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Anisotropic ferromagnet
Published in A.G. Gurevich, G.A. Melkov, and Waves, 2020
Anisotropy is a dependence of the properties of a substance or a body on the angles between the directions of applied fields and some preferred directions. These directions can be determined by the substance structure, by the shape of the body, or (if we consider the properties in ac fields) by the directions of some external steady fields. Two kinds of anisotropy were already treated in Chapter 1. First, the gyrotropy when the direction of the steady magnetization M0 was the preferred one, and the high-frequency magnetic susceptibility acquired the tensor form (1.42). Second, we have seen in Section 1.5 that the ferromagnetic-resonance conditions depend on the orientation of M0 relative to the ellipsoid axes. Such anisotropy can be referred to as the shape anisotropy. However, it was assumed throughout Chapter 1 that the substance itself (a ferromagnet), in the absence of steady magnetization, is isotropic.
Nonlinear and Anisotropic Materials
Published in Stanley Humphries, Field Solutions on Computers, 2020
Anisotropic materials have different properties along different directions. For example, shifts in polarization charge in dielectrics may differ along crystalline axes. This section covers two-dimensional finite-element models for simple anisotropic dielectrics. The crystalline axes are in the plane of solution at a right angle to each other along unit vectors a^1 and a^2 (Figure 8.4). Constant values of relative dielectric constant ϵ1 and ϵ2 apply along the two directions. An applied field Eo1 along a^1 gives a total field E1 () Eo1=ϵ1 E1.
Mechanical testing
Published in C M Langton, C F Njeh, The Physical Measurement of Bone, 2016
Christopher F Njeh, Patrick H Nicholson, Jae-Young Rho
Materials that have different properties in different directions are termed anisotropic. Bone structural and mechanical anisotropy refers to the variation in orientation of trabeculae and consequently mechanical properties and is an important architectural property of cancellous bone. As many as 21 independent elastic constants are required to characterize the mechanical behaviour of bone completely. Most materials have planes of symmetry that reduce the level of anisotropy and hence the number of material constants required to fully characterize the material. Depending on the variation with direction the material could be isotropic (no variation), transversely isotropic or ortho tropic [18]. Ortho tropic materials have properties that differ in each of the three mutually perpendicular directions, and nine elastic constants are required to characterize their mechanical properties fully. Bovine femur is an example of a tissue with orthotropic material symmetry. Materials that have properties that are constant within a given plane are termed transversely isotropic. Human osteonal bone is an example of a transversely isotropic material, because it has the same Young’s modulus in all transverse directions, but higher Young’s modulus in the longitudinal directions. Materials that have the same elastic properties in all directions have the highest order of symmetry and are termed isotropic. Complete characterization of the mechanical behaviour of anisotropic material requires mechanical testing to be performed in several different orientations. Ideally, mechanical testing of a specimen should be oriented relative to the axes of material symmetry.
Relationship among air void microstructural characteristics, stiffness, and fatigue of asphalt concrete mixtures
Published in Road Materials and Pavement Design, 2022
Thiago Delgado de Souza, Alexis Jair Enríquez-León, Patrícia Hennig Osmari, Larissa Montagner de Barros, Alex Duarte de Oliveira, Francisco Thiago Sacramento Aragão, André Maués Brabo Pereira
Anisotropy can be defined as the variation of the material physical properties when they are measured in different directions. In this paper, the degree of anisotropy is defined as a 3D structural symmetry parameter that determines the presence or absence of a preferential alignment of structures along a particular direction. This characteristic may significantly affect the mechical responses of the materials (Choudhary et al., 2019; Kastner et al., 2021 Odgaard, 1997). It can be obtained using the decomposition of the anisotropy tensor, resulting in eigenvalues and eigenvectors, which are related to the material lengths and orientation, regarding the different axes. Equation (3) (Odgaard, 1997) was used to quantify the degree of anisotropy for the air voids. It is worthy to mention that a degree of anisotropy of 0 characterises a material hypothetically isotropic, while a value of 1 represents a totally anisotropic sample.
Chebyshev pseudospectral method in the reconstruction of orthotropic conductivity
Published in Inverse Problems in Science and Engineering, 2021
Everton Boos, Vanda M. Luchesi, Fermín S. V. Bazán
Materials whose physical properties, such as elasticity moduli, Poisson coefficients, heat conductivity, etc., vary depending on spatial orientation of the physical body are referred to as anisotropic, while those materials that do not change with spatial orientation are referred to as isotropic [1]. Orthotropic material is a type of the anisotropic material whose characteristics remain unchanged along its planes of elastic symmetry. In nature, there are many materials that can be considered anisotropic such as crystal, woods, geological sediments and biological tissues. With the advent of new technologies, new anisotropic materials have been manufactured by industrial engineering, making it necessary to know their driving properties. These properties can be roughly defined by the difference in physical material or mechanical attributes when measured along different axes, such as absorbance, refraction, conductivity, tensile strength, etc.
Eigenvalue approach to hyperbolic thermoelastic problem in porous orthotropic medium with Green-Lindsay model
Published in Mechanics Based Design of Structures and Machines, 2020
Abdush Salam Pramanik, Siddhartha Biswas
Anisotropic materials are materials whose properties are directionally dependent. Unlike isotropic materials that have material properties identical in all directions, anisotropic materials properties such as Youngs modulus, change with direction along the object. Directionally dependent physical properties of anisotropic materials are significant due to the effects it has on how the material behaves. Anisotropic materials, naturally and man made, are used in multiple ares of study. Anisotropic materials are also a result of manufacturing of materials such as a rolling or deep-drawing process. Composites and other materials are used and altered for specific applications. Wave motion in an anisotropic solid is fundamentally different from motion in an isotropic solid, although the effects are often subtle and difficult to recognize. There are such a wide range of three-dimensional variations possible in anisotropic media that it is difficult to understand the behavior of wave motion without experimentation. Seismic waves penetrating such anisotropic material display a number of characteristic and diagnostic effects, which are subtly different from those of waves propagating in isotropic solids.