What is the equation of this stress-strain curve?

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SUMMARY

The discussion focuses on expressing strain in terms of stresses for a nonlinear hardening stress-strain curve. Participants emphasize the need to break down the curve into sections, identifying start and end values of strain (ε) for each segment. For each segment, a corresponding linear function must be derived, resulting in a comprehensive list of linear functions paired with their valid intervals. This method allows for a clear algebraic representation of the stress-strain relationship.

PREREQUISITES
  • Understanding of nonlinear hardening materials
  • Familiarity with stress-strain curves
  • Basic knowledge of algebraic functions
  • Ability to interpret graphical data
NEXT STEPS
  • Research methods for deriving linear functions from nonlinear curves
  • Explore the concept of piecewise functions in mathematics
  • Study applications of stress-strain analysis in material science
  • Learn about different types of material hardening behaviors
USEFUL FOR

Material scientists, mechanical engineers, and students studying material behavior under stress will benefit from this discussion.

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For this nonlinear hardening stress strain curve, how do you express strain in terms of stresses ?

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Arguably you already have .That plot tells you everything .

If you mean though how to write it down using algebraic functions then you have to do it in sections . For each of the line segments on that plot identify the start and end values of ε for that segment and find a linear function which is valid for that line segment .

You then have a list of linear functions matched with a list of the intervals over which they are valid .
 
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