Stress 
An applied force or system of forces that tends to strain
or def
orm a body.


Strain  A deformation produced by stress. 
It sounds simple enough, but you should realize that there are still some choices to make. Specifically, what area should be used for the crosssectional area? Should you use the original area or the current area as the load is applied? By the same token, should changes in length always be compared to the original length of the specimen?
The answer is that we will define different types of stress and strain measures according to the way we perform the calculations. Engineering stress and strain measures are distinguished by the use of fixed reference quantities, typically the original crosssectional area or original length. More precisely,
(1) 
Engineering vs. True

Engineering stress and strain measures incorporate fixed reference quantities. In this case, undeformed crosssectional area is used. True stress and strain measures account for changes in crosssectional area by using the instantaneous values for area, giving more accurate measurements for events such as the tensile test. 
(2) 
True stress can be related to the engineering stress if we assume that there is no volume change in the specimen. Under this assumption,
(3) 
True Strain: The true strain is defined as the sum of all the instantaneous engineering strains. Letting
(4) 
ln  (5) 
ln ln ln  (6) 
In closing, you should note that the true stress and strain are practically indistinguishable from the engineering stress and strain at small deformations, as shown in Figure 4. You should also note that as the strain becomes large and the crosssectional area of the specimen decreases, the true stress can be much larger than the engineering stress.
Key note: 
As the strain becomes large and the crosssectional area of the specimen decreases, the true stress can be much larger than the engineering stress. 
Exercise: The first first movie file of the tensile test is shown below. Pause the movie at the beginning, and use the scroll to view the specimen at different times. At what point in the test do you begin to notice a real change in the crosssectional area? Roughly what percentage of the total time of the test has elapsed?
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