The relaxation modulus is represented by the image below.
To compute for relaxation modulus, two essential parameters are needed and these parameters are Time Dependent Stress (σ(t)) and Strain Level (εo).
The formula for calculating relaxation modulus:
Er(t) = σ(t)/εo
Where:
Er(t) = Relaxation Modulus
σ(t) = Time Dependent Stress
εo = Strain Level
Let’s solve an example;
Find the relaxation modulus when the time dependent stress is 12 and the strain level is 6.
This implies that;
σ(t) = Time Dependent Stress = 12
εo = Strain Level = 6
Er(t) = 12/6
Er(t) = 2
Therefore, the relaxation modulus is 2 Pa.
Calculating the Time Dependent Stress when the Relaxation Stress and the Strain Level is Given.
σ(t) = Er(t) (εo)
Where:
σ(t) = Time Dependent Stress
Er(t) = Relaxation Modulus
εo = Strain Level
Let’s solve an example;
Find the time dependent stress when the relaxation modulus is 18 and the strain level is 5.
This implies that;
Er(t) = Relaxation Modulus = 18
εo = Strain Level = 5
σ(t) = Er(t) (εo)
σ(t) = 18 (5)
σ(t) = 90
Therefore, the time dependent stress is 90.
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