Before going into strain in mechanical analysis and simulation, let’s first have a look of how
strain is measured in a testing lab for a real experiment. This will help us to understand the
nature of strain. Besides, engineers are often given lab data for material
definition and for evaluating material status. So in a testing lab, one common way to measure
strain of a specimen is to use strain gauge. The gauge is attached to the object. As the object
is deformed, the foil of the strain gauge is deformed, causing its electrical resistance to
change, so that strain is detected and reported. Note that the reported strain is an averaged
value over the strain gauge area. And there are different sizes of
strain gauge to use for different situations. In one test, using different size of strain gauge,
you might get different strain values. Strain is local, each material point over
the body has its own strain value. Ideally, if there’s an extremely
small strain gauge, it can report the accurate local value. But in real life,
there’s always a size for the strain gauge, so what is reported will be an averaged strain.
Let’s move forward to the definition of strain. First of all, let’s think of “Deformation” instead
of strain for now. How is deformation defined? As we know, deformation is measured by subtracting
the original shape from the deformed shape. This definition of deformation is unique. No
matter at what condition, to calculate deformation, this is the way to go.
However, for “strain”, the definition of it, is not unique. There are various of strain
definitions and each of them has its own feature or purpose.
Here, we will use the uniaxial tensile test to explain
strain definition for 1-Dimension problems. The uniaxial tensile test is one of the most
commonly used tests in a lab. A metal sample is held fixed on one
end and stretched from the other end. The original length of the sample is L_0,
with the stretching, the length is increased by delta_L. Eventually, the metal sample will break
and before that we can see necking, but our discussion here is limited to uniform tensile
deformation far before any failure happens. The statement of this mechanical problem can
be represented by this sketch with fixed boundary condition
and a displacement control on the top. As I mentioned before, strain definition
is not unique. Imagine that if you were a pioneer in mechanics, how would you
define strain for the uniaxial tensile test. The key is to use this quantity to describe the
distortion of the body, given the original length and the change of length.
How about define the strain as the ratio between change of length and the original length?
Or, the ratio between the total deformed length to the original length?
Or, how about the natural logarithm of the first idea?
Are these all valid strain definitions？ In fact, although strain does not has a unique
definition, there are some base rules when defining a strain measurement.
Rule number 1 is: as a strain measurement, when there is no deformation, the strain
value should be absolutely zero. So when the part of the body is remained undeformed,
the strain quantity should read as 0. Rule number 2 is, for all valid strain
measurements, when deformation is very small, the strain value from different strain measurements
should be very close to each other. So for small deformation problem,
we expect same or very similar strain value, no matter which strain definition is used.
Keep these two rules in mind, you might find your own strain definition.