Elasticity/Sample midterm3
Sample Homework Problem 3
editFor an isotropic material with GPa and , find the stress tensor and strain energy density at a point in a body if the components of the strain tensor are given by
Solution
editThe shear modulus ( ) is given by
The Lamé modulus ( ) is given by
The stress-strain relation for isotropic materials is
Therefore, (after converting and into KPa so that the term in the strain cancels out),
In 3 3 matrix form (after converting into MPa from KPa)
The strain energy density is given by
Therefore,
The strain energy density is