Contact stress analysis of an elastic half-plane containing multiple inclusions

This paper presents a two-dimensional contact stress analysis to investigate the effects of multiple inclusions on the contact pressure and subsurface stresses in an elastic half-plane. The boundary element method is used to analyze the contact problem where a set of integral equations is derived on the contact region and the matrix–inclusion interfaces. As the contact region is unknown a priori, an iterative procedure is implemented to determine the actual contact region and the contact pressure, and the tractions and displacements on the matrix–inclusion interfaces are obtained by solving the integral equations numerically. Numerical results show that the inclusions near contact surface could cause significant alterations in the contact pressure distribution. The stiff inclusions could toughen the surrounding material and reduce the internal stresses while the soft inclusions could increase the subsurface stresses.     

Stress field of a coated arbitrary shape inclusion

This paper presents an effective method for the plane problem of a coated inclusion of arbitrary shape embedded in an isotropic matrix subjected to uniform stresses at infinity. Based on the complex variable method combined with the expansion of Faber series and Laurent series, the complex potentials in the matrix, the coating and the arbitrary shape inclusion are given in the form of series with unknown coefficients. The stress and displacement continuous conditions on the interfaces are then used to produce a set of linear equations containing all the coefficients. Through solving these linear equations, the complex potentials are finally obtained in the three phases. Additionally, numerical results are presented and graphically shown to investigate the influence of inclusion geometry and coating on the stress distribution along the interfaces for the cases of a coated elliptic, square and triangle inclusions, respectively. It is found that the coating has little effects on the interface stress for a hard inclusion, while it impacts greatly for a soft inclusion. Especially, it is also found that the stresses show the nature of intense fluctuations near the corner of the triangle inclusion, since the inclusion in this case is similar to a wedge.     

线夹杂和线夹杂的相互作用

以短纤维复合材料为工程背景，本文利用线夹杂的工程计算模型以及无限平面中单夹杂的基本解，导出了线夹杂和线夹杂相互作用的平面问题的奇异积分方程。给出了夹杂端点的应力强度因子和夹杂界面应力的表达式，并作了具体的数值计算。     

THE INTERACTION PROBLEM BETWEEN THE ELASTIC LINE INCLUSIONS

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The Stress State of Three-Dimensional Bodies with Nonsmooth Inclusions

The stress state of a three-dimensional body with inclusions bounded by surfaces with singular lines (sets of corner points) and a conical point is studied. By determining the asymptotics of displacements and stresses at the singularities of interfaces and using the generalized elastic potentials of single and double layers, the problem posed is reduced to a system of singular integral equations. The results obtained are used to analyze the stress state of a body with a circular conical inclusion     

Fourier series based FE analysis of a disc under prescribed displacements–elastic stress study

This paper examines the numerical displacements and stresses developed around a disc under horizontal prescribed displacements and at the interface separating it from the surrounding elastic soil. Since the geometry of the problem exhibits axial symmetry and the loading is non-axisymmetric, the semi-analytical FE approach is used as it proves to be efficient and economical. First, both analytical and numerical expressions for soil reaction are established and compared. Results of comparison show a very good agreement. Then, for different values of the soil Poisson’s ratio, normal radial stresses, orthoradial stresses and shear stresses distributions along radial distance reaching 20r _d (r _d is the disc radius) are presented for a disc that has either perfectly smooth or perfectly rough interfaces with the elastic medium. The paper finishes by showing the effect of the soil Poisson’s ratio as well as the relative soil/interface stiffness on the stresses developed at the interface locations.     

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model, the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces. By using the complex function method and the technique of conformal mapping, the exact solutions of the electroelastic fields in fiber, coating, and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads. Furthermore, the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces. Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers, the aspect ratio of the fiber section, and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites. The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding, but it can be improved by the surface/interface stresses at the small scale, which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.     

Problem of interaction of thin rigid needle-shaped inclusions located between different elastic materials

We study a piecewise-homogeneous elastic plane composed of two half-planes with different elastic parameters and two thin rigid needle-shaped inclusions located between them. One inclusion is rigidly connected with the environment, and the other inclusion is not, while contacting with it like a smooth rigid punch. We consider the plane deformed state generated by stresses given at infinity. The problem is reduced to a combination of a matrix Riemann boundary-value problem from the theory of analytic functions and a matrix Hilbert problem, which can be solved in terms of integrals through the reduction to two separate scalar Riemann boundary-value problems on a twosheeted Riemann surface.We explicitly obtain the complex potentials of the composite elastic plane, the stress intensity factors near the tips of the inclusion, and the rotation angles of the inclusions. We also present numerical examples illustrating how the stresses near the inclusions depend on the elastic and geometric parameters of the problem.     

Interface crack with a contact zone in an isotropic bimaterial under thermomechanical loading

A plane problem for a thermally insulated interface crack with a contact zone in an isotropic bimaterial under tension–shear mechanical loading and a temperature flux is considered. The expressions for the stresses and the electrical flux as well as for the derivatives of the displacement and the temperature jumps at the material interfaces via sectionally holomorphic mechanical and thermal potential functions are given. After the solution of the thermal problem the inhomogeneous combined Dirichlet–Riemann boundary value problem is formulated and solved exactly. The stresses at the interface and the stress intensity factors at the singular points are presented in a clear analytical form. Special attention is devoted to the case of a small contact zone when the stress intensity factors can be presented in form similar to the associated presentation for an “open” crack model. A transcendental equation and an asymptotic analytic formula for the determination of the real contact zone length are derived. It is shown that for a certain bimaterial this length as well as the correspondent stress intensity factor are defined by a single parameter which depends on the normal-shear loading and the heat flux.     

兼具基体蠕变和轻度界面蠕变的复合材料的本构特性

金属基复合材料的基体蠕变特性在一定的温度与应力下表现明显，当界面为非理想并具有粘弹性性质时，其对复合材料的整体蠕变亦有重要影响．本文利用具有非理想界面的复合材料的Ｍｏｒｉ－Ｔａｎａｋａ方法，研究了既具有基体蠕变又具有界面轻度蠕变的复合材料的本构关系，给出了各微结构参量对复合材料整体蠕变特性的影响     

Determination of stresses in ellipsoidal rigid inclusions

A problem of determining stresses in isolated ellipsoidal rigid inclusions contained in an isotropic elastic space exposed to the impact of external forces uniformly distributed at infinity is considered. Examples of inclusions in the form of oblate and prolate spheroids are studied when the problem has a unique solution.     

兼具基体蠕变和轻度界面蠕变的复合材料的本构特性

金属基复合材料的基体蠕变特性在一定的温度与应力下表现明显，当界面为非理想并具有粘弹性性质时，其对复合材料的整体蠕变亦有重要影响．本文利用具有非理想界面的复合材料的Ｍｏｒｉ－Ｔａｎａｋａ方法，研究了既具有基体蠕变又具有界面轻度蠕变的复合材料的本构关系，给出了各微结构参量对复合材料整体蠕变特性的影响     

Effect of interface stresses on the image force and stability of an edge dislocation inside a nanoscale cylindrical inclusion

Dislocation mobility and stability in inclusions can affect the mechanical behaviors of the composites. In this paper, the problem of an edge dislocation located within a nanoscale cylindrical inclusion incorporating interface stress is first considered. The explicit expression for the image force acting on the edge dislocation is obtained by means of a complex variable method. The influence of the interface effects and the size of the inclusion on the image force is evaluated. The results indicate that the impact of interface stress on the image force and the equilibrium positions of the edge dislocation inside the inclusion becomes remarkable when the radius of the inclusion is reduced to nanometer scale. The force acting on the edge dislocation produced by the interface stress will increase with the decrease of the radius of the inclusion and depends on the inclusion size which differs from the classical solution. The stability of the dislocation inside a nanoscale inclusion is also analyzed. The condition of the dislocation stability and the critical radius of the inclusion are revised for considering interface stresses.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

Dynamic stress concentration for multiple multilayered inclusions embedded in an elastic half-space subjected to SH-waves

The dynamic stress concentration factor (DSCF) is evaluated along the interfaces of multiple multilayered inclusions embedded in a half-space when subjected to a plane harmonic SH-wave. A weak form of Helmholtz equation is utilized to derive a non-hypersingular boundary integral equations to compute the stresses. Eliminating the need to rely on hypersingular integrals, greatly simplifies the procedure. The numerical results obtained by the proposed method, are validated against analytical solutions.Various contributing factors that can influence the DSCF are investigated, including multiple scattering, layering, stiffness of the adjacent inclusions, and impedance contrast of the layers. The DSCF is found to be highly prone to these changes, particularly with the soft materials. Therefore, accurate analysis of stresses requires models that consider multiple scattering and layering. The presented result could be used for predicting the seismic failure of pipes and underground tunnels and for estimating the stress failure in strong ground motion seismology due to subsurface irregularities.     

Thermomechanics of solids with general imperfect coherent interfaces

The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect coherent interfaces in view of their thermomechanical behavior and to establish a unified computational framework to model all classes of such interfaces using the finite element method. Conventionally, imperfect interfaces with respect to their thermal behavior are often restricted to being either highly conducting (HC) or lowly conducting (LC) also known as Kapitza. The interface model here is general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Clearly, in extreme cases, the current model simplifies to HC and LC interfaces. A new characteristic of the general imperfect interface is that the interface temperature is an independent degree of freedom and, in general, is not a function of only temperatures across the interface. The interface temperature, however, must be computed using a new interface material parameter, i.e., the sensitivity. It is shown that according to the second law, the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. In particular, even if the temperature jump at the interface vanishes, the interface temperature may be different from the temperatures across the interface. This finding allows for a better, and somewhat novel, understanding of HC interfaces. That is, a HC interface implies, but is not implied by, the vanishing temperature jump across the interface. The problem is formulated such that all types of interfaces are derived from a general imperfect interface model, and therefore, we establish a unified finite element framework to model all classes of interfaces for general transient problems. Full details of the novel numerical scheme are provided. Key features of the problem are then elucidated via a series of three-dimensional numerical examples. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites and also thermal interface materials.     

3D printed,bio-inspired prototypes and analytical models for structured suture interfaces with geometrically-tuned deformation and failure behavior

Geometrically structured interfaces in nature possess enhanced, and often surprising, mechanical properties, and provide inspiration for materials design. This paper investigates the mechanics of deformation and failure mechanisms of suture interface designs through analytical models and experiments on 3D printed polymer physical prototypes. Suture waveforms with generalized trapezoidal geometries (trapezoidal, rectangular, anti-trapezoidal, and triangular) are studied and characterized by several important geometric parameters: the presence or absence of a bonded tip region, the tip angle, and the geometry. It is shown that a wide range (in some cases as great as an order of magnitude) in stiffness, strength, and toughness is achievable dependent on tip bonding, tip angle, and geometry. Suture interfaces with a bonded tip region exhibit a higher initial stiffness due to the greater load bearing by the skeletal teeth, a double peak in the stress–strain curve corresponding to the failure of the bonded tip and the failure of the slanted interface region or tooth, respectively, and an additional failure and toughening mechanism due to the failure of the bonded tip. Anti-trapezoidal geometries promote the greatest amplification of properties for suture interfaces with a bonded tip due the large tip interface area. The tip angle and geometry govern the stress distributions in the teeth and the ratio of normal to shear stresses in the interfacial layers, which together determine the failure mechanism of the interface and/or the teeth. Rectangular suture interfaces fail by simple shearing of the interfaces. Trapezoidal and triangular suture interfaces fail by a combination of shear and tensile normal stresses in the interface, leading to plastic deformation, cavitation events, and subsequent stretching of interface ligaments with mostly elastic deformation in the teeth. Anti-trapezoidal suture interfaces with small tip angles have high stress concentrations in the teeth and fail catastrophically by tooth failure, whereas larger tip angles exhibit a shear failure of the interfaces. Therefore, larger tip angles and trapezoidal or triangular geometries promote graceful failure, and smaller tip angles and anti-trapezoidal geometries promote more brittle-like failure. This dependence is reminiscent of biological systems, which exhibit a range of failure behaviors with limited materials and varied geometry. Triangular geometries uniquely exhibit uniform stress distributions in its teeth and promote the greatest amplification of mechanical properties. In both the bonded and unbonded cases, the predictions from the presented analytical models and experimental results on 3D printed prototypes show excellent agreement. This validates the analytical models and allows for the models to be used as a tool for the design of new materials and interfaces with tailored mechanical behavior.     

双周期分布圆形弹性夹杂平面热弹性问题

研究了含双周期分布圆形弹性夹杂的无限弹性平面在均匀拉伸和均匀温变下的弹性响应问题．运用Isida的区域单元法和复势函数的级数展开技术,将问题转化为线性方程组的求解．数值结果表明：相邻夹杂问距过大或过小都不利于减小界面应力,当相邻夹杂中心间距与夹杂半径之比为2．2～2．8时,界面剪切应力与环向应力的极大值最小;比值为2．5～3．5时,界面最大径向应力值最小;并且该比值范围不随两相材料弹性模量之比和热膨胀系数之比而变化．     

Interface Forces in Laterally Impacted Steel Tubes

In engineering mechanisms, solid bodies frequently come to a contact with a variety of geometric and kinematic situations. There has been a trend to express the interaction of the contacted bodies in the form of equivalent interface forces. The interface force represents the level of load transferred from one body to another. In a static or quasi-static contact problem, the interface forces could be sensibly evaluated by integrating the normal and the shear stresses over the common interfaces. In a dynamic contact, the interface stresses and subsequently the interface forces happen to be more complicated. They are, furthermore, affected by other parameters such as inertia forces, stress waves propagation, the material strain rate dependency and damping. This paper reports interface forces recorded in a series of experimental impact tests on axially pre-compressed steel tubes along with those from the numerical simulations of the tests. To monitor the so called impact loads, two small steel rings as load cells have been built in the striker. Based on the experimental and numerical results, the concept of equivalent interface forces in the impacted tubes has been verified. It has been highlighted that the interface forces (or the impact loads) may vary on the striker or the specimen themselves, depending on the measuring locations. Effects of axial compressions on the interface forces picked up by the striker load cells, impact loads imparted to the specimen supports and on the impact duration have been discussed. It has been reported that the initial compression applied to the tubes does not remain constant during and after the impact event. The amount of variations also depends on the initial level of the tube compression.