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touqra
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Can we curl a stress tensor? What physically meaning will it be?
Incidentally, the defn of curl resembles the antisymmetrized derivative (F in electromagnetism & the curvature tensor in GR). That's not accidental, is it?chroot said:The term "curl" usually applies to vector fields. If there is an equivalent definition of curl for tensor fields, I am not familair with it.
- Warren
Indeed, Thrice, this is not accidental. I am learning much of the nature of axial vectors, curl, and the Minkowski tensor. I need to understand the forms expressed in spherical terms and fields for magnetism.Thrice said:Incidentally, the defn of curl resembles the antisymmetrized derivative (F in electromagnetism & the curvature tensor in GR). That's not accidental, is it?
touqra said:Can we curl a [second rank] tensor?
nike^^ said:i think that the rotor (curl) of a bilinear tensor T can be defined as follows:
touqra said:I was thinking of something like Helmholtz's theorem, where if you specify the div and curl of a vector field, you then know everything there is to know about the field.
Maybe there's something similar for rank 2 tensor, like the stress tensor, or higher tensors.
A stress tensor is a mathematical concept used in physics to describe the stress or force per unit area acting on a material. It is a 3x3 matrix that represents the distribution of forces and torques on an infinitesimal element of a material.
In materials science, the stress tensor is used to understand the mechanical properties of materials, such as how they deform under stress. It can also be used to predict how a material will behave under different conditions and how it will respond to external forces.
Curling a stress tensor refers to taking the curl of the stress tensor, which is a mathematical operation that describes the tendency of a vector field (in this case, the stress tensor) to rotate. This can provide insights into the rotational forces acting on a material.
Exploring the meaning of curling a stress tensor can help us understand the complex forces and deformations that occur in materials under stress. It can also provide insights into the stability and failure mechanisms of materials, which is crucial in engineering and design processes.
Curling a stress tensor is not only used in materials science but also has applications in fluid mechanics, electromagnetism, and other areas of physics. It is a fundamental concept in understanding how forces and fields interact and can be applied to a wide range of systems and phenomena.