Effects of Initial Defects on Effective Elastic Modulus of Concrete with Mesostructure

An exquisite mesostructure model was presented to predict the effective elastic modulus of concrete,in which concrete is realized as a four-phase composite material consisting of coarse aggregates,mortar matrix,interfacial transition zone(ITZ),and initial defects.With the three-dimensional(3D)finite element(FE)simulation,the highly heterogeneous composite elastic behavior of concrete was modeled,and the predicted results were compared with theoretical estimations for validation.Monte Carlo(MC)simulations were performed with the proposed mesostructure model to investigate the various factors of initial defects influencing the elastic modulus of concrete,such as the shape and concentration(pore volume fraction or crack density)of microspores and microcracks.It is found that the effective elastic modulus of concrete decreases with the increase of initial defects concentration,while the distribution and shape characteristics also exert certain influences due to the stress concentration caused by irregular inclusion shape.

INTERFACE EFFECT ON THE EFFECTIVE BULK MODULUS OF A PARTICLE-REINFORCED COMPOSITE

Classical micromechanical methods for calculating the effective moduli of a heteroge- neous material are generalized to include the interface(surface)effect.By using Hashin's Composite Sphere Assemblage(CSA)model,a new expression of the bulk modulus for a particle-reinforced com- posite is derived.It is emphasized that the present study is within the finite-deformation framework such that the effective properties are not influenced by the interface stress itself solely,but influenced by the change of the interface stress due to changes of the shape and size of the interface.Hence some inadequacies in previous papers are pointed out.

The influence of defects on the effective Young's modulus of a defective solid

It is difficult to establish structure-property relationships in a defective solid because of its inhomogeneous-geometry microstructure caused by defects. In the present research, the effects of pores and cracks on the Young’s modulus of a defective solid are studied. Based on the law of the conservation of energy, mathematical formulations are proposed to indicate how the shape, size, and distribution of defects affect the effective Young’s modulus. In this approach, detailed equations are illustrated to represent the shape and size of defects on the effective Young’s modulus. Different from the results obtained from the traditional empirical analyses, mixture law or statistical method, for the first time, our results from the finite element method （FEM） and strict analytical calculation show that the influence of pore radius and crack length on the effective Young’s modulus can be quantified. It is found that the longest crack in a typical microstructure of ceramic coating dominates the contribution of the effective Young’s modulus in the vertical direction of the crack.

An improved model for predicting effective Young's modulus of the twisted structure under cyclic loading:taking into account the untwisting effect

Twist structures have diverse applications, ranging from dragline, electrical cable, and intelligent structure. Among these applications, tension deformation can＇t be avoided during the fabrication and working processes, which often leads to the twist structure rotation （called untwisting effect） and twist pitch increasing. As a consequence, this untwisting behavior has a large effect on the effective Young＇s modulus. In this paper, we present an improved model based on the classical Costello＇s theory to predict the effective Young＇s modulus of the basic structure, twisted by three same copper strands under cyclic loading. Series of experiments were carried out to verify the present model taking into account the untwisting effect. The experimental results have better agreements with the presented model than the common Costello＇s model.

Theoretical prediction of effective elastic constants for new intermetallic compound porous material

Based on microstructure analysis of the new Ti-A1 intermetallic compound porous material, a micromechanics model of heterogeneous Plateau porous structure was established and calculation formulas of elastic constants （including effective elastic modulus, effective shear elastic modulus and effective Poisson ratio） were derived by the energy method for this porous material. Calculation results show that both the effective elastic modulus and effective shear elastic modulus increase with the increase of the relative density while the effective Poisson ratio decreases. Compared with the currently-existing hexagonal honeycomb model and micromechanics model of composite materials, the micromechanics model of heterogeneous Plateau porous structure in this study is more suitable for characterizing the medium-density porous material and more accurate for predicting the effective elastic constants of the medium-density porous material. Moreover, the obtained explicit expressions of the effective elastic constants in term of the relative density rather than the microstructural parameters for the uniform and regular Plateau porous structure are more convenient to engineering application.

MODULUS PREDICTION AND DISCUSSION OF REINFORCED SYNTACTIC FOAMS WITH COATED HOLLOW SPHERICAL INCLUSIONS

The elastic properties of syntactic foams with coated hollow spherical inclusions have been studied by means of Mori and Tanaka's concept of average stress in the matrix and Eshelby's equivalent inclusion theories.Some formulae to predict the effective modulus of this material have been derived theoretically.Based on these formulae,the influences of coating parameters such as the thickness and (Poisson's) ratio on the modulus of the syntactic foams have been discussed at the same time.

THE EFFECTIVE MODULI OF COMPOSITE REINFORCED BY SPHERICALCOATING PARTICLES

The effective moduli of composite reinforced by spherical coating particles are investigated by the four phase spheroidal model and the theory of equivalent media. The theoretical predicting formulae of bulk modulus and shear modulus have been derived for this kind of composite in this paper. These formulae can reduce to the results of three phase spheroidal model which had been obtained by others for composite reinforced by particles.

A Modulus Variation Model of Concrete under External Sulfate Attack:New Perspective from Statistical Evolution of Microcracks

A numerical model was proposed to describe the modulus variation of mortar exposed to external sulfate attack and the effectivity was verified by experiments. The model joints statistical evolution of microcracks to effective elastic modulus with microcracks and is applied to predict the damage degree of mortar attacked by sulfate. The experimental results show that the model can predict the modulus variation development of the specimen and the microcraks density. The elastic modulus values calculated by the model are consistent with that measured by experiments. The model focuses on nucleation of microcracks and finds that the theoretical results of microcracks number density show a linear growth over time in mortar. Compared with other sulfate attack damage model, this model provides a more suitable damage evolution equation that can be used to analyze the chemically assisted damage.

EXACT SOLUTION FOR ORTHOTROPIC MATERIALS WEAKENED BY DOUBLY PERIODIC CRACKS OF UNEQUAL SIZE UNDER ANTIPLANE SHEAR

Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.

Quantifying Creep of Concrete Filled Steel Tubes

Using age adjusted effective modulus(AAEM)method,creep of concrete filled steel tube(CFST)member was formulated considering of creep coefficient and aging coefficient.Ten CFST specimens were tested including eight for creep and two for shrinkage.The experimental result was compared with the computed result using AAEM in which the creep coefficient was taken from calibration of ACI model based on experimental result on sealed concrete,and aging coefficient was supplied from relaxation test on sealed concrete specimen.Furthermore,the creep of CFST member was analyzed using author's own subroutine to input concrete properties through user programmable feature(UPF)in ANSYS software.Comparison was made on authors' own experimental database,some existing experimental results,and results from AAEM and numerical analysis.Finally,the conditions of applicability of AAEM method are put forward,and numerical approach to compute creep of CFST specimen is delineated.

Research on vertical deformation during construction of Shanghai World Financial Center

Shanghai World Financial Center is one of the highest buildings in the world, of which cumulation of vertical deformation during construction is significant and worth investigating. A refined finite element model was developed to conduct full-process analysis of construction of super-high rise buildings like Shanghai World Financial Center, in which the discrete analysis method of time-varying structures and age-adjusted effective modulus method were both used. In the finite element analysis, the whole construction process was divided into a series of stages, each with a structural system that is a part of the whole structure and with different material parameters, geometrical parameters, loading and boundary conditions. The whole construction process of Shanghai World Financial Center in consideration of creep of concrete was simulated successfully by using the finite element model and the analytical method developed. With respect to different construction stage, the total vertical deformation, inter-floor compression deformation and the relative deformation between the outer frame and the core-wall were obtained through the analysis. The comparison between the results from the stage-wise full-process analysis of construction with and without considering the creep and the results from the conventional analysis of the whole building under the total load from all self-weight and construction applied to the structure "in one go" shows that the cumulative effect on the deformation from the construction process and the creep effect need to be considered in analyzing the deformation of Shanghai World Financial Center, and the super-high rise buildings suchlike. Finally, the simulation results correlate well with the monitoring results-a proof of the feasibility and the validity of this paper.

DIFFERENTIAL GEOMETRICAL METHOD IN ELASTICCOMPOSITE WITH IMPERFECT INTERFACES

A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions. All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions. Based on this, the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived. Under three limiting conditions of sphere, disk and needle shaped inclusions, the results of this paper will return to the bounds obtained by Hashin([6]) (1992).

Analytical and Numerical Modeling for Flexible Pipes

The unbonded flexible pipe of eight layers, in which all the layers except the carcass layer are assumed to have isotropic properties, has been analyzed. Specifically, the carcass layer shows the orthotropic characteristics. The effective elastic moduli of the carcass layer have been developed in terms of the influence of deformation to stiffness. With consideration of the effective elastic moduli, the structure can be properly analyzed. Also the relative movements of tendons and relative displacements of wires in helical armour layer have been investigated. A three-dimensional nonlinear finite element model has been presented to predict the response of flexible pipes under axial force and torque. Further, the friction and contact of interlayer have been considered. Comparison between the finite element model and experimental results obtained in literature has been given and discussed, which might provide practical and technical support for the application of unbonded flexible pipes.

Vibration analysis of foam plates based on cell volume distribution

In this paper, vibration analysis of irregular-closed-cell foam plates is per- formed. A cell volume distribution coefficient is introduced to modify the original Gibson- Ashby equations of effective Young＇s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution pa- rameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure.

FM-BEM Evaluation for Effective Elastic Moduli of Microcracked Solids

A fast multipole boundary element method （FM-BEM） was applied for the analysis of microcracked solids. Both the computational complexity and memory requirement are reduced to O（N）, where N is the number of degrees of freedom. The effective elastic moduli of a 2-D solid containing thousands of randomly distributed microcracks were evaluated using the FM-BEM. The results prove that both the differential method and the method proposed by Feng and Yu provide satisfactory estimates to such problems. The effect of a non-uniform distribution of microcracks has been studied using a novel model. The numerical results show that the non-uniform distribution induces a small increase in the global stiffness.

Effective properties of a porous inhomogeneously polarized by direction piezoceramic material with full metalized pore boundaries:finite element analysis

This paper concerns the homogenization problems for porous piezocomposites with infinitely thin metalized pore surfaces.To determine the effective properties,we used the effective moduli method and the finite element approaches,realized in the ANSYS package.As a simple model of the representative volume,we applied a unit cell of porous piezoceramic material in the form of a cube with one spherical pore.We modeled metallization by introducing an additional layer of material with very large permittivity coefficients along the pore boundary.Then we simulated the nonuniform polarization field around the pore.For taking this effect into account,we previously solved the electrostatic problem for a porous dielectric material with the same geometric structure.From this problem,we obtained the polarization field in the porous piezomaterial;after that,we modified the material properties of the finite elements from dielectric to piezoelectric with element coordinate systems whose corresponding axes rotated along the polarization vectors.As a result,we obtained the porous unit cell of an inhomogeneously polarized piezoceramic matrix.From the solutions of these homogenization problems,we observed that the examined porous piezoceramics composite with metalized pore boundaries has more extensive effective transverse and shear piezomoduli,and effective dielectric constants compared to the conventional porous piezoceramics.The analysis also showed that the effect of the polarization field inhomogeneity is insignificant on the ordinary porous piezoceramics;however,it is more significant on the porous piezoceramics with metalized pore surfaces.

Analysis of porosity influence on the effective moduli of ceramic matrix PZT composite using the simplified finite element model

The problem of determining the effective moduli of a ceramic matrix piezocomposite with respect to multiscale porosity was considered.To solve the homogenization problem,the method of effective moduli in the standard formulation,the finite element method and the ANSYS computational package were used.Various models of two-phase and three-phase composites consisting of a piezoceramic matrix,elastic inclusions of corundum and pores of various sizes have been investigated.Finite element models of representative volumes of 3–0 and 3–0–0 connectivities were developed.The results of computational experiments showed that effective moduli depend quite significantly not only on the volume fractions of inclusions and pores,but also on the structure and size of pores in comparison with the characteristic sizes of inclusions.

Variational bounds of the effective moduli of piezoelectric composites

The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric materials.The auxiliary problem is very much simplified by selecting the reference medium as a linearly isotropic elastic medium.The electromechanical fields in the inhomogeneous piezoelectrics are simulated by introducing into the homogeneous reference medium certain eigenstresses and eigen electric fields.A closed-form solution can be obtained for the disturbance fields,which is convenient for the manipulation of the energy functional.As an application,a two-phase piezoelectric composite with nonpiezoelectric matrix is considered.Expressions of upper and lower bounds for the overall electromechanical moduli of the composite can be developed.These bounds are shown better than the Voigt-Reuss type ones.

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scat- tered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluat- ed. The influences of surface stress are discussed based on the numerical results.

Effects of domain unfolding and catch-like dissociation on the collective behavior of integrin-fibronectin bond clusters

To gain more understanding of cell-matrix adhesion,we consider an idealized theoretical model of a cluster of integrin-fibronectin bonds at the cell-matrix interface subjected to a dynamic ramping.The distributions of bond traction and interfacial deformation are assumed to obey classical elastic equations,whereas the dissociation/association of individual bonds as well as unfolding/refolding of fibronectin domains are described by stochastic equations.Through stochastic-elasticity coupling,we perform Monte Carlo simulations to investigate how the collective behavior and adhesion performance of the integrin-fibronectin-mediated interface are influenced by two characteristics newly incorporated in the modeling,i.e.,catchlike dissociation between integrin and fibronectin,and unfolding of repeated domains in fibronectin.The probable unfolding of fibronectin domains is found to have profound effects on the resultant adhesion energy of the integrin-fibronectin-mediated interface,and governs the failure model transiting between uniform decay and catastrophic crack-like rupture.