. Finally, the stiffening effects of strain gradients are examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Our analysis shows two physical mechanisms of interfaces that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the increased atomic spacings in interface regions, and another is the baffling effect due to the existence of boundary layers between the interface phase and the crystalline phase.

Transient response of a crack in piezoelectric strip subjected to the mechanical and electrical impacts: mode-III problem

The linear piezoelectricity theory is applied to investigate the dynamic response of a center-situated crack perpendicular to the edges of the piezoelectric strip subjected to anti-plane mechanical and electrical impacts. Integral transforms and dislocation density functions are employed to reduce the problem to Cauchy singular integral equations. Numerical results show the effects of loading combination and the ratio of crack length to strip width on the dynamic stress intensity factor and the dynamic energy release rate. Two cases of crack surface conditions, impermeable and electrical contact, are considered. For an impermeable crack, the dynamic energy release rate may be used as the crack extension force, whereas for an electrical contact crack, the dynamic stress intensity factor remains the fracture parameter at the crack tip since the electrical field does not contribute to the dynamic energy release rate.

Interface effects on the diffraction of plane compressional waves by a nanosized spherical inclusion

Effects of surfaces/interfaces become prominent in micro- and nanosized materials and devices. In the present paper, the diffraction of plane harmonic compressional waves (P wave) by a spherical nanoinclusion is studied theoretically using the surface/interface elasticity theory. The results demonstrated that when the inclusion size shrinks to nanometers, surface/interface elasticity plays a significant role in the diffraction of elastic waves. For incident waves of different frequencies, the interface effects on the dynamic stress concentration around the spherical inclusion are examined in detail.

Twisting of nanowires induced by anisotropic surface stresses

Many natural and synthetic quasi-one-dimensional materials are of helical or twisting shape and understanding the physical mechanisms underlying the asymmetric shape is of both theoretical and technological significances. In this letter, we pointed out that anisotropic surface stresses present as a possible reason for the formation of some micro-/nanohelices. Using Gurtin’s theory of surface elasticity, we quantitatively investigated the twisting deformation of nanowires due to anisotropic surface stresses. The present model can also elucidate the formation of some other helical materials at micro- and nanoscales, e.g., twisting lamellae in polymer spherulites, spiraled bacteria, and flagella.