Tensors, Mechanics, Loose Ends...
I have not yet had my math-physics friend look this over (the math
definitions part) to make sure it is all correct. I do know that
scalars, arrays, matrices, ... are all examples of tensors. I also
know that tensors are used to define stress and strain in mechanics.
- A Tensor has an order.
- A
zero order tensor is a scalar. Numbers are scalars.
- A
first order tensor is a set of numbers, or an array.
- A
second order tensor is a matrix.
- A
third order tensor--doesn't have a common name.
- Note difference between 'order' and 'dimension.' A 3 x 5 matrix has
the dimensions 3 and 5, but is second order. You could think of 'order'
as the number of different "dimensions" that a tensor has.
- [Wang-1]Stress is a tensor because in addition to
the vector which defines
the force, stress also depends on a second vector which represents
the surface upon which the stress force is acting upon.
- Stress can be resolved into two components:
- normal stress- the stress component which is normal to the surface.
- shear stress- the stress component which acts in the plane of the surface.
This resolution into two components is quite similar to taking a ray in
R2 (two dimensional Real) space, and resolving into its x and y components.
- A normal stress which acts in the direction away from a surface is called
a tensile stress, and it has a positive value.
- A normal stress which acts in the direction toward a surface is called
a compressive stress, and it has a negative value.
Last Update- January 15, 1995- wld