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Creep Stresses and Strains in Ceramic Discs Exhibiting Transversely Isotropic Nano- and Macro-Structural Symmetry Subjected to Centrifugal Forces
Published in Satya Bir Singh, Prabhat Ranjan, A. K. Haghi, Materials Modeling for Macro to Micro/Nano Scale Systems, 2022
Shivdev Shahi, S. B. Singh, A. K. Haghi, S. Saranya
Ceramic discs are characterized by chemical inertness, high melting point, low electrical, and thermal conductivity. Traditional ceramics included insulating materials, glass, abrasives, and enamels. In the present times, as typical examples, thermal and electrical insulations for various structural components are manufactured using ceramics as a base. Ceramic discs are presently being extensively used in the manufacture of capacitors, filtration discs, automobile breaking systems, gas turbines, etc. A material is said to exhibit transverse isotropy when the physical properties for that material are alike in a single preferential direction. This particular property provides an edge in the manufacture of thin structural components under state of plane stress. Creep strains of such materials are accompanied by changes in their structure, which are irreversible. Creep analysis of such dynamic structural components is necessary for predetermining their deformation, fracture points, and for stable design. In this chapter, we will examine creep deformation of annular ceramic discs experiencing high centrifugal forces and exhibiting transversely isotropic macro-structural symmetry. Numerical values of elastic stiffness constants for two ceramic materials have been used to calculate the trends of creep stresses and strains. The centrifugal forces are added to the analysis by altering the equation of equilibrium accordingly. Wang and Cao [18] determined the elastic constants of lead zirconate titanate [PZT-5H] using ultrasonic wave propagation. Elastic constants for barium titanate have been given by Royer and Dieulesaint [9].
Numerical identification of anisotropic rock parameters using uniaxial compression test
Published in G.N. Pande, S. Pietruszczak, H.F. Schweiger, Numerical Models in Geomechanics, 2020
The presence of bedding or cleavage planes and due to some preferred orientation of the fabric or microstructure, the behaviour of many rocks is anisotropic. It is possible to use the simplest form of anisotropy, transverse isotropy, in design analyses to avoid the computational complexity and the difficulty of determining the elastic constants preciously. The strength and elastic parameters can be evaluated by systematic laboratory testing of specimens drilled in different directions from an oriented block sample. Triaxial compression tests at different sets of confining pressures for each given orientation can then be used to estimate the strength and the elastic parameters (Goodman 1980). The procedure dictates the performance of many triaxial tests, which is not so simple compared with the uniaxial test. Moreover, with todays measuring equipment it is almost impossible to determine reliable material parameters for anisotropic rock.
Finite element modelling
Published in C M Langton, C F Njeh, The Physical Measurement of Bone, 2016
Material properties for linear elastic materials, as they need to be specified for FE analyses, are fully described by the components of a fourth-rank stiffness or compliance tensor in the generalized Hook’s law [3, 4]. The stiffness and compliance tensors are usually represented by symmetric six-by-six matrices. In its most general form, these matrices hold 21 independent components that must be determined from experiments. If planes of elastic symmetry exist in the material, some of these coefficients are interdependent or zero when measured in a coordinate system aligned with the normals to the symmetry planes. In the case of orthotropy, with three orthogonal planes of elastic symmetry, nine independent elastic coefficients remain to be determined [5]. The number of independent engineering constants is reduced further to five for the case of transverse isotropy when each plane through a longitudinal axis is a plane of elastic symmetry. In the case of isotropy only two independent engineering constants remain. Bone displays significant anisotropy [6], but the elastic symmetries are dependent on the level of structural organization. The anisotropic models that best describe the elastic behaviour at each of these levels will be described in the next section.
Research on transversely isotropic in-situ stress logging prediction of transitional shale reservoir: a case study of Daji Block, Eastern Ordos Basin, North China
Published in Petroleum Science and Technology, 2023
Haiyu Lin, Xiangjun Liu, Jian Xiong, Lixi Liang, Yi Ding, Jianjun Wu, Bing Li
Crampin (1981) divided the anisotropic medium into eight categories, such as complete anisotropy, orthotropic anisotropy, transverse isotropy, and isotropy. And the transverse isotropy refers to the medium with a vertical symmetry axis; that is, the physical properties of the medium along the symmetry axis are different, but the physical properties of the medium perpendicular to the symmetry axis are the same. The transitional shale reservoirs have good stratified structure as a result of the influence of the sedimentary environment and other factors, and the physical characteristics of acoustics, electricity, and mechanics are obviously different in the vertical direction, showing the characteristics of a vertical transverse isotropic medium (VTI). Based on generalized Hooke’s law, the stress-strain relationship of shale formation can be expressed as Equation 1. where σij is the component form of stress tensor, εkl is the component form of strain tensor, and Cijkl is the fourth-order stiffness coefficient matrix that characterizes material properties.
Spectral element method for dynamic response of transversely isotropic asphalt pavement under impact load
Published in Road Materials and Pavement Design, 2018
Lingyun You, Kezhen Yan, Yingbin Hu, Jun Liu, Dongdong Ge
The solution of multi-layered medium’s dynamic response under impact load is very important for parameter identification and structural evaluation in the non-destructive tests. To solve the above problem, it requires structural and material models to predict the displacements and stresses from the given model parameters. Traditionally, the structural materials were often assumed to be homogeneous, isotropic, and linearly elastic continuous (Al-Khoury, Scarpas, Kasbergen, & Blaauwendraad, 2001; Ameri, Yavari, & Scullion, 2009; Sebaaly, Mamlouk, & Davies, 1986). However, many materials in geotechnical engineering and pavement engineering are multi-layered and transversely isotropic (or cross-anisotropic). Transverse isotropy means that the materials have the same properties in one plane (e.g. the horizontal plane) and different properties in the direction normal to this plane (e.g. the vertical direction). For example, natural soils are often formed through a sedimentation process and have different mechanical properties in different directions (Ai, Cheng, & Zeng, 2011). Recently, several researches have concluded that asphalt concrete and unbound base layers also exhibit cross-anisotropic properties because of the orientation of aggregate, which is controlled by its shape, stress-induced compaction, and vertical traffic-loading conditions (Adu-Osei, Little, & Lytton, 2001; Wang, Hoyos, Wang, Voyiadjis, & Abadie, 2005). Therefore, it is more realistic to consider asphalt concrete and unbound base layers’ anisotropic properties than to treat them as homogeneous when investigating the solutions of stress and displacement for asphalt pavements.
Equivalent dynamic stiffnesses and 3D wave propagations of a transversely isotropic elastic ground in rocking and torsional interactions with a harmonically loaded rigid foundation
Published in Mechanics of Advanced Materials and Structures, 2023
Yazdan Hayati, Abolfazl Eslami, Alireza Rahai
Many researchers obtained the dynamic stiffnesses of the foundations using the exact analytical methods. In the analytical methods which are based on the three-dimensional elastodynamic relationships, firstly the mixed boundary conditions of the problem are determined in terms of displacement and stress components. Then the related dual integral equations are determined and they are reduced to several Fredholm integral equations. Solving the Fredholm integral equations numerically, all responses of the problem are determined. Several researches are available in the literature for dynamic/static rocking and torsional interactions of surface and embedded foundations with isotropic half-space and full-space elastic mediums, such as the researches done by Gladwell [15], Luco [16], Selvadurai [17], Luco and Mita [18], Pak and Saphores [19] and Pak and Abedzadeh [20]. In the past decades, the theory of anisotropic materials has received more attention because of their applications in modeling composite materials which are used widely in many fields of industry and engineering practice. May be the “transverse isotropy” is a form of anisotropy that has the most applications in modeling composite structures and layered materials such as grounds. Some of the researchers presented the dynamic Green’s functions and analytical solutions for transversely isotropic materials such as the works done by Ai and Li [21] and Ai et al. [22]. Moreover, several researchers investigated the dynamic/static rocking, torsional and vertical interactions of rigid foundations with a transversely isotropic elastic half-space or full-space ground, such as the works done by Selvadurai [23], Kirkner [24], Ahmadi and Eskandari [25], Ai et al. [26], Ai and Zhang [27], and Ai and Ye [28, 29].