Poroelastodynamic responses and elastic moduli of a transversely isotropic porous cylinder under forced deformation test

Existing transversely isotropic poroelastodynamics solutions are limited to infinite domains and without experimental validation. Furthermore, there is a lack of analytical simulations for the elastic moduli dispersion of fluid-saturated porous cylinders. To address these three limitations and investigate the mechanisms of moduli dispersion, we present the analytical solutions of the poromechanical responses and the elastic moduli dispersion of a transversely isotropic, fluid-saturated, finite porous cylinder subjected to a forced deformation test. Through an example, we demonstrate the effects of loading frequency, boundary conditions, and material's anisotropy, dimension, and permeability on the responses of pore pressure,force, displacement, and dynamic elastic moduli of the cylinder. The specimen's responses are significantly influenced by the frequency of the applied load, resulting in a drained state at low frequencies and an undrained state at high frequencies. At high frequencies, the sample behaves identically for an open or a closed lateral boundary, and permeability has insignificant effects. The dynamic elastic moduli are mainly controlled by the loading frequency and the ratio of the sample's radius to its height. Lastly,we show excellent matches between the newly derived analytical solution and laboratory measurements on one clay and two shale samples from Mont Terri.

Orlicz空间中带指数权的多项式逼近

在Orlicz空间中研究了带指数权w(x)=e^(-(1-x^(2))^(-α))(α>0)的多项式逼近问题,通过引入新的光滑模和相关K-泛函,运用Hölder不等式以及相关分析技巧证明了Orlicz空间中带指数权的Jackson定理和它的弱形式,并得到了一个新的Bernstein不等式.

A novel approach to the dynamic response analysis of Euler-Bernoulli beams resting on a Winkler soil model and subjected to impact loads

This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading.The approach considers that damping has much less importance in controlling the maximum response to impulsive loadings because the maximum response is reached in a very short time,before the damping forces can dissipate a significant portion of the energy input into the system.The development of two sine series solutions,relating to different types of impulsive loadings,one involving a single concentrated force and the other a distributed line load,are presented.This study revealed that when a simply supported Euler-Bernoulli beam,resting on a Winkler soil model,is subject to an impact load,the resulting vertical displacements,bending moments and shear forces produced along the span of the beam are considerably affected.In particular,the quantification of this effect is best observed,relative to the corresponding static solution,via an amplification factor.The computed impact amplification factors,for the sub-grade moduli used in this study,were in magnitude greater than 2,thus confirming the multiple-degree-of-freedom nature of the problem.

Effects of porosity on seismic velocities, elastic moduli and Poisson's ratios of solid materials and rocks

The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E, G, K and l of each material are systematically different and display consistent correlations with the Poisson’s ratio of the nonporous material(v0). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson’s ratio(n) remains constant is at v0=0.2, and J(G) > J(E) > J(K) > J(l) and J(G) < J(E) < J(K) < J(l) for materials with v0> 0.2 and v0< 0.2, respectively.J(Vs) > J(Vp) and J(Vs) < J(Vp) for the materials with v0> 0.2 and v0< 0.2, respectively. The effective n increases, decreases and remains unchanged with increasing porosity for the materials with v0< 0.2,v0> 0.2 and v0=0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the n fixed point decreases nonlinearly with decreasing pore aspect ratio(a: width/length). With increasing depth or pressure, cracks with smaller a values are progressively closed, making the n fixed point rise and finally reach to the point at v0=0.2.

DETERMINATION OF EFFECTIVE MODULI FOR FOAM PLASTICS BASED ON THREE PHASE SPHEROIDAL MODEL

The relations of bulk modulus, shear modulus, Young's modulus and the Poisson's ratio with porosity of foam plastics are determined by a three phase spheroidal model commonly used in Composite Mechanics. The results are compared with those using differential scheme. It is shown that the material properties derived from the present model normally are larger than those obtained by differential scheme for foam plastics with identical porosity. The differences in shear moduli and Young's moduli obtained by the two methods are small but they are larger for bulk moduli of incompressible matrix and Poisson's ratios. The Young's moduli of high density foam plastics derived by the present model agree better with experimental ones.

Generalized thermoelasticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.

Prediction of Compressive and Shear Moduli of X-cor Sandwich Structures for Aeronautic Engineering

The so-called″X-cor sandwich structure″is a highly promising novel material as an alternative to honeycomb used in aircraft.Although much work has been conducted on the performance of the X-cor sandwich structure,the gap is still hardly bridged between experimental results and theoretical analyses.Therefore,a method has been innovated to establish semi-empirical formula for the prediction of compressive and shear moduli of X-cor sandwich structure composites,by combining theoretical analyses and experimental data.In addition,aprediction software was first developed based on the proposed method,of which the accuracy was verified through confirmatory experiments.This software can offer a direct reference or guide for engineers in structural designing.

Model of homogenisation for analysing the effect of micrometre pore sizes on the elastic moduli of porous materials

A homogenisation model for analysing the effect of micrometre pore sizes on the engineering moduli of elasticity of porous materials was proposed.In the proposed model,the engineering coefficients of localization of total strains(LTS coefficients)are considered instead of the classical strain localization tensors.For a pore,these coefficients represent the ratio of the sum of the strains in the volume of the pore to the sum of the strains in the volume of the porous body.To estimate the elastic moduli of a material with an arbitrary pore size,it is sufficient to have information about the elastic moduli and the LTS coefficient of a material with one basic pore size.Then,in Eshelby's model of equivalent inclusion,a transition to LTS coefficient for material with arbitrary pore size is achieved,and its elasticity moduli are determined.The results for Young's modulus of porous titanium,with different sizes of spherical pores,completely conform with the experimental data.We have obtained a model theoretic estimate of the upper bounds of Young's modulus of porous materials with infinitely small pore size.For the spherical pores,the proposed assessment coincides with the upper limits of the Hashin-Shtrikman bounds.

Displacement of surrounding rock in a deep circular hole considering double moduli and strength-stiffness degradation

The problem of cavity stability widely exists in deep underground engineering and energy exploitation.First,the stress field of the surrounding rock under the uniform stress field is deduced based on a post-peak strength drop model considering the rock’s characteristics of constant modulus and double moduli.Then,the orthogonal non-associative flow rule is used to establish the displacement of the surrounding rock under constant modulus and double moduli,respectively,considering the stiffness degradation and dilatancy effects in the plastic region and assuming that the elastic strain in the plastic region satisfies the elastic constitutive relationship.Finally,the evolution of the displacement in the surrounding rock is analyzed under the effects of the double modulus characteristics,the strength drop,the stiffness degradation,and the dilatancy.The results show that the displacement solutions of the surrounding rock under constant modulus and double moduli have a unified expression.The coefficients of the expression are related to the stress field of the original rock,the elastic constant of the surrounding rock,the strength parameters,and the dilatancy angle.The strength drop,the stiffness degradation,and the dilatancy effects all have effects on the displacement.The effects can be characterized by quantitative relationships.

System Identification Method for Evaluating the Effect of Thickness Error on Backcalculated Pavement Layer Moduli

Based on system identification theory and FWD testing data, the effect of thickness error on backcalculating pavement layer moduli is studied and the method of singular value decomposition (SVD) is presented to solve the morbidity problem of sensitivity matrix in this paper.The results show that the thickness error has great effects on the backcalculated pavement layer moduli. The error of backcalculated moduli can be controlled within the range of ±15% by limiting the thickness error within the range of ±5%.

EFFECTIVE ELASTIC MODULI OF INHOMOGENEOUS SOLIDS BY EMBEDDED CELL MODEL

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional two-phase composites.

A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials

We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation rondel was based on the large deflection of the inclined members of the cells of celluar materials, The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensioned cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.

PREDICTION OF THE OVERALL MODULI OF A CYLINDRICAL SHORT-FIBER REINFORCED COMPOSITE

With respect to obtaining the effective elastic moduli of the composite, the present theory dif- fers from both Eshelby's equivalent inclusion method and Hill's self-consistent one, both of which only consid- er the mechanical properties of the matrix and inclusions(fibers). In fact, the inclusion-inclusion interaction is more pronounced when the volume fraction of inclusions of the composite increases. Hence, in this paper the effective elastic moduli of the composite are derived by taking into account the shapes, sizes and distribution of inclusions, and the interactions between inclusions. In addition, it is more convincing to assume short-fibers as cylindrical inclusions as in the present paper than as ellipsoidal ones as in others. Finally, numerical re- sults are given.

EFFECTIVE ELASTIC MODULI OF AN INHOMOGENEOUS MEDIUM WITH CRACKS

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material.

THE REAL HYPER-ELLIPTIC SUBSPACES OF TEICHMüLLER SPACE AND MODULI SPACE

Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials are constructed in [5, 6]. The Strebel rays [3] and the eventually distance minimizing rays [9] are important in Teichmüller spaces and moduli spaces, respectively. Motivated by the study of [3, 9], two special kinds of Strebel rays in the real hyper-elliptic subspace of Teichmüller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article.

THE EFFECTIVE PROPERTIES OF PIEZOCOMPOSITES, PART Ⅱ: THE EFFECTIVE ELECTROELASTIC MODULI

Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal inclusions. Based on the closed-from solutions of the electroe- lastic Eshelby's tensors obtained in the part I of this paper and the generalized Bu- diansky's energy-equivalence framework, the closed-form general relations of effective electroelastic moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison between predicted and exper- imental results shows that the theoretical values in this paper agree quite well with the experimental results. These expressions can be readily utilized in analysis and design of piezocomposites.

Some new generalized difference sequence spaces defined by a sequence of moduli

The idea of difference sequence sets X（△） = {x = （xk） ： △x ∈ X} with X = l∞, c and co was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence spaces and give some inclusion relations.

THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES

The eventually distance minimizing ray（EDM ray） in moduli spaces of the Riemann surfaces of analytic finite type with 3 g ＋ n-3 〉 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmu¨ller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given.

Penrose Transform on Induced <i>D_G/H</i>-Modules and Their Moduli Stacks in the Field Theory

We consider generalizations of the Radon-Schmid transform on coherent DG/H-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) characterizing conformal classes in the space-time that determine a space moduli [1] on coherent sheaves for the securing solutions in field theory [2]. In a major context, elements of derived categories like D-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets [3]) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding Hecke category.

Effective elastic moduli of in-situ A356/TiB_2 composites

The effective elastic moduli （EEM） of A356/TiB2 composites formed by gravity casting and adjusted pressure casting （APC） were measured and compared. The results show that the EEM of A356/TiB2 composites are improved obviously by TiB2 particles and affected by forming methods. The EEM of the specimens formed by APC are higher than those in the gravity casting case. For 9.5%A356/TiB2（volume fraction）, the EEM of the specimens formed by APC reaches 93GPa, which is 9GPa higher than those in the gravity casting case. An analytic model is established to explain the mechanics of the EEM of composites reinforced with TiB2 particles.