Elastic˗Plastic Stress˗Strain Model for Material Response

Key Concept: One model to represent nonlinear material response is to assume a linear relationship between stress and strain up to the yield stress followed by a constant stress. Again, the slope in the

linear range is G, the Modulus of Rigidity also called Shearing Modulus. See the figure below.

In a Nut Shell: The equation relating stress and strain in the linear range remains as:

τ = G γ

where τ is the shear stress (lb/in², mPa, N/mm²)

γ is the shear strain (in/in, mm/mm, microstrain)

G is the Modulus of Rigidity (a material property ˗ psi, GPa)

Also τ_y is the yield stress for the material (lb/in², mPa, N/mm²)

Material	Value of Modulus of Rigidity, G
Mild Steel	11 x 10^6 psi	77 GPa
Aluminum	4 x 10^6 psi	27 GPa

Return to Notes on Solid Mechanics

Copyright © 2019 Richard C. Coddington
All rights reserved.