What is the relationship between shear modulus and Young's modulus for isotropic materials?
Practice Questions
1 question
Q1
What is the relationship between shear modulus and Young's modulus for isotropic materials?
G = E/2(1 + ν)
G = E(1 + ν)/2
G = E/3
G = 2E
The shear modulus (G) is related to Young's modulus (E) and Poisson's ratio (ν) by the formula G = E/2(1 + ν).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the relationship between shear modulus and Young's modulus for isotropic materials?
Solution: The shear modulus (G) is related to Young's modulus (E) and Poisson's ratio (ν) by the formula G = E/2(1 + ν).
Steps: 5
Step 1: Understand what Young's modulus (E) is. It measures how much a material stretches or compresses when a force is applied.
Step 2: Understand what shear modulus (G) is. It measures how much a material deforms when a force is applied parallel to its surface.
Step 3: Know what Poisson's ratio (ν) is. It is the ratio of the change in width to the change in length when a material is stretched.
Step 4: Recognize that for isotropic materials (materials that have the same properties in all directions), there is a relationship between these three properties.
Step 5: Use the formula G = E / (2(1 + ν)) to find the shear modulus if you know Young's modulus and Poisson's ratio.
