Concept explainers
To show that the total true strain is additive and the engineering strain is not additive.
Answer to Problem 2.49P
It is proved that the true strain is additive in nature and the engineering strain is not additive in nature.
Explanation of Solution
Given:
Original length of strip is
Length of strip after first step is
Length of strip after second step is
Length of strip after third step is
Concept used:
Write the expression for true strain in material.
Here,
Write the expression for total true strain.
Here,
Write the expression for engineering strain of material.
Here,
Write the expression for total engineering strain.
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, as the value of true strain is same in both conditions it can be concluded that the true strain is additive in nature.
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, as the value of engineering strain is not same in both conditions it can be concluded that the engineering strain is not additivein nature.
Conclusion:
Thus, it is proved that the true strain is additive in nature and the engineering strain is not additive in nature.
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Chapter 2 Solutions
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