Answer and Explanation:
Engineering Stress of a material is defined as the applied load or force divided by the original cross sectional Area of the material.
σ(engineering) = F/(Ao)
True Stress is defined as the applied load or force divided by the actual cross-sectional area (the changing area with respect to time) of the material at that point in time. It's an instantaneous stress.
σ(true) = F/A
Engineering strain is a measure of how much a material deforms under a particular load. It is the amount of deformation in the direction of the applied force divided by the initial length of the material.
ε(engineering) = Δl/lo
True Strain measures instantaneous deformation. It is obtained mathematically by integrating strain over small time periods and summing them up. Hence,
ε(true) = In (lf/lo)
The calculations,
First step, 10m to 10.1m, Δl = 0.1m, lf = 10.1m, lo = 10m
ε(engineering) = 0.1/10 = 0.01
ε(true) = In (10.1/10) = 0.00995
Second step, 10.1m to 10.2m, Δl = 0.1m, lf = 10.2m, lo = 10.1m
ε(engineering) = 0.1/10.1 = 0.0099
ε(true) = In (10.2/10.1) = 0.00985
Overall, 10m to 10.2m, Δl = 0.2m, lf = 10.2m, lo = 10m
ε(engineering) = 0.2/10 = 0.02
ε(true) = In (10.2/10) = 0.0198
QED!
