Surface stresses can significantly impact the physical, chemical, and mechanical behaviors of materials and structures, particularly at the nanoscale. The Gurtin-Murdoch theory of surface elasticity offers a continuum framework to account for surface stress effects. In this paper, we apply the Gurtin-Murdoch theory to solve the Melan problem, a fundamental problem of elasticity, in which an elastic half-plane body is subjected to an internal point force. Both residual surface stress and surface elasticity effects are considered. An analytical solution for the elastic fields is derived using the Airy stress function method combined with the Fourier integral transform technique. The solution is presented in an elegant closed-form, expressed through two series of key functions, which can be further derived via partial derivatives of a single explicit function and its limit. Comparative analyses show that surface effects can substantially redistribute the stress and displacement fields, especially when the loading site is close to the surface. The new solution can reduce to several known results for special cases, including the classical two-dimensional (2D) Kelvin solution, the classical Melan solution without surface effects, and the Flamant and 2D Cerruti solutions with complete surface effects. This fundamental solution serves as Green's function in the 2D Gurtin-Murdoch theory when a unit point force is adopted. It has potential for diverse applications in nanomechanics, such as in nanocomposites and defects in nano-crystalline materials where surface and interface effects are significant.

Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.

针对弹性力学课程的教学现状,从线上线下混合式教学模式设计、可视化教学方法、多样化的课程考核评价方式三方面进行课程教学改革,从根本上创建以能力与素质培养为主旨的新型人才培养模式,以适应新时代对学生实践能力培养的要求.该教学改革对丰富弹性力学课程的教学内容和教学资源、提升课程教学质量、培养学生自主学习能力具有重要意义.

In order to study the deformation-failure law of deep buried weakly cemented soft rock roadway and determine reasonable control countermeasures, taking the south main return laneway of Yuwu Coal Mine as an example, the strain softening model parameters were adjusted to reflect the argillization and volume expansion characteristics of weakly cemented soft rock. The stress, deformation and failure evolution of surrounding rock during roadway excavation were numerically analyzed. On this basis, the combined support control countermeasure of “bolt-shotcrete + grouting + inverted arch” was obtained. The results show that the radial displacement of roof, floor and two sides of surrounding rock in deep buried weakly cemented soft rock roadway will reach 734.2 mm, 490.3 mm and 549.6 mm after tunneling 24 m forward. At the same time, the depth of loose zone will increase to 5.6 m, 2.8 m and 3.0 m respectively, while the depth of plastic zone will expand to 9.5 m, 8.8 m and 13.7 m respectively. After adopting the combined support of “bolt-shotcrete + grouting + inverted arch”, the radial displacement and plastic zone depth of roadway will be reduced by 91%-94% and 71%-74%, respectively, and the time to reach stability is greatly shortened.

深埋巷道掘进遇到断层时,其围岩变形破坏特征发生极大变化,严重影响安全生产.为此,以海石湾煤矿一条深埋进风巷道为例,研究其临近断层掘进过程中围岩应力、位移、塑性区和剪应变演化特征,分析断层倾角、破碎带宽度和侧压力系数对巷道围岩稳定性的影响.结果表明:当深埋巷道与断层净间距小于5m时,随着深埋巷道掘进移近断层,巷道周边塑性区岩体剪应变逐渐增大,进而导致深埋巷道围岩位移呈指数式增长;随着侧压力系数增大,深埋巷道顶底板塑性区破坏深度逐渐增大,帮部则出现先减小后增大的变化规律;当深埋巷道与断层净间距大于5m时,断层倾角和宽度对深埋巷道围岩位移与塑性区分布影响很小,反之,深埋巷道位移在断层倾角90°时最大,且与破碎带宽度呈指数衰减关系.

The filling material of the karst collapse column (KCC) is easy to be activated by mining. During this process, the mechanical properties of KCC fillings change, and its water resisting capacity constantly deteriorates and thus often leads to water inrush disaster. In this study, the samples of KCC fillings were taken on-site and then were remolded by the consolidation drainage method. The variation laws of the compressive strength, tensile strength, cohesive stress, internal friction angle, and permeability of the filling samples with respect to the consolidation pressure and moisture content were tested and analyzed. Based on an engineering example, the yield and activation and particle loss of the filling material of the KCC are analyzed. A mechanism for the lagging water inrush of KCC in the process of mining is proposed. The main results of the present study can be concluded concisely as follows. (1) The KCC fillings show obvious soft rock characteristics in the process of uniaxial compression and Brazilian split. The ratio of the uniaxial compressive strength to splitting tensile strength is between 12 : 1 and 8 : 1. The larger the consolidation pressure or the smaller the moisture content, the larger the ratio. (2) With the increase of consolidation pressure or the decrease of moisture content, the uniaxial compressive strength, elastic modulus, splitting tensile strength, cohesive stress, and internal friction angle of the filling material of the KCC increase linearly, while its permeability increases exponentially. (3) When the crack field of the surrounding rocks of the stope is connected with the KCC, its filling material will continue to yield, activate, and migrate under the fluid-solid coupling effect and finally result in the lagging water inrush from the KCC.

In order to determine the reasonable control countermeasures when a deep-buried roadway encounters a fault with high-water pressure, a transport roadway in Xingdong Coal Mine was taken as an example, and the strength drop and permeability mutation of rocks after failure were considered. The numerical simulation results of the displacement, plastic zone, and permeability coefficient and water inflow of the roadway surrounding rocks were carried out. A combined support control measure of “advance pre-grouting + anchor mesh beam + anchor cable + I-steel shed + shotcrete” was proposed. The research results show that when the advancing face of deep-buried roadway is less than 21 m from the high-pressure fault, as the roadway advances, the displacement, plastic zone and water inflow of the roadway surrounding rocks without support will be exponentially increase. The roof and left side of the deep-buried roadway is the place where the surrounding rock loses stability and water inrush occurs at first. After adopting “advance pre-grouting + anchor mesh beam + anchor cable + I-steel shed + shotcrete” combined support, the convergent displacement, plastic zone depth and water inflow of the roadway near the high-pressure fault will be controlled within 110 mm, 3.2 m and 16 m3/h respectively, which can effectively reduce the probability of water inrush disaster.

In order to study the reasonable support technology of weakly cemented soft rock roadway under water spraying condition, the 12307 return airway of Selian No.2 mine was taken as the background. The stress, deformation and plastic zone change characteristics of roadway surrounding under the condition of “anchor belt net and cable beam” support were studied by considering the strength and volume change of weakly cemented sandy mudstone with water spraying time, and the several improvement measures for support plan were proposed. The results of the study show that: under the condition of “anchor belt net and cable beam”, the surrounding rock radial displacement of weakly cemented soft rock roadway will continue to increase exponentially under the influence of water spraying. Finally, its moving distance from roof to floor and two sides will reach 750 mm and 200 mm respectively. After the improved support of “increasing the length of anchor bar, changing metal mesh to reinforced mesh sprayed concrete, and strengthening the support of roadway roof and two sides with anchor ropes”, the surrounding rock maximum radial displacement of weakly cemented soft rock roadway is only 29.0 mm, and the failure plastic zone depth is basically stable at 3.0 m, which well guarantees the safety of the roadway.

In the present paper, the issue of the thermomechanical definitions of intrinsic surface elastic properties is addressed in the context of infinitesimal elasticity, utilizing two fundamental ideas of Gibbs surface thermodynamics, i.e., the Gibbs dividing surface and the associated surface excesses. Firstly, we introduce a novel scalar yet implicitly oriented thermomechanical function, called the Reissner free energy, as a partial Legendre transformation of the conventional Helmholtz free energy function. It naturally facilitates the application of fundamental principles in classical Gibbs surface thermodynamics of fluids to purely elastic solids. In view of the diffusionless characteristic of elastic surfaces, surface elastic parameters that are invariant with altering the position of the Gibbs dividing surface are defined. Resorting to the construction of a fictitious elastic field in the comparison system, we obtain a fundamental thermodynamic identity, i.e., the isothermal surface Gibbs-Duhem type relation. Thereby the modified Shuttleworth-Herring equation as well as the generalized Nozières-Wolf equation, which could be regarded respectively as the defining equations for the intrinsic surface stress and surface strain, are derived. The oriented thermomechanics treatment of elastic surfaces presented here is expected to serve as an essential basis for further developments of an intrinsic surface elasticity theory.

In this paper, a phenomenological continuum theory of surface piezoelectricity accounting for the linear superficial interplay between electricity and elasticity is formulated primarily for elastic dielectric materials. This theory is inspired by the physical idea that once completely relaxed, an insulating free dielectric surface will sustain a nontrivial spontaneous surface polarization in the normal direction together with a tangential self-equilibrated residual surface stress field. Under external loadings, the surface Helmholtz free energy density is identified as the characteristic function of such surfaces, with the in-plane strain tensor of surface and the surface free charge density as the independent state variables. New boundary conditions governing the surface piezoelectricity are derived through the variational method. The resulting concepts of charge-dependent surface stress and deformation-dependent surface electric field reflect the linear electromechanical coupling behavior of nanodielectric surfaces. As an illustrative example, an infinite radially polarizable piezoelectric nanotube with both inner and outer surfaces grounded is investigated. The novel phenomenon of possible surface-induced polarity inversion is predicted for thin enough nanotubes.

As an extension of the well accepted concept of surface elasticity and based on the modernday understanding of surface thermodynamics, a continuum theory for nanosized piezoelectric and piezomagnetic solids was developed. This theory allows us to account for size-dependent mechanical-electric/magnetic behaviours of piezoelectric and piezomagnetic materials at nanoscale associated with surface effects.

This paper studies the surface instability of an elastic thin solid film lying on a rigid substrate and subjected to van der Waals-like surface interactions. The effect of film?substrate interfacial slippage is accounted for by using a simplified linear cohesive interface model. It is found that the interfacial slippage generally plays a destabilizing role in the surface instability of the thin film. For highly compressible films with Poisson's ratio smaller than 0.25, the surface wrinkling behaviour previously inconceivable in the case of a perfectly bonded interface is now feasible if film?substrate interface slipping is permitted. In addition, our linear perturbation analysis shows that the critical conditions for the onset of surface instability can be modulated by adjusting the slippery stiffness of the interface. The result might be helpful for developing novel techniques to create micro-/nanosized surface patterns.

Physisorption may cause a dimple on a deformable solid surface due to adsorbate-substrate interaction. The interactive force between the adsorbate and the crystal atoms depends on their distances, which may change with substrate deformation. This feature of displacement-dependence indicates that the equilibrium problem is a force-deformation coupled nonlinear procedure. In the present study, a continuum mechanics model, in which the force is considered as a function of the displacement field of the medium, is presented to calculate the physisorption-induced deformation in a semi-infinite elastic medium. It is found that the nonlinear effect due to force-deformation coupling should be taken in consideration in the adsorbate-substrate interaction analysis.