Estimating Subgrade Reaction Modulus for Transversely Isotropic Rock Medium

Most of the rock medium possesses intrinsic grain orientation or preferred bedding and joint directions, thus requiring the use of at least transverse isotropy to describe its elastic behavior. This paper presents a series of charts, based on extensive finite element parametric studies along with nonlinear regression analysis of FE simulation results, for estimating the subgrade reaction modulus (or initial tangent to the p-y curve) using five elastic constants of a transversely isotropic rock mass. The proper characterization of subgrade reaction modulus is critical for accurate prediction of the elastic lateral deflection of a rock socketed drilled shaft under the applied lateral loads. The sensitivity of the response of a laterally loaded drilled shaft to the degree of anisotropy and orientation of the plane of anisotropy (bedding plane direction of the rock medium) was demonstrated in this paper for an actual lateral load testing case in Ohio. It is highly recommended to use five elastic constants to estimate subgrade reaction modulus of rock medium exhibiting high degree of cross anisotropy.     

Propagation of Love Waves in an Inhomogeneous Fluid Saturated Porous Layered Half-Space with Properties Varying Exponentially

Based on Biot’s theory for transversely isotropic fluid saturated porous media, the complex dispersion equation for Love waves in a transversely isotropic fluid-saturated porous layered half-space is derived with the consideration of the inhomogeneity of the layer. The equation is solved by an iterative method. Detailed numerical calculation is presented for an inhomogeneous fluid-saturated porous layer overlying a purely elastic half-space. The dispersion and attenuation of Love waves are discussed. In addition, the upper and lower bounds of Love wave speed are also explored.     

Coefficients of thermal expansion of metal-matrix composites for electronic packaging

Finite element analyses of the effective coefficient of thermal expansion (CTE) of metal-matrix composites are presented, with a focus on composites with potential for use in electronic packaging applications. The analyses are based on two-dimensional plane strain and axisymmetric unit-cell models. The brittle phase is characterized as an isotropic elastic solid with isotropic thermal expansion. The possibility of plastic deformation, described by an isotropic-hardening flow rule, is allowed for in the ductile phase. A wide range of reinforcement volume fractions is considered. The effects of phase geometry, phase contiguity, ductile phase material properties, processing-induced residual stresses, and brittle particle fracture are considered. The CTE is found to be much less sensitive to phase distribution effects than is the tensile stiffness. The results show that there is a significant dependence of the overall CTE on the phase contiguity (i.e., on whether the brittle or the ductile phase is continuous).     

Molecular genetics and clinical-pathology features of hereditary nonpolyposis colorectal carcinoma (Lynch syndrome): historical journey from pedigree anecdote to molecular genetic confirmation

The myocardium of the left ventricle of the heart is a fibrous structure, the fibres being wound helically anticlockwise on the epicardium and changing progressively through the wall thickness to being wound helically clockwise on the endocardium. At any point, therefore, the material can be considered as transversely isotropic. For mechanically modelling the ventricle, two independent material properties, the along-fibre and across-fibre moduli of elasticity are required. This paper describes a computer method for determining these by using a finite element model and matching cavity volume and ventricle length against values derived from cineangiographic and pressure data. The method is applied to a group of patients with various cardiac diagnoses and the modular ratios for their myocardia are derived.     

Effective Toughness of Damaged Solids Containing Ribbon Cracks

The crack-tip toughness of materials with two-dimensional random orientation of ribbon cracks is evaluated theoretically. The effective elastic moduli reduce when the cracks exist within the isotropic material so as to enhance the material toughness. The results show that the crack density and the Poisson ratio of the matrix dominate the behavior of the overall effective toughness. As crack density η = 1, the toughness increment is 0.44–0.48 of the original toughness approximately, but three out of five moduli, μ12, μ23, and κ23, reduce at least 0.57 of their moduli. The explicit forms of the crack-tip toughness and five transversely isotropic moduli of the material containing ribbon cracks are also shown.     

Finite element analysis of static loading in donkey hoof wall

A finite element model of donkey hoof wall was constructed from measurements taken directly from the hoof capsule of the left forefoot. The model was created with a 2 mm mesh and consisted of 11,608 nodes. A linear elastic analysis was conducted assuming isotropic material properties in response to a 375 newton (N) load, to simulate static loading. The load was applied to the wall via 400 laminae in order to simulate the way in which the pedal bone is suspended within the donkey hoof capsule. Displacement, stress concentration, principal strain, and force distribution across the hoof wall were evaluated. The hoof wall model revealed loading responses that were in broad agreement with previously reported in vivo and modelled observations of the equid hoof. Finite element analysis offers the potential to model hoof wall function at the macroscopic and microscopic level. In this way, it could help to develop further our understanding of the functional relationship between the structural organisation and material properties of the hoof wall.     

Elastic constants of transversely isotropically porous (TIP) materials

We derive formulas describing the dependence of the elastic characteristics of multicapillary materials on the capillary porosity. The investigated materials are classified as transversely isotropic, and the anisotropy in their properties is the result of the directionality of the capillary pores. Analysis of the dependences obtained has shown that the elasticity moduli of these materials may be calculated using formulas suggested for reinforced materials, in which the elastic constants of the fibers are assumed to be equal to zero. We derive a relation between the Poisson's ratios and the capillary porosity.Institute of Problems of Materials Science, National Academy of Sciences of the Ukraine, Kiev. Translated from Poroshkovaya Metallurgiya, No. 5–6, pp. 104–109, May–June, 1994.     

Micromechanical modeling of reinforcement fracture in particle-reinforced metal-matrix composites

Finite element analyses of the effect of particle fracture on the tensile response of particle-reinforced metal-matrix composites are carried out. The analyses are based on two-dimensional plane strain and axisymmetric unit cell models. The reinforcement is characterized as an isotropic elastic solid and the ductile matrix as an isotropically hardening viscoplastic solid. The reinforcement and matrix properties are taken to be those of an Al-3.5 wt pet Cu alloy reinforced with SiC particles. An initial crack, perpendicular to the tensile axis, is assumed to be present in the particles. Both stationary and quasi-statically growing cracks are analyzed. Resistance to crack growth in its initial plane and along the particle-matrix interface is modeled using a cohesive surface constitutive relation that allows for decohesion. Variations of crack size, shape, spatial distribution, and volume fraction of the particles and of the material and cohesive properties are explored. Conditions governing the onset of cracking within the particle, the evolution of field quantities as the crack advances within the particle to the particle-matrix interface, and the dependence of overall tensile stress-strain response during continued crack advance are analyzed. Formerly Graduate Research Assistants, Brown University     

Effective elastic response of two-phase composites

We present finite element analyses of the overall elastic properties of two-phase composites as a function of the shape, concentration and spatial distribution of the reinforcement. The analyses of the geometrical effects of constituent phases on the overall elastic moduli have been carried out within the context of axisymmetric and plane strain unit cell formulations. In most calculations, the phases are taken to be isotropic and linear elastic, and the interface perfectly bonded. These finite element results are compared with available analytical results for a variety of geometrical arrangements of the constituent phases of the composites. Computations which predict the effective elastic properties for the limiting case where all the reinforcing particles fracture are carried out. The competition between stiffening due to reinforcement and increased compliance due to cracking of the reinforcement is evaluated for metallic, ceramic and intermetallic matrices with brittle reinforcements, and the numerical results are compared with analytical solutions. The paper also includes discussions of the role of thermal residual stresses in influencing apparent initial moduli and the effects of interfacial compliance on the stress distribution within the reinforcement.     

Asymmetric Dynamic Green’s Functions in a Two-Layered Transversely Isotropic Half-Space

By virtue of a complete representation using two displacement potentials, an analytical derivation of the elastodynamic Green’s functions for a transversely isotropic layer underlain by a transversely isotropic half-space is presented. Three-dimensional point-load and patch-load Green’s functions for stresses and displacements are given in the complex-plane line-integral representations. The formulation includes a complete set of transformed stress-potential and displacement-potential relations in the framework of Fourier expansions and Hankel integral transforms, that is useful in a variety of elastodynamic as well as elastostatic problems. For the numerical computation of the integrals, a robust and effective methodology is laid out. Comparisons with the existing numerical solutions for a two-layered transversely isotropic half-space under static surface load, and a homogeneous transversely isotropic half-space subjected to buried time-harmonic load are made to confirm the accuracy of the present solutions. Selected numerical results for displacement and stress Green’s functions are presented to portray the dependence of the response of the two-layered half-space on the frequency of excitation and the role of the upper layer.     

Porochemoelastic Solution for an Inclined Borehole in a Transversely Isotropic Formation

A porochemoelastic model which couples the chemical interactions effected by solute and ionic transport with the diffusion-deformation processes is presented. The chemical effects are encompassed within the model assuming the saturating pore fluid to be a two species constituent comprising of the solute and the solvent. Governing equations are presented in their anisotropic forms and specialized for the transversely isotropic material. The resulting system of equations is applied to obtain the porochemoelastic analytical solution for an inclined borehole subjected to a three-dimensional state of stress in a transversely isotropic formation. In obtaining the analytical solutions, it is assumed that the borehole axis is perpendicular to the plane of isotropy of the transversely isotropic formation. Chemical effects on the stress and pore pressure distributions and their impact on borehole stability is demonstrated in the numerical examples included.     

Consolidation of a Finite Transversely Isotropic Soil Layer on a Rough Impervious Base

A semianalytical solution to axisymmetric consolidation of a transversely isotropic soil layer resting on a rough impervious base and subjected to a uniform circular pressure at the ground surface is presented. The analysis uses Biot’s fully coupled consolidation theory for a transversely isotropic soil. The general solutions for the governing consolidation equations are derived by applying the Hankel and Laplace transform techniques. These general solutions are then used to solve the corresponding boundary value problem for the consolidation of a transversely isotropic soil layer. Once solutions in the transformed domain have been found, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore-water pressure and fluid discharge can finally be obtained by direct numerical inversions of the integral transforms. The accuracy of the present numerical solutions is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Further, some numerical results are presented to show the influence of the nature of material anisotropy, the surface drainage condition, and the layer thickness on the consolidation settlement and the pore pressure dissipation.     

The elastic strain energy of coherent ellipsoidal precipitates in anisotropic crystalline solids

The elastic strain energy of coherent ellipsoidal precipitates (ellipsoids of revolution) in anisotropic crystalline solids has been calculated as a function of ellipsoid aspect ratio using the method of Eshelby. When the precipitate is eithermuch softer or harder, elastically, than the matrix, the results are similar to those previously obtained using isotropic elasticity. When this condition is not met, however, anisotropic elasticity can yield quite different results which vary markedly with the orientation relationship between precipitate and matrix. When the precipitate has a non-cubic crystal structure, the elastic strain energy often passes through a maximum or a minimum at shapes which are neither thin discs nor spheres. During this study, the isotropic elasticity result that the strain energy associated with a disc-shaped precipitate is independent of the matrix elastic constants was also shown to hold under the conditions of anisotropic elasticity, and in such circumstances it depends only on the elastic properties of the precipitate in the direction of the principal directions of the disc. Incorporation of the anisotropic elastic strain energy into the calculation of ΔG ^*, the free energy of activation for the formation of a critical nucleus for the basic case of homogeneous nucleation with boundary-orientation independent interfacial energy, showed that the ratio of the strain energy to the volume free energy change must usually be somewhat larger than 3/4 in order to cause the shape of the critical nucleus to differ from that of a sphere.     

Automatically Computing the Displacements and Stresses Induced by Three-Dimensional Arbitrarily Shaped Loads in a Transversely Isotropic Medium

Since the planes of foundations are not usually regularly shaped, and the loads are often applied on the anisotropic materials, such as transversely isotropic soils or rocks, calculating the induced displacements and stresses by an arbitrarily shaped load for a transversely isotropic medium is rather tedious and time consuming. Hence, how to estimate those values correctly and quickly by computer was the major objective in constructing the fast anisotropic displacements and stresses (FADAS). FADAS is based on the solutions of displacements and stresses in a transversely isotropic half space subjected to three-dimensional buried right-angled triangular loads, which were derived by the first writer. Utilizing these solutions, the displacements and stresses for a general triangular region at any point can be obtained by superposition. An illustrative example is given to demonstrate a few features of FADAS, and to elucidate how to compute the vertical displacement induced by a uniform vertical circular load in an equivalent medium. Results from FADAS reveal that the usage of it is correct, easy, and very fast to offer a good tool for practitioners.     

Behavior of Piled Raft Foundations Under Lateral and Vertical Loading

This article presents a new method of analysis of piled raft foundations in contact with the soil surface. The soil is divided into multiple horizontal layers depending on the accuracy of solution required and each layer may have different material properties. The raft is modeled as a thin plate and the piles as elastic beams. Finite layer theory is employed to analyze the layered soil while finite element theory is used to analyze the raft and piles. The piled raft can be subjected to both loads and moments in any direction. Comparisons show that the results from the present method agree closely with those from the finite element method. A parametric study for piled raft foundations subjected to either vertical or horizontal loading is also presented.     

Mechanisms of Small-Strain Shear-Modulus Anisotropy in Soils

In this paper, experimental studies using a true triaxial apparatus and a bender element system, and numerical simulations based on the discrete element method (DEM) were used to investigate the stress- and fabric-induced shear-stiffness anisotropy in soils at small strains. Verified by experiments and DEM simulations, the shear modulus was found to be relatively independent of the out-of-plane stress component, which can be revealed by the indistinctive change in the contact normal distribution and the normal contact forces on that plane in the DEM simulations. Simulation and experimental results also demonstrated that the shear modulus is equally contributed by the two principal stress components on the associated shearing planes. Fabric-induced stiffness anisotropy, i.e., the highest Gxy or Ghh, can be explained by simulation findings in which more contact normals prefer to distribute along the horizontal direction. The experiments and simulations also reveal that the fabric-induced stiffness anisotropy increases with an increasing aspect ratio of the particles. The assumption of transversely isotropic fabric in soils is valid based on the DEM simulation results; however, this assumption is not completely supported by the experimental results.     

Elbow flexion strength curves in untrained men and women and male bodybuilders

The mechanical response of intervertebral joints is deeply influenced by disc degeneration. The phenomenon is expressed in terms of variations in the biomechanical properties of the material, whose compressibility characteristics change because of the liquid content loss in the tissue and, what is even more important, to prolapse. In this work, the problem is investigated by means of a computational mechanics approach; a coupled material and geometric non-linear model is developed, representing vertebra, annulus and nucleus submitted to an axial load. A transversely isotropic law is assumed for cortical bone in the vertebral body and an isotropic law for the cancellous portion; a hyperelastic formulation is assumed for the disc, allowing effective interpretation of the mechanical characteristics of degeneration. The results obtained are reported with regard to bony endplate and annulus behaviour; interaction phenomena between bony endplate and nucleus are emphasized.     

Time-Domain Boundary Element Method for Underground Structures in Orthotropic Media

Based on the fundamental solutions due to Dirac’s δ function for transversely isotropic media, a numerical scheme for wave propagation in two-dimensional orthotropic media is developed within the boundary element method in the time domain. Criteria for selection of the time and space discretizations for convergent and accurate results are established. The applicability and accuracy of the scheme are verified by a number of benchmark problems including dynamic responses of an orthotropic half plane under uniform harmonic surface loadings and a circular cavern in slightly orthotropic media under the incidence of pseudo-P and -SV waves. The procedure is then applied to examine wave propagation for an underground tunnel with different ratios of orthotropy in the media. The effects of different wave parameters and ratios of orthotropy on dynamic response of the tunnel are presented.     

Stress Path Testing of an Anisotropic Sandstone

The Berea sandstone used in this study is transversely isotropic with respect to elastic response, with P-wave velocities of 2,160?m/s normal to bedding and 2,290?m/s parallel to bedding, a variation of only 6%. Triaxial compression and extension tests involving failure by loading and unloading were performed along the two directions of symmetry. With axial stress applied parallel to bedding, the internal friction angle was approximately 55° for compression and extension, indicating no intermediate stress effect for the linear Mohr-Coulomb criterion. However, for axial stress normal to bedding, the friction angle in compression was 50°, whereas in extension it was 44°. This anomalous behavior was attributed to strength anisotropy of the sandstone.     

金属内部裂纹的超声衰减特性与近表面缺陷识别

建立了包含裂纹缺陷的二维金属板模型.采用有限元方法,对具有不同深度裂纹的材料内部超声波场进行计算,获得了不同裂纹深度金属材料上表面的回波信号,分析了裂纹深度对超声波传播特性的影响规律.进一步分离提取不同阶次底面回波的频谱特征,获得了由裂纹缺陷引起的超声衰减系数随频率的变化关系.最后提出了通过底面回波频谱图辨识近表面裂纹缺陷的方法.