- #1
camilo
- 5
- 0
Does a sphere made of an elastically anisotropic material (eg. a material of cubic symmetry) subject to an hydrostatic pressure retains its spherical shape ?
DrDu said:cubic symmetry is still isotropic, but for lower symmetries (like, e.g., orthorhombic), the pressure will lead to a deformation of the sphere.
Sorry, I had optical properties in mind. As the constitutive stress strain equation involves a fourth order tensor (as opposed to the second order dielectric tensor), a cubic material will not behave isotropically.camilo said:How a cubic symmetric is isotropic ?
In the cubic symmetry there are three independent elastic constants, s_11, s_12 and s44. In a cubic crystal structure there are directions along which the material is softer and others along which is is stiffer. For instance, Silver, which has an fcc structure has a Young modulus of 94 GPa along (110), whereas along (100) it is 50 GPa.
So it would retain its spherical shape ?Orodruin said:That being said, the symmetries of the fourth order tensor for cubic symmetry are such that the resulting strain tensor must be isotropic if the stress tensor is, which is the case when you subject an object to hydrostatic pressure. As such, the material with cubic symmetry would deform isotropically.
DrDu said:I.e. the sphere will be deformed into an ellipsoid with their main axes are the symmetry axes of the material.
An elastically anisotropic sphere under pressure refers to a spherical object that has different elastic properties in different directions when subjected to external pressure. This means that the sphere's response to pressure will vary depending on the direction in which the pressure is applied.
Unlike isotropic spheres, which have the same elastic properties in all directions, anisotropic spheres have varying elastic properties depending on the direction of applied pressure. This means that the stress and strain experienced by these spheres will also vary depending on the direction of pressure.
The elastic behavior of an elastically anisotropic sphere under pressure is influenced by factors such as the material properties, the magnitude and direction of the applied pressure, and the shape and orientation of the sphere. Other factors such as temperature and external forces can also affect the elastic behavior.
The elastic behavior of an elastically anisotropic sphere under pressure is typically studied through experimental methods, such as mechanical testing or using specialized equipment like a stress-strain analyzer. Theoretical models and simulations can also be used to analyze and predict the elastic behavior of these spheres.
Understanding the elastic behavior of anisotropic spheres under pressure has important applications in various industries, such as materials science, geology, and engineering. This knowledge can help in designing and optimizing structures and materials for specific purposes, such as building stronger and more durable structures or developing new materials with unique properties.