Stress Tensor vs Stress Matrix: What's the Difference?

Click For Summary

Discussion Overview

The discussion centers around the difference between the stress tensor and the stress matrix, exploring theoretical and conceptual aspects of these terms in the context of mechanics and material science.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants assert that there is no difference between the stress tensor and the stress matrix, stating that stress is a second-rank tensor equivalent to a matrix.
  • Others argue that while a matrix can represent a tensor, the tensor itself exists independently of any coordinate system, and a matrix representation is only valid once a coordinate system is defined.
  • A later reply acknowledges the nuance in the argument regarding the representation of tensors and matrices.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between stress tensors and stress matrices, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

The discussion highlights the dependence on definitions and the implications of coordinate systems in the representation of tensors.

DC.Shivananda
Messages
6
Reaction score
0
Hi,can u please tell me the difference between the Stress tensor & the Stress matrix...
 
Engineering news on Phys.org
Hi DC.Shivananda, welcome to PF!

There is no difference. Stress is a second-rank tensor, which is equivalent to a matrix. (For comparison, a first-rank tensor is a vector, and a zero-rank tensor is a scalar.)
 
Mapes said:
Hi DC.Shivananda, welcome to PF!

There is no difference. Stress is a second-rank tensor, which is equivalent to a matrix. (For comparison, a first-rank tensor is a vector, and a zero-rank tensor is a scalar.)
That's somewhat true, depending on how rigorous you want to be.

A matrix is the representation of a tensor in a certain coordinate system. The tensor itself exists regardless of coordinate system, but you can only put it in matrix form once you define a coordinate system.
 
Ah, good point!
 

Similar threads

What is the relationship between force lines and the stress tensor field?
  • · Replies 18 ·
Replies
18
Views
2K
Understanding the Cauchy Stress Tensor: Clearing Up My Confusion
  • · Replies 7 ·
Replies
7
Views
3K
Cauchy's Formula for Stress tensor
  • · Replies 12 ·
Replies
12
Views
2K
Understanding elastic tensor matrix intuitively
  • · Replies 4 ·
Replies
4
Views
2K
Invariants of the stress tensor (von Mises yield criterion)
  • · Replies 2 ·
Replies
2
Views
2K
Confidence in FEA stress values?
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Is the Cauchy stress tensor really a tensor?
  • · Replies 8 ·
Replies
8
Views
3K
Principal Stresses in a Shear Flow
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Chain Link Strength: Which Method Should You Use?
  • · Replies 7 ·
Replies
7
Views
5K
What are the causes of thermal stress?
  • · Replies 8 ·
Replies
8
Views
2K