# Ming DaiNanjing University of Aeronautics & Astronautics · College of Aerospace Engineering

Ming Dai

Doctor of Philosophy

## About

65

Publications

11,761

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584

Citations

Introduction

Additional affiliations

July 2020 - present

October 2018 - June 2020

May 2017 - October 2018

Education

April 2013 - March 2017

September 2010 - March 2013

September 2006 - June 2010

## Publications

Publications (65)

Since the pioneering work of Eshelby on a single ellipsoidal inclusion embedded in an infinite space, much attention has been devoted in the literature to the question of the uniformity of the stress field inside inclusions surrounded by an elastic matrix. Over the last decade or so, researchers have established the existence of multiple (interacti...

We re-examine the three-dimensional linearly elastic deformations of a composite structure consisting of an infinite isotropic elastic matrix into which is embedded a macro-sized spherical compressible gas/liquid inclusion. Our main focus lies on the contribution resulting from changes in the initial pressure inside the inclusion during deformation...

In the context of classical interface elasticity theory, the existence and uniqueness of elliptical neutral inhomogeneities in an isotropic plane have been verified in the literature for plane deformation when the interface effects are described by variable interface parameters and the matrix is subjected to a uniform external loading. In this pape...

The mechanical analysis of a tunnel buried in an elastic half-space whose surface undergoes a certain external loading is of basic interest and importance in underground engineering. In this paper, we consider the problem of a long straight tunnel within an isotropic elastic half-space subjected to a certain surface loading, in which the generatrix...

We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion. In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale, we refer to the Gurtin-Murdoch model of inte...

Hollow fibers are often placed into flexible thermoelectric materials for various engineering applications. The presence of hollow fibers usually leads to a non-uniform temperature field in corresponding thermoelectric materials and high temperature concentration near the fibers, which threatens the reliability of the thermoelectric materials and m...

This paper studies the axisymmetric vibration of a soft elastic rod with surface tension based on the modified Gurtin–Murdoch model. In contrast to the original Gurtin–Murdoch model (GM model) in which surface tension is treated as a finite value while the residual stress in the bulk induced by it is however treated as an infinitesimal quantity, th...

The problem as to whether an inclusion when embedded in an elastic infinite matrix with a perfectly bonded interface could achieve uniform internal stress has been studied extensively in the literature. It has been shown that in almost all cases ellipsoidal shape (including elliptical shape for two-dimensional deformation) is the only inclusion sha...

A modified closed-form solution is presented for the problem of a finite interface rigid line between two bonded half-planes under remote in-plane heat flux in the context of linear plane thermoelasticity. Different from the existing analytical solutions in the literature, the influence of the expansion of the rigid line caused by thermal load is i...

It is known that the heat flux inside a circular nanoinhomogeneity remains uniform when taking interface phonon scattering into account. We use a combination of complex variable methods and numerical techniques to design a non-circular nanoinhomogeneity with internal uniform heat flux embedded in an infinite plate subjected to uniform remote heat l...

The conformal mapping, which transforms a half-plane into a unit disk, has been used widely in studies involving an isotropic elastic half-plane under anti-plane shear or plane deformation. However, very little attention has been paid to the possibility of utilizing this mapping in the study of an anisotropic elastic half-plane under the same defor...

The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials. In anti-plane shear and plane deformations, certain sufficient conditions have been established in the l...

In the analysis of the elastic behavior of a composite system composed of a solid matrix and a number of compressible liquid/gas inclusions, it is customary to incorporate the change in the magnitude of an inclusion's internal pressure (induced by the change in its volume) during deformation. However, when an inclusion has a relatively high initial...

Small deformation theory plays an important role in analyzing the mechanical behavior of various elastic materials since it often leads to simple referential analytic results. For some specific mechanical problems however (for example, those dealing with small-scale materials/structures with significant surface energies or soft solids containing ga...

An alternative method is proposed to solve the spherical indentation problem of an elastic thin layer with surface tension bonded to a rigid substrate. Based on the Kerr model, we establish a simple modified governing equation incorporating the surface tension effects for describing the relationship between the pressure and downward deflection of t...

The classical Green’s functions used in the literature for a heat source in a homogeneous elastic medium cannot lead to finite remote thermal stresses in the medium, so that they may not work well in practical thermal stress analyses. In this paper, we develop a practical Green’s function for a heat source disposed eccentrically into an elastic dis...

We consider the thermoelastic problem of an interface crack between two dissimilar semi-infinite isotropic materials under a uniform remote heat flux in plane deformation. The crack face is assumed to be partially thermopermeable (defined by a partial insulation coefficient of the crack), while the interface is assumed to be perfectly bonded except...

It is widely appreciated that surface tension plays a central role in the mechanics of soft solids such as gels. The original Gurtin–Murdoch (G–M) surface model incorporated the contribution of surface tension also via the dependence of surface stress on surface deformation. In many subsequent researches, this contribution was neglected presumably...

In elasticity theory, harmonic holes are designed to leave the mean stress inside the surrounding material as a constant. In this paper, we present the design of periodic harmonic holes with surface tension in an elastic plane under a uniform remote loading. We identify the special shapes of such holes by solving a problem of the existence of a hol...

In the analysis of continuum-based models describing the dislocation mechanism for a film–substrate system, it is customary to treat the surface of the film as ‘traction-free’ or ‘perfectly bonded’ to the substrate. For an ultra-thin film, however, the appreciable surface to volume ratio is known to be responsible for considerable surface energies...

We study the interaction between a line edge dislocation and a bi-material interface located between two elastic half-planes subjected to plane strain deformations. Our interface model is based on the extension of the Gurtin–Murdoch model developed in a series of seminal papers by Steigmann and Ogden and incorporates the effects of interface stretc...

The special solutions proposed by Muskhelishvili for a particular kind of homogeneous Riemann–Hilbert problems are very important in the mechanical analysis of cracked materials. The numerical implementation of these special solutions relies on specific choices of the arguments of relevant parameters. We establish here a unified principle to specif...

In the large majority of papers utilizing the Gurtin-Murdoch (G-M) model of a material surface, the complete model is avoided in favor of various modified versions often because they lead to simpler representations of the corresponding stress boundary condition. We propose in this paper an integral-type stress boundary condition for the plane defor...

We consider the plane deformations of an infinite elastic solid containing an arbitrarily-shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin-Murdoch (G-M) interface model...

The deformation-induced change in the curvature of a material surface is a fundamental parameter used in establishing accurate boundary conditions on the surface of a solid when the incorporation of surface energies becomes necessary in the model of deformation. In the context of small strain plane deformations of an elastic solid, the literature b...

Based on the complex variable techniques, the stress concentration around a nanosized hole with rough surface in an elastic plane under uniform remote in-plane loadings is studied in this paper. The hole is nearly circular with its surface asperities defined by a conformal mapping. The nanoscale effects on the stress field around the hole are descr...

We examine the plane strain deformations of a bimaterial system consisting of a line edge dislocation interacting with a flat interface between two dissimilar isotropic half-planes in which the additional effects of interface elasticity are incorporated into the model of deformation. The entire system is assumed to be free of any external loading....

In the micromechanical analysis of composite materials, the objective is to predict the overall behavior of the composite from known properties of its individual constituents. When applied to fibrous composites, stress distributions in a composite material subjected to applied stresses can be modelled using inhomogeneity-matrix systems in which the...

We analyze the contribution of couple stresses to the interaction between a screw dislocation and a bi-material interface. Using Fourier integral transforms, we develop analytical representations for the stress distributions in each of the adjoining materials as well as the interaction force acting on the dislocation. Our results are illustrated wi...

In the mechanical analysis of composites containing nano-inhomogeneities, it is customary to consider only the stretching resistance of the inhomogeneity-matrix interface but neglect the bending resistance of the interface. In this paper, we consider a circular nano-inhomogeneity in an infinite elastic plane subjected to an arbitrary uniform remote...

In the mechanical analysis of a structure/composite with periodic holes/inhomogeneities based on analytic techniques, the holes/inhomogeneities are usually assumed to be circular. In this paper, we develop an efficient method (based on complex variable techniques) to calculate the surface tension-induced stress field in a porous material containing...

Investigated in this paper is the surface tension-induced stress field around a nanoscale inclusion of arbitraryshape embedded in an infinite elastic plane, with an emphasis on the combined effects of surface tension and arbitraryinclusion shape. Muskhelishvili’s complex variable method is employed to formulate the basic equations that are solved w...

Harmonic holes are designed to leave undisturbed the mean stress in an uncut body subjected to a system of prescribed remote loadings. The role of residual surface tension in the design of harmonic holes is an important consideration which is usually neglected at the macroscale but remains a significant factor in the design of such holes at the nan...

This work presents a complex variable-based scheme to calculate the anti-plane shear properties of a porous structure containing periodic holes under uniform (anti-plane shear) loadings. The scheme is featured by practically arbitrary shapes of the holes and the surface effects (resulting from surface elasticity) incorporated on each hole’s boundar...

We propose an innovative numerical scheme (based on complex variable techniques) for the calculation of the effective properties of a composite containing unidirectional periodic fibers in which we additionally incorporate the separate contribution of the ‘interface effect’ between the fibers and the surrounding material. The incorporation of inter...

We study the uncoupled steady-state thermo-elastic problem of a circular nano-inhomogeneity embedded in an elastic plane subjected to a uniform remote heat flux. Nanoscale influences are included in the continuum-based model of deformation by incorporating interface effects arising from both heat conduction and elasticity (in the absence of surface...

We use conformal mapping techniques to derive a semi-analytical solution to the problem of a (straight) screw dislocation embedded in a thin solid film. The surfaces of the film are assumed to incorporate surface effects which result in deformation-dependent tractions imposed on the surfaces of the film. A number of examples are used to illustrate...

‘Inhomogeneities’ usually refer to the particles or fibers in composite materials. The study of inhomogeneities greatly stimulates the mechanical analysis and design of particle- or fiber-reinforced composite materials. In recent years, some researchers presented a kind of composite materials containing inhomogeneities of special shapes which guara...

We consider the interaction of a screw dislocation with a thin film–substrate interface in the anti-plane deformations of a couple stress elastic solid. We formulate and solve the corresponding boundary value problem in three main cases: when the screw dislocation is located inside the substrate; when the screw dislocation is located inside the fil...

This paper constructs multiple elastic inclusions with prescribed uniform internal strain fields embedded in an infinite matrix under given uniform remote anti-plane shear. The method used is based on the sufficient and necessary conditions imposed on the boundary values of a holomorphic function, which guarantee the existence of the holomorphic fu...

We consider the anti-plane shear of a composite containing a periodic array of circular inclusions which incorporate separate interface effects in the presence of uniform remote loading. Using complex variable methods, the corresponding stress distributions and effective shear modulus of the composite are obtained by analyzing a representative unit...

We develop a new method to construct periodic inclusions with uniform internal hydrostatic stress in an elastic plane subjected to uniform remote in-plane loading. The method is based on two particular conformal mappings which lead to a system of nonlinear equations from which the inclusion shapes are determined. We illustrate our results with seve...

We incorporate the mechanics of the interface to construct optimal shapes of periodic inclusions which achieve uniform internal strain fields in an elastic plane subjected to uniform remote anti-plane shear loading. These shapes are determined by solving a problem of the existence of a holomorphic function which is defined outside the unit circle i...

In elasticity theory, a neutral inhomogeneity is defined as a foreign body which can be introduced into a host solid without disturbing the stress field in the solid. The existence of circular neutral elastic nano-inhomogeneities has been established for both antiplane shear and plane deformations when the interface effect is described by constant...

Based on the complex variable method, the problem of an elliptic plate with an elliptic hole or a crack is addressed under uniform tension or pressure imposed on the boundary of the hole and on the edge of the plate. A series solution for the stress field inside the plate is derived using conformal mapping techniques, Faber series and Fourier expan...

We present a rigorous solution of the problem of an arc-shaped interface crack embedded between a circular electrostrictive fiber and a foreign matrix subjected to uniform remote electric loadings. The crack faces are assumed to be permeable to an electric field. Mode-I and Mode-II stress intensity factors for the oscillatory singular stress field...

24th International Congress of Theoretical and Applied Mechanics, 21-26 August 2016, Montreal, Canada

We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate defor...

We derive a series solution for the electro-elastic field inside an anisotropic piezoelectric half-plane
containing an elliptical hole or a crack when the half-plane is subjected to in-plane mechanical and
electric loadings. Our solution is based on a specific type of conformal map which allows for the mapping
of a complete half-plane (without a ho...

In the problem of a half-plane containing a nearby nanosized hole, it is customary to assume that the edge of the half-plane is traction free. In the context of nanomechanics, however, the more realistic scenario is to incorporate surface effects not only on the edge of the hole but also on the edge of the half-plane. Our results indicate that the...

This paper verifies the existence of a single non-circular nano-inclusion with interface effect that achieves a uniform internal strain field in an elastic plane under uniform remote anti-plane shear loadings. The uniform strain field inside such a non-circular inclusion is prescribed via perturbations of the uniform strain field inside the analogo...

This paper addresses the question of whether it is possible to design a nano-inclusion (characterized here by the incorporation of interface effects along the material interface) to achieve a screw dislocation-induced uniform internal strain field when a composite is subjected to anti-plane shear deformation. We demonstrate the existence of such an...

We re-examine the conclusion established earlier in the literature that in the presence of a homogeneously imperfect interface, the circular inhomogeneity is the only shape of inhomogeneity which can achieve a uniform internal strain field in an isotropic or anisotropic material subjected to anti-plane shear. We show that under certain conditions,...

Stress and electric field concentration around two arbitrarily-shaped holes in a finite electrostrictive solid subjected to uniform remote electric field are studied. The edge of the solid and the shapes of the holes are defined via several conformal mappings. The electro-elastic field of the solid as well as the electric fields both outside the so...

In existing literature, it remains an unexplored question whether any inclusion shape can achieve a uniform internal strain field in an elastic half-plane under either given uniform remote loadings or given uniform eigenstrains imposed on the inclusion. This paper examines the existence and construction of such single or multiple non-elliptical inc...

Multiple elastic inclusions with uniform internal stress fields in an infinite elastic matrix are constructed under given uniform remote in-plane loadings. The method is based on the sufficient and necessary condition imposed on the boundary value of a holomorphic function that guarantees the existence of the holomorphic function in a multiply conn...

This paper studies surface tension-induced stress concentration around a nanosized hole of arbitrary shape inside an elastic half-plane. Of particular interest is the maximum hoop stress on the hole’s boundary with relation to the point of maximum curvature and the distance between the hole and the free surface of the half-plane. The shape of the h...

Surface tension plays an important role in nanosized materials. In this paper, the stress field induced by surface tension around an arbitrarily shaped nanosized hole is investigated through complex variable method using truncated series, with an emphasis on the relationship between the hoop stress and the curvature of the hole’s boundary curve. Ou...

This paper presents a perturbation solution to a two-dimensional problem of two arbitrarily shaped holes within an infinite piezoelectric solid subjected to uniform mechanical and electric loads at infinity. Of particular interest are the stress field and electric field around hole with relation to the distance between the two holes. The shape of e...

## Projects

Projects (4)

The objective of this project is to derive some analytic solutions for elastic fields induced by dislocations in films and bimaterial systems at the nanoscale, by using nonlocal elasticity theories or surface energy models.

This project is regarding the stress concentration around holes/cracks in piezoelectric/electrostrictive materials.

This project focuses on the identification of the shapes of holes/inclusions satisfying special properties, for example, enclosing uniform stress fields or not disturbing the stress field in the matrix. The interfaces between inclusions and matrix are treated as being either 'perfect' or 'imperfect'.