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2022 Vol. 43, No. 3
Published: 2022-06-28
243
True stress theory of matrix in a composite
Zheng-Ming HUANG
In mechanics of continuum media, the theories for isotropic materials have been well established. Namely, one is almost always able to find out an existing theory to resolve any mechanics problem of an isotropic material satisfactorily. In the contrast, only elastic theories for anisotropic or composite materials have been matured. The other mechanical property of the composite, such as a plastic deformation or failure and strength behavior, is essentially not well understandable through an available theory. The fundamental reason is that only the homogenized stresses in the fiber and matrix of a composite are obtainable by an existing theory. They must be converted into true values before the plastic behavior and, especially, the failure and strength property of the composite can be estimated. In this paper, the true stress theory of the matrix together with the formulae for calculating all of the matrix true stresses established by the author is summarized. The role of the matrix true stress theory in the analysis of composite plastic behavior and failure and strength property is highlighted.
2022 Vol. 43 (3): 243-256 [
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257
Energy conversion efficiency and Mechanical properties of thermoelectric composites with hollow fibers
Hollow fibers are often used in the design of thermoelectric composites structures. The presence of hollow fibers usually leads to an inhomogeneous temperature field in corresponding thermoelectric materials and local stress concentration near the fibers, which threatens the reliability of the thermoelectric materials and may eventually cause their failure. In this paper, the hollow fiber is simulated as a annular inclusion. The energy conversion efficiency and mechanical response of a thermoelectric matrix with a hollow fiber under remote current and energy flow are studied. Analytical solutions for the thermoelectric field and stress field in the composite are obtained, in the case of fully coupled nonlinear thermoelectric constitutive equations, by using the complex variable formalism and the series expansion method. The effects of the conductivity and geometric parameters of the hollow fiber on the temperature distribution, stress field and thermoelectric conversion efficiency are discussed in numerical results. It is shown that the stress around the interface increases with the inner radius of hollow fiber and interface thermal resistance, whilst the stress distribution keeps the same. In addition, it is found that the geometric parameters can have a more significant effort on the temperature field and stress field, if compared with the interface thermal resistance.
2022 Vol. 43 (3): 257-270 [
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271
Micro-mechanical Analysis of Effective Modulus of Composite Materials Based on the Principle of Equivalent Eigenstrain
One of the main objectives of micromechanics is to predict the effective modulus of composites. Most of micromechanics models are based on Eshelby’s equivalent inclusion method under the hypothesis of ellipsoidal inclusion. An appropriate theoretical treatment for the non- ellipsoidal inclusion problems in an inhomogeneous media is still needed to be done. In this work, we proposed a principle of averaged equivalent eigenstrain, and then developed a new analytical micromechanics method for determining the effective elastic modulus of composites. By introducing the concept of averaged eigenstrain, the average stress and average strain in the matrix and inclusion of the representative volume element are analyzed. The principle of averaged equivalent eigenstrain is thus developed based on the principle of equivalent eigenstrain. Identical to the principle of equivalent eigenstrain which was built on the corner-stone of principle of virtual work, this new principle is also applicable to the inclusions with arbitrary shapes (either convex or concave), and multiple inclusions within a solid of finite volume. Then, focusing on the long-fiber-reinforced two-phase composites, we obtain the analytic relations of the average stresses and average strains in the matrix and fiber. A combination of the averaged equivalent eigenstrain and direct homogenization method of micro-mechanics thus can determine the effective elastic moduli of two-phase composites, by selecting the different deformation model and the corresponding boundary conditions. Finally, the effective moduli of composites is predicted using the mechanical properties of fiber and matrix constituents and the volume fraction of fiber, through a MATLAB program. The engineering constants such as tensile modulus, shear modulus and Poisson’s ratio of nine types of commonly used composites were discussed in detail. After comparing the predicted values with the experimental results and the predictions from other theoretical models, it is found that the averaged relative errors of the new approach are less as that of Halphin-Tsai model and Mori-Tanaka model, which thus the new analytical method is inherently suitable for the effective modulus of more general composites (either two-phase or multi-phase composites, containing inclusions/damage of either convex or concave shapes).
2022 Vol. 43 (3): 271-283 [
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284
Study on two-dimensional contact problem for piezoelectric coating - functionally graded piezoelectric interface layer - substrate system
The sudden change of material composition and properties at the interface of multilayer elements often leads to stress concentration at the interface, resulting in cracking or creep of the interface layer, which greatly shortens the service life of piezoelectric elements.As an interface layer, functionally graded piezoelectric materials can effectively alleviate the damage caused by interface material mismatch.This paper mainly studies the electromechanical response of the structure under the action of cylindrical indenter when the interface layer of functionally graded piezoelectric material is used to connect the piezoelectric coating and substrate.Using Fourier integral transform technique, the two-dimensional plane strain contact problem of piezoelectric coating functionally graded piezoelectric layer substrate structure under the action of rigid cylindrical indenter is transformed into a singular integral equation with Cauchy kernel.Using Gauss Chebyshev integral formula, the singular integral equation is transformed into linear equations and solved numerically. The stress distribution and potential shift distribution of piezoelectric coating functionally graded piezoelectric layer substrate structure under the action of cylindrical indenter are obtained.The numerical results show that the variation of gradient piezoelectric material parameters has an important influence on the electromechanical response of the structure.The research results of this paper have important theoretical guiding significance for using functionally graded piezoelectric interface layer to eliminate the interface failure caused by stress discontinuity at the interface. The research results can provide help for the design of functionally graded piezoelectric interface layer.
2022 Vol. 43 (3): 284-295 [
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Study on vibration characteristics of curved wall honeycomb sandwich plates
The curved-wall honeycombs have negative stiffness characteristics, which can absorb energy and isolate shocks during large deformations. They can recover themselves instead of being crushed like the traditional honeycombs after the impact loads. In this paper, the curved-wall negative stiffness honeycombs are used as the core layer and then the dynamic model of the sandwich plate is established. The equivalent elastic parameters of the curved-wall honeycomb cells are deduced including the Young's modulus, Poisson's ratio and the shear modulus. Afterwards the negative stiffness honeycomb cells are arranged periodically as the core layer of the sandwich plate. By using the Reddy’s higher-order shear deformation theory, Von-Karman large deformation relationship and Hamilton principle, the nonlinear dynamical equations of the honeycomb sandwich plate are derived. The Navier method is used to calculate the natural frequencies of the plate under the boundary conditions of simply supported on four sides. Simultaneously, the finite element model of the sandwich plate is established by the solid units, and the natural frequencies are derived by using ABAQUS software. The results show that the natural frequencies from the two methods are in good consistency, which verify the validity of the equivalent elastic parameters of the curved wall honeycomb layer. Finally, the variation characteristics of natural frequencies of the sandwich plate with different core thickness, different core thickness ratio and different curved-wall thickness are discussed when the energy absorption capacity of the honeycomb cells is better. The results obtained in this paper will provide a basis for further research on the dynamics of negative stiffness honeycomb plates and will give certain guidance for the applications of negative stiffness honeycombs to sandwich structures and vibration isolation mechanisms.
2022 Vol. 43 (3): 296-306 [
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307
Second-order approximated alogrithm of using K-S function to intergrate local performance constraints in structural topology optimization
The K-S ( Kreisselmeier-Steinhauser ) function is used to integrate local performances such as stress and fatigue life in structural topology optimization; and then a method of solving the model was proposed. First, for the single objective and multiple constraints model ( called s-model ) and multiple objective and single constraint model ( called m-model ) in the inverse programming, optimization models are established by utilizing K-S function integration based on the ICM method. The first and second order derivatives of constraint ( s-model ) and objective ( m-model ) functions on design variables are deduced. The sequential quadratic programming model is used to solve the optimization model iteratively. The iterative formula for quadratic programming model is given according to the K-T condition. Then, based on the K-S function integration, the iterative solution to s-model is described, that is, the integration method. Finally, based on K-S function integration, the iterative solution to s-model and m-model alternately is described, that is, the integration-integration method. The results show that the integration-integration method converges faster than the integration method.
2022 Vol. 43 (3): 307-317 [
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Numerical fracture analysis of fiber-reinforced concrete based on the Cosserat peridynamic model
Fiber-reinforced concrete (FRC) is a composite material made up of concrete and fibers. FRC has higher tensile strength and toughness than conventional plain concrete because of the reinforcement of fibers. Understanding the fracture behavior of FRC is vital for its application and design in construction work. The size effect of the FRC experimental specimen affects the accuracy of predicting the mechanical properties because of the micro-structures. Most existing numerical methods are unable to reproduce the complex fracture patterns of FRC, due to the lack of methods to characterize the FRC’s micro-structure. This paper proposes a numerical model of FRC based on the Cosserat peridynamic model and analyzes the crack propagation of FRC. The material points in Cosserat peridynamic model have independent rotational degrees of freedom and have the internal length to represent the size of micro-structure, which is appropriate for describing the mechanical behavior of FRC. The full-discrete method is applied in fiber modeling, and the relation of pullout displacement and shear stress is applied to obtain the peridynamic force between the fibers and the concrete matrix. And a fabric tensor of fiber distribution is defined to represent the local reinforcement and its direction. The proposed model is validated by simulating the single fiber pullout test and the numerical results show consistent with the experimental data and existing numerical results. The tension test of the notched plate and the three-point bending beam test with randomly distributed fibers are simulated to analyze the influences from the micro-structure and the fibers on crack propagation. The results indicate that the influence from micro-structure on the load-displacement curve mainly exists at the post-peak stage and has little impact on the peak value and pre-peak stage. And the micro-structure mainly influences the local damage and has little impact on the main direction of the crack path.
2022 Vol. 43 (3): 318-331 [
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Influence of Heating-Cooling Process on Residual Stress of Double Wall Metal Heat Exchanger Tube
The steam generator in the nuclear power plant of lead or sodium-cooled fast reactor is used for heat exchange between liquid metal and water. The heat exchange part of the steam generator is composed of heat exchange tubes arranged in a row. Bonded double-wall pipe is a kind of pipe with high heat transfer efficiency and resistance to crack propagation. Residual pressure exists between the inner and outer tubes of this kind of tubee, which is a sign that the inner and outer tubes are pressed together. However, after rising to high temperature and then getting cooled, the residual pressure between the inner and outer tubes may disappear and cause detachment. Temperature in order to know the specific influence of joint type double-wall tube, this paper designs a stretch of the double-wall pipe, and at the same time, the finite element numerical simulation method, the simulation of the pipe processing preparation and residual stress between the inner and outer pipe is obtained, and then simulated the process of cooling down after heating, analyzed the change of residual stress and strain state of the heat exchanger tube, and verified by preliminary tests. Through the study, the results show that the plastic deformation caused by the temperature change is the main reason for the change of residual stress between the tubes. The method of controlling the degree of tube processing by controlling the tube processing is expected to cope with the effect of temperature variation on tube stability.
2022 Vol. 43 (3): 332-343 [
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344
Research on Vibration, Bending and Buckling Characteristics of Functionally Graded Sandwich Microbeams with Size Effects
This paper proposed a functionally graded sandwich microbeam model considering size effects within the frameworks of the modified strain gradient theory and a refined high-order shear deformation theory. The material distributions were assumed to vary in the thickness direction and estimated through the Mori-Tanaka homogenization scheme. A two-node differential quadrature finite element with 18 degrees of freedom was established by combining the differential quadrature rule and Gauss-Lobatto quadrature rule to solve the high-order boundary value problems.The efficacy of our theoretical model and numerical method was validated by comparing the degenerated results with the reported ones. Finally, the effects of boundary conditions, material length scale parameters, functional gradient index, slenderness ratio, and thickness ratio on the static and dynamic characteristics of functionally graded sandwich microbeams were discussed. It was revealed that the introduction of strain gradients has significant impact on the static responses, vibration frequencies, buckling loads together with the related mode shapes of functionally graded sandwich microbeams. The results obtained were expected to provide data accumulation and methodological basis for the design of load-bearing devices in MEMS.
2022 Vol. 43 (3): 344-359 [
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360
Multiple scattering analysis of elastic wave propagation in defective rock mass
Multiple scattering effect of elastic waves propagating in rocks with defects is studied theoretically and numerically. First, a double elliptical model is established to describe the multiple scattering paths of elastic wave between two elliptical defects. Second, the wave equations and boundary conditions on the defect interface governing opening displacement generating scattering field are derived based on the basic solution of Green function and the boundary integral method. The opening displacement of the defect boundary induced by the interaction of waves and defects are characterized in terms of a "stiffness matrix" that depends on both the incident harmonic and material properties. The problem of multiple scattering of elastic wave propagation in rocks is then analyzed for the dispersion and attenuation in order to evaluate the multiple scattering effect on the wave speed and amplitude. The calculation results show that compared with the single elliptical defect model, the dispersion and attenuation of the elastic wave are stronger due to the effect of multi-scattering. Moreover, the affected region of a defect is given quantitatively about six times of characteristic scale of the defect, which is basically consistent with the macro porosity limit of multiple scattering. This scale separates the multiple scattering strong interaction from the linear superposition of the single scattering effect. The multi-scale effect of elastic wave propagation is further discussed. It is found that the frequency of Rayleigh peak, Mie peak on the dispersion curve and attenuation peak has a definite quantitative relationship with the ratio of the long axis of the ellipse to the incident wavelength. The corresponding numerical simulation results show that the interaction between elastic wave and defect induces the interface wave at the defect interface, and the frequency dependence of these interface waves affects the dispersion and attenuation characteristics of the macroscopic propagation of elastic wave. Within this double defect model, the multiple scattering for interaction of the elastic waves and the defect can enhance dispersion and attenuation.
2022 Vol. 43 (3): 360-368 [
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