Transcription of e vs. engineering strain ε - john.maloney.org
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e vs. engineering strain ε - john.maloney.org
Notes on true strainevs. engineering strain John MaloneySept. 20, 2006 strain is normalized deformation. We can express this relationship in differential form fora bar undergoing axial deformation asd( strain )=dLL, or an infinitesimal deformationdLnormalized to lengthL. We properly find the total axial straine(known as thetrue strain ) by integrating this expres-sion from the initial lengthL0to the final lengthLF:e LFL0dLL=ln(L)|LFL0=ln(LFL0)=ln(L0+ LL0)=ln(1+ LL0)where Lis the amount of deformation (positive for elongation). The lengthLis kept insidethe integral because it changes as the bar deforms from lengthL0to lengthLF. If Lis small compared to the length of the bar, thenL L0at all stages of the deformationprocess and the1 Lterm can be taken outside the integral. The resulting approximate strain is known as theengineering strain : 1L0 LFL0dL=1L0L|LFL0=LF L0L0= LL0 The same result is acquired through a Taylor series expansion ofe=ln(1+ LL0). The Taylorseriesf(x0+ x)=f(x0)+ f(x) x x0 x+12!
• Characteristics of true strain e: 1. It’s the exact value, not an approximation. 2.Sequentialstrainscanbeadded: iftwostrainse 1 ande 2 areexecutedsequentially,thetotal strain is e 1 +e 2 …
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