Isotropy refers to the characteristic that the physical, chemical and other properties of an object will not change due to different directions, that is, the performance values of an object measured in different directions are identical, which is also called homogeneity.physical propertyCharacteristic that does not change with the direction of measurement.That is, the performance measured along different directions of the object shows the same value.Such as all gases, liquids (except liquid crystals) andAmorphousAll objects show isotropy.
Also called homogeneity.The property that physical properties do not change with the direction of measurement.That is, the performance measured along different directions of the object shows the same value.For example, all gases, liquids (except liquid crystals) and amorphous objects show isotropy.For example, although metals and rocks do not have regular geometric shapes and their physical properties are the same in all directions, they are composed of many grains. In fact, they are crystals and have certain melting points.Because the grains are arranged irregularly in the spatial direction, the whole metal is isotropic.Of course, the atmosphere is also isotropic.What you mentioned is the atmosphere in different regions. Due to pressure and other factors, the performance will be different, but the properties of all directions at a point are the same.[1]
Relevant knowledge
Announce
edit
Orthoanisotropy
Orthotropic，If every point in the elastic body has such a plane, which has the same elastic properties as the symmetrical direction of the plane, the plane is called the elastic symmetry plane of the object.(The elastic symmetry plane refers to the symmetry plane of the elastic modulus, such as isotropy, where the elastic modulus is equal in all directions at a point, transversely isotropic, and the elastic modulus rotates at a point by any angle around the axis, and remains unchanged. Since isotropy is independent of position, then symmetry is also independent of position.)
The direction perpendicular to the elastic symmetry plane is called the elastic principal direction of the object.If yz is the elastic symmetry plane, the x-axis is the elastic principal direction.
Orthotropic material means that there are three mutually perpendicular symmetry planes passing through any point of the material.
Wood is a typical orthotropic material with different properties in three directions (axial, radial and circumferential).
Typical orthotropic materials
For an elastic body with an elastic symmetry plane, its elastic constants will be reduced from 21 to 13.
For an elastic body with two elastic symmetry planes, its elastic constants will be reduced from 13 to 9.
If the elastic body has three elastic symmetry planes, there will be no new changes in the constitutive equation.Therefore, if there are two elastic symmetry planes in three mutually perpendicular planes, the third must be an elastic symmetry plane.
The constitutive equations of two elastic symmetry planes show that if the coordinate axis is consistent with the principal direction of elasticity, the normal stress is only related to the normal strain, and the shear stress is only related to the corresponding shear strain, so there will be no coupling between tension and compression and shear, as well as between shear in different planes.This kind of elastic body is called orthotropic elastic body, and its independent elastic constants are 9.[2]
Constitutive equation of elastic body with two elastic symmetry planes
anisotropy
anisotropic，Anisotropy is for isotropy.For example, forsingle crystalFrom the microscopic point of view, it is composed of one grain, whose crystal lattice orientation is completely consistent, but its properties in different directions are different due to different crystal planes and different atomic arrangements in crystal orientation,Is called anisotropy。For polycrystals, it is composed of many grains. The lattice orientation inside each grain is completely consistent, but the orientation between grains is different. Its performance is the statistical average of the performance of each grain, so its performance in all directions is roughly the same,Is called isotropy。For example, the elastic modulus of pure iron, ifsingle crystalAlongUnit cellThe value in the space diagonal direction is 290000MPa, while the value along the edge of the cell is 135000MPa;if it isPolycrystalNo matter where the sample is taken, the measured value is about 210000MPa.
Anisotropic single crystal
In solid mechanics, if the properties of elastic bodies are the same in all directions, or the materials are symmetrical about any plane, then the elastic bodies are called isotropic materials[3]）。
difference
Announce
edit
Physical properties can be measured in different directions.If the measurement results in all directions are the same, it means that its physical properties are independent of orientation, and it is called isotropy.If the physical properties are closely related to the orientation, and the measurement results of different orientations are quite different, it is called anisotropy.The internal factor causing this difference is the symmetry of the material structure.
In gas, liquid orAmorphous solidIn, the arrangement of atoms is chaotic, so the statistical results are the same in all directions, so its physical properties must be isotropic.The atoms in the crystal have regular arrangement, and the structurally equivalent directions are limited to certain specific directions determined by the crystal symmetry.Therefore, in general, physical properties are anisotropic.
For example, the magnetization difficulty direction of α - iron is shown in Figure 1.
Fig. 1 Difficult and easy magnetization direction of α - iron
The elastic modulus of iron is the maximum (7700kgf/mm) along [111] and the minimum (6400kgf/mm) along [100].Crystals with low symmetry (such as crystal and calcite) have different refractive indices along different directions in space.The refractive index and elastic modulus of amorphous (supercooled liquid) are isotropic.When the symmetry of the crystal is very high, some physical properties (such as conductivity, etc.) will become isotropic.When an object is composed of many small single crystals with disordered orientation, its apparent physical properties are isotropic.The strength of general alloys takes advantage of this.If the small single crystals in the polycrystals are arranged along a specific orientation due to special processing (such as deformation "texture" of metal, directionally grown two-phase crystal mixture, etc.), the properties of polycrystals will also show anisotropy.
Silicon steel sheet is a specific application of this property.Some liquid crystals between liquid and solid have ordered molecular orientation although their molecular positions are disordered.In this way, its physical properties also have anisotropy.[1]
application
Announce
edit
When detecting from different directions of different substances, their physical or chemical properties may be the same or different.If all directions are the same, this material is called isotropic material, and this property is called isotropy;If different, this material is called anisotropic material, and this property is called anisotropy.[1]
