Stress/Strain and Youngs Modulus

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SUMMARY

The discussion centers on the calculation of work done in a Hookean material using stress and strain, specifically addressing the confusion surrounding the factor of 0.5 in the equation. The area under the stress-strain curve is identified as a triangle, leading to the formula for work done being expressed as 0.5(F/A)(e/L). The participants clarify that the work done should be calculated as the integral of Fde, resulting in 0.5Fe, which aligns with the principles of Young's Modulus. The discrepancy in answers is attributed to the misunderstanding of the variable nature of force during the deformation process.

PREREQUISITES
  • Understanding of Hooke's Law and its application in material science
  • Familiarity with stress and strain concepts in mechanics
  • Basic knowledge of calculus, specifically integration
  • Knowledge of Young's Modulus and its significance in material properties
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  • Study the derivation of the stress-strain curve for different materials
  • Learn about the applications of Young's Modulus in engineering design
  • Explore advanced integration techniques for calculating work done in non-linear materials
  • Investigate the implications of variable force in dynamic loading scenarios
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Students in mechanical engineering, materials science professionals, and anyone involved in the analysis of material behavior under stress and strain conditions.

ravsterphysics
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Homework Statement


1.JPG


Homework Equations

The Attempt at a Solution


The shaded area is a triangle so the area of a triangle for this particular graph is this:

0.5 (Stress)(Strain) which gives:

0.5(F/A)(e/L) so the top would give work done and the bottom would give volume but we're still left with 0.5 in front of this so the answer should be A yet the answer is B? Why has the half disappeared?
 
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The work done is not F*e because F is not constant throughout the process. The work done is the integral of Fde, which for a Hookean process is 0.5Fe
 

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