Equations of vertical and horizontal displacements in a half space rock foundation caused by aflexible plate loading test using concrete facing which restricts free horizontal displacements of the underlying rock surface, are developed. An optimal point of measurements for displacements in order to obtain Young's modulus and Poisson's ratio of the intact rock foundation is also discussed.

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Before considering about numerical analysis for earthquake-faults, we have to get much data for it. We have to get displacements of model experiment and constitutive relation of materials, for example. In this research, we perform model experiment of earthquake-faults and measure surface displecements by image analysis. And then we tried to estimate constitutive relation of the material (zeratin) using back-analysis for stress field.

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Considering the cracks which are related to shear failure in reinforced concrete member model subjected to four point bending, we discuss the extension behavior of fracture cracks by using the maximum energy release rate criterion. For the calculation of energy release rate, we use E-integral method by the finite element method.The numerical analyses for some ratios of shear span to effective depth (a/d) are examined. The numerical results arerepresented in the relationship between the energy release rate of shear crack and bending crack for several a/d.It becomes clear that there are two areas which either the energy release rate of shear crack or of bending crack is dominant. The detailed fracture modes of shear failure are also examined for several a/d.

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Present paper describes how to solve the governing differential equations based on Reddy's third-order shear deformable plate theory. First the differential operator method is developed to uncouplethe governing equations of an orthotropic plate, and then the uncoupling of the governing equations results in an eighth-order partial differential equation. Secondary, a potential function method is applied to the governing equations to recast the governing equations of transversely isotropicand isotropic plates into two independent equations, i. e. one is a second-order partial differential equation and the other is sixth-order one. Finally, Levy type single series solutions for an isotropic plate are derived, and then numerical results are presented for the square plates with different boundary conditions and subjected to a uniform load.

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A stochastic approach to estimate the elastic buckling strength of truss structures is developed by combining the bifurcation and probabilistic theories, and applied to the actual data of a truss dome structure. According to the data of the initial imperfection of truss members, which can be regarded as statistical variables, the analytical expression for the probability density function of the strength of the overall structure is obtained together with several parameters that canbe determined by a few computations. The applicability of the approach is evaluated in the context of structural design and its feasibility is compared with the result by Monte-Carlo simulation.

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This paper proposes a non-iterative identification method to estimate the structural parameters of existing structure subject to seismic loading. The generalized inverse matrix obtained from singular value decomposition was employed to identify the unknown parameters in frequency domain. Because of non-iterative analysis, it requires neither the initial estimate nor the calculation of Jacobean matrices. Thus, it can reduce the CPU time. In this paper, the numerical simulation was carried out to verify the validity and to grasp the basic characteristics of proposed method. Furthermore, this method applied to the observed data of shaking table model tests. From the both investigations, the validity of proposed method was confirmed for the structural parameter identification.

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Strong earthquake motion record obtained from a seismometer array record at Kobe Port Island during the Hogoken Nambu earthquake of January 1995 is employed to inversely analyze the dynamic soil parameters, i. e. dynamic shear modulus and damping ratio of each layer. The extended Baysian method (EBM) is employed to overcome the problem of illposedness. Some trade off between the shear modulus and the damping ratio is observed. Also the solution is not unique. Such kind of trade off have been successfuly solved by EBM for relatively smaller earthquake motion records in the previous studies (Honjo et. al, 1997, 1998). It is speculated that this problem arose because of the extraordinarily strong earthquake motion record obtained, and approximating this phenomena by the equivalent linear model. Discussion is made both from statistical and soil dynamic view points on the problem.

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The covariance matrix of observation error is very important to estimate the credibility of the updated model. Besides the accuracy of the measurement devices, modeling error is also very importan as a factor of observation error. However, it is very difficult to consider every factor of the modeling error. In order to determine the level of the observation error from observation data statistically, the objective function for the inverse analysis is extended based on the maximum likelihood method. As an example, we discuss the identification problem of dynamic soil properties, in which the estimation of observation error and model selection by using information criteria such as AIC are demonstrated.

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Most of the inverse problems encountered in geotechnical inverse analysis are illposed, thus some type of regularization procedure need to be applied. In this presentation, several regularization procedures are compared through a simple problem, a laterally loaded pile (2.4m long) in homogeneous sand in a laboratory pit. The regularization procedures employed are the minimum norm solution based on the singular value decomposition, Kitagawa's solution, L curve method and the extended Bayesian method (EBM) with ABIC (Akaike Bayesian Information Criterion). The obtained solutions are compared with the maximum likelihood solution (ML), and characteristic of each type of solution is discussed. Furthermore, the observation noise of different levels are applied to the original data to see the change of solutions for each method. The EMB showed superiority to other types of regularization procedure in a sense it automatically accomplished the best matching between the observation data and the prior information.

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In database, there has been a growing interest in efficient discovery, which is beyond the power of current dataprocessing functions, of interesting knowledge rule from huge database. The technology is called“data mining”.
In this paper, we introduce data mining with a view to discuss applications of artificial life theory for data mining. The mechanism and major physical parameters for the generation of red tide are investigated within the framework of statistical data mining. Data mining means to discover objectively knowledge hidden in vast amountof data, and by means of neural network, data of Tokyo bay are analyzed. It is found that the usefulness of this data mining procedure for non-structural system identification.

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Residual stress in an elastic body is a divergence free, second order symmetric tensor whose traction vanishes at the boundary. We consider the problem of determining the residual stress and the Lame parameters of an elasitic body by measuring the displacements and the tractions at the boundary. Mathematically, these measurements made at the boundary are encoded in the so-called Dirichlet to Neumann map. We prove that it is possible to recover all the components of the residual stress together with the Lame parameters at the boundary from the Dirichlet to Neumann map by making use of an explicit form of the surface impedance tensor.

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We overview the Fast Multipole Method (FMM) and the Barnes-Hut tree method. These algorithms evaluate mutual gravitational interaction between N particles in O (N) or O (N log N) times, respectively. We present basic algorithms as well as recent developments, such as Anderson's method of using Poisson's formula, the use of FFT, and other optimization techniques. We also summarize the current states of two algorithms. Though FMM with O (N) scaling is theoretically preferred over O (N log N) tree method, comparisons of existing implementations proved otherwize.

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The scattering problem for cracks in the three-dimensional elastic body is formulated by the boundary integral equations. The process to solve the boundary integral equations is briefly summarized and the expression of the scattering cross-section is shown for the scattering problem by cracks. In the numerical analysis, the frequency property of the scattering cross-section is considered for planar configurations of cracks. The multiple scattering effect is investigated for the scattering cross-section and the influence of the crack distance is discussed.

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Since scattering and propagation of elastic waves in anisotropic materials are quite different from those in isotropic materials, it is necessary to investigate scattering characteristics for quantitative nondestructive evaluation of anisotropic materials. In this study, a time domain boundary element method is developed with use of fundamental solutions for a general anisotropic solid. The boundary element method is applied to the scattering of elastic waves by various defects such as a cavity and an inclusion, and the radiation patterns and phases of scattering waves are discussed.

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The boundary element method (BEM) is extensively applied to numerical analysis. Because the formulation represents solutions of the governing equations, the method is applicable to analyze a variety of quantitative measurements. Acoustic emission (AE) is a phenomenon where elastic waves are detected due to microcracking. Thus, BEM formulation of elastodynamics is applied to quantitative waveform analysis of AE waveforms. Results of the inverse analysis are discussed on creak kinetics and kinematics.

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Time domain boundary element method of viscoelastic wave propagation problems is presented and some numerical implementations are pointed out. In time domain, the time domain fundamental singular solutions of viscoelastic wave propagation problem cannot given analytically in closed form. If the fundamental singular solution of dynamic viscoelasticity is obtained, the formulation of the boundary integral equation and discretized equation of BEM are directed by the theory of reciprocity as well as elastodynamics. In frequency domain, however, the fundamental singular solutions of viscoleastic wave propagation problems are given analytically in closed form. So, the fundamental singular solutions in time domain are derived from corresponding frequecny domain fundamental singular solutions by Fourier transformation with numerical integration method. In this paper, time domain boundary element method is derived from corresponding frequecny domain boundary element method by Fourier transformation with numerical integration method. The numerical implementations are shown to prove the availability of this numerical method to solve time domain wave propagation problems in dynamic viscoelasticity.

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This paper discusses the boundary element method with use of new scheme and procedure applied to numerical simulation of non-linear water wave motions in a tank with wave maker. The methods based on the mixed Lagrangian-Eulerian scheme and direct differentiation procedure are verified its effectiveness with the motion of a solitary wave in a water tank with various configurations. Numerical results are compared with other existing solutions. Our solution procedure can be tracked large deformation of free surface caused by the mutual action between water wave and geometrical configuration of tank. The numerical simulations in the case of tank with gentle slope make clear difference on deformation process of breaking wave. The existence of similar phenomena to collision and fission which are well-known as the solutions of K-dV equation is pointed out through our numerical simulations on water wave over mound or trench and wave propagation in a steep slope tank.

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Wavelets are employed in the boundary element analysis. A wavelet BEM provides a sparse coefficient matrix by truncating a small value in the matrix entries based on a specifiedthreshold. In discretization process, the collocation method requires the wavelets as bases of anapproximate solution, while the Galerkin method requires wavelets not only as bases of numerical solutionbut as weighting functions. The wavelet BEM is usually derived by the Galerkin method because of high sparsity and good condition of the matrix. However the Galerkin method requires double integration on the boundary. Therefore, in conventional BEMs, the discretized equations are derived based on the collocation method. In this study, improvement of the wavelet collocation BEM is attempted by applying the discrete wavelet transform to the system matrix. Through numerical examples, comparison of performance of the proposed method with the collocation and Galerkin methods is carried out and the validity of the method is investigated.

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Wavelet BIEM (boundary integral equation method) has been developed as a method to reduce time and memory requirements in solving big size problems. We apply this method to two dimensional crack problems governed by the Laplace equation. The resulting algebraic equation is solved with GMRES (generalized minimum residual method). It is shown that the wavelet BIEM is more effcient than conventional method when the size of the problem is large.

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In this paper, an application of the computing point method, proposed by the authors for boundary only computation of nonlinear and inhomogeneous problem by boundary element method, is presented tothe problem with biharmonic differential operator. The original problem is decomposed into a system of simultaneous differential equations with similar harmonic operator and then boundary element formulation is employed. Nonlinear and/or inhomogeneous terms multiplied by the fundamental solution areconverted into domain integrals. Solution procedure and example computation are shown for two-dimensional problems.

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An efficient numerical method is proposed for non-axisymmetric three-dimensional corrosion problems involving axisymmetric structures. The knowledge of physical quantities (potential and current density) on the surface of corroding materials is very important in corrosion monitoring and corrosion protection. Boundary element method is suitable for corrosion analysis, because it doesn't require discretization of internal elements. Although geometry of a structure is axisymmetric, enormous number of elements is necessary to discretize the realstructure, since surface physical quantities of the axisymmetric structure are affected by otherstructures and electrodes. To reduce the boundary elements, our method is based on complex Fourier series expansion of boundary quantities in circumferential direction of axisymmetricstructures. When axisymmetric structures depart from other structures and electrodes, this method has the advantage of decreasing the number of series, because surface physical quantities are more axisymmetric. In order to demonstrate the usefulness of the method, two example problems of buried pipelines in soil and a sea-water pump for cathodic protection system are presented.

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The purpose of this paper is to present an attempt at a numerical treat ment of a kind ofunder-determined problem of the Laplace equation in two spatial dimensions. A resolutionis sought for the problem in which the Dirichlet and Neumann data are arbitrarily imposedon each part of the boundary of the domain. This new problem can be regarded as aboundary inverse problem, in which the proper boundary conditions are to be identified for the rest of the boundary. The solution of this problem is not unique. The treat mentis based on the direct variational method, and a functional is minimized by the method of the steepest descent. The minimization problem is recast into successive primary anddual boundary value problems of the Laplace equation. After numerical computations byusing the boundary elements, it is concluded that our scheme is stable, but the numericalsolutions converge to the nearest local minimum.

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A numerical method for the analysis of the wave breaking process capable of handling complex sea-beds and a free-surface was developed on the basis of the time-dependent, incompressible Navier-Stokes equations. The numerical method used the Boundary-Fitted Coordinate transformation (BFC) method consisting of the Boundary-Fitted Coordinates and Numerical Grid Generation techniques. Smoothing and relocation techniques were used to enhance accuracy and stability of the calculations. The accuracy of the present method was examined by performing calculations for the sloshing motions and plunging breaker on a uniform slope. A comparison of both the numerical method and the experimental results from LDV and image processing immediately before the breaker confirmed the validity of the numerical method.

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In the problem of incompressible media such as the Stokes flow or incompressible elasticity, the mixed finite element approximation employing the MINI element, in which the velocity field is approximated by P1 field and bubble function and pressure is approximated by P1 continuous field, is known as one of those satisfying the inf-sup (or LBB) condition. Recently, it has been shown that the MINI element is equivalent to a stabilized finite element by P¹-P¹approximation with pressure stabilization term. In this aspect, the stabilizing effect of the MINI element is evaluated by stabilizing parameter determined by the shape of the bubble function. In this work, the numerical stability of the bubble elements including the nonconforming elements in two and three dimensional problems is evaluated in the sense of the stabilized method.

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The Petrov-Galerkin finite element approximation employing the trilinear element with a bubble function is presented in this paper, which is equivalent to the stabilized finite element method in case of P¹ approximation in certain problems such as steady advection-diffusion and viscous fluid flows. As an approximated function of the weighting funciton, the trilinear interpolation function with a special bubble function called stabilized bubble is used. The stabilized bubble element is establised using the stabilized bubble function with a control parameter. The shape of the bubble function as the weighting function can be changed to attain optimal numerical viscousity. The rotating cone, the standing vortex and the driven cavity problems are performed for the numerical examples.

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A new finite element formulation and adaptive remeshing method with linear bubble function for the incompressible Navier-Stokes equations are proposed in this paper. As the numerical approach, the spacial discretization is applied the mixed interpolations for velocity and pressure fields by the bubble element and linear element, respectively. The fractional step method based on the implicit time integration is used for the discretization. To verify applicabilityof presented linear bubble function, Rayleigh-Benard convection and flow past a circular cylinder are performed for the numerical examples.

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This paper presents a parallel finite element method based on a domain decomposition method for the analysis of free-surface flows. The ALE technique is usefully applied to the deforming fluid domain. Parallel implementation of the unstructured grid based formulation is carried out on the Fujitsu AP3000. For the discretization of basic equations and boundary conditions, the stabilized finite element method including a shock capturing term is applied to the analytical domain. The method is applied to the three dimensional sloshing problem in a rectangular tank. The effect of parallelization on the efficiency of the computations are examined.

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The application of the reduction method to 1D problems such as continuous beams has been established. The method can be easy applied to 2 or 3D frameworks which are constructed as open systems. However, application of the method to closed frameworks is not genenerallized, and can not be easily understood. One of authers has proposed a method of application to closed systems. The method includes not only the deformation method but also the force method, because equilibrium and compatibility conditions are used in the simultaneous equation, and as independent variables deformations at the ends of beams are used. This paper proposes an application of the method to continua.

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This paper shows a method of an active seismic feedback control of structure. To take into account the time delay of control force, kalman filtering prediction algorithm is used for the prediction of mode response in a multi degree of freedom system. The relation between the characteristics of sturucture and the precision of prediction was examined by caluculating a single degree of freedom system. Simulation analysis was used to clarify the usefulness and the characteristics of the proposed method. It is concluded that the proposed method has effective control efficiency than a system not taking account of time delay of control force.

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In analyses of buckling and geometrical nonliner buckling behavior of structures which deform largely, tangent stiffness matrix and geometric stiffness matrix play an important role. This paper shows that a general form of the geometric stiffness is derived from differentiating two shape matrices, the connection matrix and the equilibrium matrix, with respect to any joint displacement. When the general equation mentioned above is used, even the buckling analysis and the finite displacement analysis of frames costituting of arbitary curved member and rigid joints such as arch structures can be possible.

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Present paper describes a new development for axi-symmetric rigid body spring model (RBSM). Usual RBSM does not take into account an element strain. In oder to analyze accurate stress wave propagation phemomenon, in this study, the concept of element strain has been introduced to estimate exact element properties. Numerical results obtained for axi-symmetric impact problems have a good agreement with the exact solutions based on the theory of elastodynamics.

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The concept of cover is employed from manifold method into voxel analysis and applied to large deformation analysis of 3D solid structure. To overcome the problem of locking due to distorted element in large deformation analysis of solid structure, remeshing technique using voxel cover is proposed. Also, the mapping technique of displacements and stresses when remeshing is carried out is discussed. Finally, the treatment of the boundary conditions is discussed, and the technique of balancing forces at the displacement boundary conditions is proposed. Finally, the separate analysis model and geometric model whose shape is updated as the analysis proceed are used for the easy re-generation of analysismodel.

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The nonlinear mechanical behavior of cellular solids is mainly caused by the buckling of cells. We here develop a multi-scale computational method for periodic cellular solids with buckling. However, theoretical studies so far reported some difficulties for choosing appropriate models of microstructures that minimize non-convex potential functionals. Therefore, we here discuss appropriate models of unit cell for the local unstable problems by symmetry of the system and some numerical examples of micro-scale problems by the presented method.

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A formulation of Element Free Galerkin Method (EFGM) for saturated soil is presented. A weak form of equation of stress equilibrium is derived and its discretization based on the EFGM strategy is presented under the elastic constitutive equation. The continuity equation of pore water is discretized through two different schemes. The accuracy of numerical computation is examined through one-dimensional consolidation problems by comparing with closed and usual finite element solutions.

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A single step digital filering time in tegration (SSDFTI) scheme that filters out high frequency noise by applying digital filter in the process of computation is proposed. The proposed scheme can realize adjustable algorithmic damping and it includes various time integration methods, such as the Newmark β method and the generalized α method, as its simplifed form.
The proposed scheme uses two time series (“filtered time series” and “unfiltered time series”), and it realizes algorithmic damping by using digital filltering technique. Usage of digital filer enables employment of wider variety of algorithmic damping compared to that of existing time integration schemes. It is also possible to apply different filters for displacement, velocity and acceleration.
Dynamic analysis of asimple 2 DOF system which has astrong trend of divergence is conducted as a numerical example using the proposed scheme. The result shows that it can conduct accurate analysis eliminating the effect of high frequency noise.
The proposed scheme is not unconditionally stable, however, and further research is required about conditions for stable computation.

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This paper presents a velocity controlled dynamic analysis to predict the dynamic toughness of post-tension prestressed reinforced concrete beam. In order to evaluate properly the flexural resistance and ultimate deformation under a dynamic loading condition, the velocity controlled dynamic analysis method is proposed. Since the displacement velocity of the loading point is controlled constantly, the flexural resistance of the beam can be evaluated with the negligibly small vibration effect caused by the inertia force. In addition to the rate effect materials, the increment ofthe bond-slip stress between the PC tendon and the concrete under dynamic deformation condition is also taken into account. The proposed method is verified by comparing with the high speed loading test results in this paper.

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Mechanical behaviors of geological material are governed by the existences and behaviors of microstructures such as joints or microcracks in rock mass. During cavern excavation, not only the mechanical properties but also permeability of jointed rock mass are changed due to joint deformation. In this article, the coupled modeling of deformation and flow of the jointed rock mass is carried on the basis of the Micromechanics-Based Continuum approach (MBC approach). The derived model is implemented into the MBC analysis, which enables us to carry the excavation analysis of a cavern and obtain the distribution of displacement, stress, strain and permeability of rock mass and the deformation of joints.

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An approach to the elasto-plastic constitutive modeling of structural sands is presented. The hardening parameter expressible of the degeneration of structure is macroscopically defined for normally consolidated and overconsolidated states of sands. The constitutive model is formulated from the stress dependent dissipation function within the framework of the thermomechanical principle. The sub-loading surface model is applied in order to describe the soil behavior of the overconsolidated state. The proposed model is verified with the triaxial tests of a sand

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The aim of this study is to investigate experimentally the vibration properties of rigid body placed on dense sand ground surface. The rigid body with variable mass, inertial moment and base size was prepared, and its vibration behavior was observed in a series of free vibration tests. From the observed behaviors the natural vibration period, critical damping factor and vibration mode were analyzed. It was found that the natural vibration period is dependent not only on the mechanical properties of footing and foundation ground, but also on the vibration amplitude. This suggested the notable effect of nonlinear strain dependent stiffness of ground material on the vibration properties of the body underlined. The stiffness coefficients of springs modeling the interactive mechanical behavior between rigid body and ground, were assessed from the observed behaviors based on the modal analysis. The influence of base pressure and basesize on the spring coefficients is discussed.

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This paper is devoted to develop a numericaml ethod using fiber model and explicit time integration scheme for the seismic response analysis of RC rahmens tructures. The fiber model is applied to acquire the sectional forcedeformation relations. RC cross sections are divided into multi-layers of concrete and steel bar.Nonlinear properties of steel bar and concrete are introduced between adjacent rigid elements. Numerical calculations for a RC Rahmen structure are carried out under the observed ground accelerations at Hyogoken Nanbu Earthquake (Kobe, 1995), and nonlinear dynamic propertieos of deformation and resultant force are discussed in detail.

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So far, many researchers have mainly studied the relationship between the principal stress ratio and the principal strain increment ratio of sand. However, it's not uniquely obtained for various stress conditions like b-value yet. The purpose of this paper is to reveal the fundamental stress-train relation ship of sand with inherent transverse isotropy, taking the effect of b-value and non-coaxiality into consideration. Towards this end, the monotonic loading tests with fixed principal stress axeswere carried out at the range of b-value from 0.0 to 1.0 using a large hollow cylindrical apparatus. Through the analysis of the experimental results, it is clarified that the relationship between the principal deviatoric stress increment and the principal deviatoric strain increment is more essential for sand even in the case that b-value is changed.

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This paper examines the diffuse bifurcation mode of a two-layer specimen consisting of a non-coaxial Cam-clay model. The specimen undergoes a deformation by a prescribed velocity with no friction on the ends and a constant lateral hydrostatic pressure on the sides. We obtain several bifurcation loads and examine the effect of several material parameters on the bifurcation load. We finally investigate the sites where the slip planes first occur from the maximum shear strain point of view.

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The void damage theory can express quantitatively the growth and coalescence of voids which are inherently included in any material and are caused by the accumulated microcrack. In this paper, 2-dimensional deformation analysis by the elasto-plastic FEM is carried out to show some numerical examples for the relationships between initial value of void volume fraction and the deterioration of overall stiffness. From this result, an estimation method of material deterioration is presented to evaluate the damage of materials.

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The effects of the initial imperfections on the nonlinear behaviors and ultimate strength of thethin-walled members subjected to the axial loads, obtained by the finite element stability analysis, are examined. As the initial imperfections, the buckling mode shapes of the members are adopted. The buckling mode shapes ofthe thin-walled members are obtained by the transfer matrix method. In the finite element stability analysis, isoparametric degenerated shell element is used, and the geometrical and material nonlinearity are considered based on the Green Lagrange strain definition and the Prandtl-Reuss stress-strain relation following the von Mises yield criterion. The U-, box-and I-section members subjected to the axial loads are adopted for numerical examples, and the effects of the initial imperfections on the deformation shapes and ultimate strength of the members are examined

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Numerical simulation tests were carried out using the distinct element method (DEM) with paying much attention to the micro-deformation mechanism leading to the development of shear bands. To do this, the conventional DEM was modified slightly such that the effect of rolling resistance at contact points could be taken into account (called MDEM). It is found that MDEM can be a powerful tool for simulating not only the generation of large voids inside a shear band but also the high gradient of particle rotation along the shear band boundaries, in a quite similar manner to those observed in natural granular soils. It is concluded, based on the numerical simulation tests, thatthe basic micro-deformation mechanism ending up with the formation of shear bands is in the generation of column-like structure during the hardening process and its collapse in the softening process.

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Change of void ratio in granular medium during shear is examined through a trap-door test using aluminum rods with different radii. Displacement profile of circular disks and void ratio distribution of the assemblage of granules are revealed by image data processing based on the high-speed video record, while measuring the load acting on the door. Development of shear strain calculated by the displacement of disks is related to the expansion or shrinkage of voids within granular assemblage.

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Biaxial compression test for two dimensional spherical granular material was simulated by the distinct element method which takes account of a constant adhesion force acting between particles at each contact points. The effects of adhesion force on the deformation and strength of the spherical granular material were studied. It is found that these effects are similar with the effects of suction observed in the triaxail compression test results for unsaturated soil.

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The loss of interparticle bonding causes mechanical damage to cohesive geomaterials. The damagemodel is a constitutive model to obtain a relationship between stress and strain which changes with the degree of damage. The authors developed a simulation model to evaluate the degree of damage in terms of the Granular Element Method. In this model the periodic boundary is adopted to perform element tests with the minimum influence of boundary condition. By a tentative application, it was found that the stress-strain relationship was predicted fairly well even with a simple damage model.

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The constitutive model for explaining non-linear deformation mechanism of granular materials was presented by the Authors. Elliptic microstructure composed of particles in granular materials is focusedas a unit of microstructure. In the model, the macroscopic behavior of heterogeneous granular material is assumed to be controlled by the elliptic microstructures and the interactions among them. In this paper, therelation between size of microstructure and size of constituent particle is investigated with stability conditions of the structures. And the deformation behavior of granular materials with different initial fabric under shearing are examined based on the mechanism of fabric change such as collapse and revival of the microstructures. The proposed constitutive model has the capacity to explain the mechanism of non-linear deformation including the effect of initial fabric on stress-induced anisotropy and dilatancy in a unique manner based on the elliptic microstructure model.

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A numerical scheme to evaluate the elastic stiffness and strength of heterogeneous material, which have been proposed by authors based on the theory of homogenization, is applied to fiber reinforced composites, and its validity for evaluating their mechanical properties is examined. Results show that the numerical scheme can give fairly good predictions as for the elastic stiffness, but it can only predicts value of strength near to the experimental data since the numerical scheme does not take the existence of initial defects in the composites into account. However, it can conclude that our proposed method can use for evaluation of mechanical property of composite material at some first stage of design since the method needs only the mechanical properties of each materials of which the composite consists and a graphical data representingthe geometric feature of the composite structure.

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