How Is Normal Strain Derived in Continuum Mechanics?

In summary, normal strain is a measure of the deformation or elongation of a material in response to an applied force. It is calculated by dividing the change in length of a material by its original length and is represented by the symbol ε. The units of normal strain are dimensionless and a material is considered "stuck" when it reaches its maximum stress or strain limit and can no longer deform. Normal strain is directly related to being "stuck" as it is a measure of the deformation of a material.
  • #1
nissan4l0
11
0
http://imgur.com/SnHyP

What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ?

If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do we make to derive the final equation?
 
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  • #2
You make a Taylor expansion of sqrt(1+e), where "e" is regarded to be small.
Then, you have, approximately, sqrt(1+e)=1+e/2.
 

Related to How Is Normal Strain Derived in Continuum Mechanics?

What is the meaning of normal strain?

Normal strain is a measure of the deformation or elongation of a material in response to an applied force. It describes the change in length of a material in the direction of the applied force.

How is normal strain calculated?

Normal strain is calculated by dividing the change in length of a material by its original length. It is represented by the symbol ε and is typically expressed as a decimal or percentage.

What are the units of normal strain?

The units of normal strain are dimensionless, meaning they have no physical units. It is simply a ratio of lengths and does not have a specific unit of measurement.

What is meant by a material being "stuck"?

A material is considered "stuck" when it is unable to deform or elongate under an applied force. This usually occurs when the material has reached its maximum stress or strain limit and can no longer withstand any further deformation.

How is normal strain related to being "stuck"?

Normal strain is directly related to being "stuck" as it is a measure of the deformation or elongation of a material. When a material reaches its maximum strain limit, it is essentially "stuck" and unable to deform any further.

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