Is Strain a scalar quantity?

In summary: As a general rule, the answer to the question "scalar or not?" is "not".In summary, strain is not a scalar or a vector, but a tensor with multiple components. While it may appear to be unitless in simple cases, it still has a direction and is not considered a scalar quantity.
  • #1
adabistanesoophia
12
0


Hi,

I know that strain is a unit less quantity (Tensile Strain) but whether Strain is a scalar quantity or not? If it is a scalar quantity then why?

Regards,

Muhammad Rizwan Khalil
 
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  • #2
What do you think?
 
  • #3
I think its a unitless quantity as for as its types are concerned. It has two types Tensile Strain and Volumetric Starin.

But confused about the term "Strain".

So still confused that it is scaler or not?

MUhammad Rizwan Khalil
 
  • #4
Even though strain is unitless (actually unity units), it has a direction, right? What does that mean about whether it is a scalar or not?
 
  • #5
Strain is defined as "Measurement of deformation of a solid when stress is applied 2 it".

So where direction is invlved?

So can v say it is a scalar quantity or not?

Muhammad Rizwan Khalil
 
  • #6
Strain is a deformation in a direction, is it not?
 
  • #7
I have coated the defination and in defination there is nothing like this. When we consider its types and solve problem then no unit is there and we have a defination of a scalar quantity is "quantities with unit and magnitude".

But no unit when we solve the problem. SO it can be scalar?
 
  • #8
adabistanesoophia said:
I have coated the defination and in defination there is nothing like this. When we consider its types and solve problem then no unit is there and we have a defination of a scalar quantity is "quantities with unit and magnitude".

But no unit when we solve the problem. SO it can be scalar?

Every fundamental physical quantity (or one which can be derived out of these) has a unit, regardless of the type of quantity it is mathematically.
 
  • #9
So what unit strain has?
 
  • #10
adabistanesoophia said:
I have coated the defination and in defination there is nothing like this. When we consider its types and solve problem then no unit is there and we have a defination of a scalar quantity is "quantities with unit and magnitude".

But no unit when we solve the problem. SO it can be scalar?

I think you are confusing what a scalar is. Contrast "scalar" with "vector". A scalar has magnitude only (regardless of what its units are). A vector has magnitude and direction.

And as radou says, you should remember that strain actually has units of m/m. You can further say things like m/m = 1, so that's why strain is sometimes referred to as "unitless". But units have nothing to do with the difference between a vector and a scalar.

Now, do you think strain is a scalar or a vector?
 
  • #11
In ur opnion, I think it is a vector coz u have coated that

"Strain is a deformation in a direction, is it not?"

How it has direction?
 
  • #13
Actually, in its most general definition, strain is a tensor (as is stress).
 
  • #14
adabistanesoophia said:
Strain is defined as "Measurement of deformation of a solid when stress is applied 2 it".

So where direction is invlved?

So can v say it is a scalar quantity or not?

Muhammad Rizwan Khalil

OK - that is an "beginner level" definition of strain. The whole truth is not so simple.

Strain is neither a scalar nor a vector. In the most general case it's a 2-dimensional symmetric tensor, defined by 9 numbers at any point. (Only 6 of the numbers are independent, because of the symmetry). Stress is also a tensor. The thing that corresponds to "Young's Modulus" is a 4-dimensional tensor with up to 21 independent constants for a general anisotropic material. (For an isotropic material there are only 2 independent constants, not 21. Young's Modulus and Poisson's Ratio are one pair of constants that define the stress-strain behaviour of an isotropic material).

When you are considering a problem like the axial stress in a rod producing an axial strain, the things you are calling "stress" and "strain" are single components of the complete stress and strain tensors. The others are either zero, or you are not interested in them.

You don't need all this heavyweight tensor stuff to handle the simple cases like constant axial stress in a uniform rod. In the equations you have probably seen like

"stress" = force/area
"stress" = Youngs Modulus times "strain"
Extension = "strain" * length

the terms I put in quotes (like "stress") are actually single components of the full stress and strain tensors. They may look like scalars, but they are not.

Obviously until you have studied tensors some of this explanation won't mean much - but as an example, the product of a 2-D tensor times a vector is another vector. The product of the stress tensor with a unit vector gives the force vector on the plane normal to the unit vector. This is completely general and gives you the force on ANY plane section through a body with ANY state of stress in it. For a rod with axial tension, most of the terms in the tensor and the vector are zero, so you can use equations that look like scalar equations, even though they are not really scalars.
 
Last edited:

1. What is strain?

Strain is a measure of the deformation or change in shape of an object in response to an applied force or stress.

2. Is strain a scalar or vector quantity?

Strain is a scalar quantity, meaning it has only magnitude and no direction. This is because it is defined as the ratio of the change in length or shape of an object to its original length or shape, which does not have a specific direction.

3. How is strain different from stress?

Stress and strain are related but different concepts. Stress is the force per unit area applied to an object, while strain is the resulting deformation or change in shape of the object. In other words, stress causes strain.

4. What are the different types of strain?

There are several types of strain, including tensile strain, compressive strain, shear strain, and volumetric strain. Tensile strain is when an object stretches in response to an applied force, compressive strain is when an object contracts, shear strain is when an object experiences a change in shape without changing in volume, and volumetric strain is when an object changes in volume without changing in shape.

5. How is strain measured?

Strain is typically measured using the strain gauge, a device that detects changes in length or shape of an object. It works by converting mechanical displacement into an electrical signal, which can then be measured and used to calculate the strain.

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