What is a Tensor? | Practical Uses & Difference from Vector

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Discussion Overview

The discussion revolves around the concept of tensors, their practical applications, and how they differ from vectors. Participants explore the theoretical underpinnings of tensors, particularly in the context of structural engineering and fluid mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant defines a tensor as a vector generalized to three dimensions, highlighting its use in structural engineering with anisotropic materials.
  • Another participant presents an analogy comparing scalars, vectors, matrices, and tensors.
  • A further contribution describes tensors in terms of their matrix representation, specifically referencing the components of strain and stress tensors in fluids.

Areas of Agreement / Disagreement

Participants present various definitions and analogies regarding tensors, indicating that multiple competing views exist on how to conceptualize and apply tensors in different contexts. The discussion remains unresolved regarding a singular definition or understanding of tensors.

Contextual Notes

Some definitions and examples provided may depend on specific contexts, such as structural engineering or fluid mechanics, which could limit their general applicability. There are also unresolved aspects regarding the mathematical representation and properties of tensors.

Who May Find This Useful

This discussion may be useful for students and professionals in physics, engineering, and mathematics who are interested in the foundational concepts of tensors and their applications in various fields.

yaswanth_040
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Hi all,
What is a tensor? Can any give a practical use of it? How it is different from Vector?

Thank You,
Yaswanth
 
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Tensor is a vector generalized to 3Dimensions. Tensors are typically found in structural engineering for instance with anisotropic materials with characteristics which change in direction. Here you can see a typical strain tensor

http://en.wikipedia.org/wiki/Deformation_(mechanics)#Shear_strain

Other topics include inertia, and strength.
 
Try thinking of a vector but with two dimensions that is written down in matrix form. For example the strain tensor in a solid like Viscousflow mentioned. Or the stress tensor in a fluid. The the components of the stress tensor are

Txx Txy Txz
Tyx Tyy Tyz
Tzx Tzy Tzz

So for an element in the fluid Txx would be the stress on the x face in the x direction. So it is a normal stress or pressure. Txy would be the stress on the x face in the y direction, shear stress caused by viscosity.
 

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