Introduction to Elasticity/Sample midterm3

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Sample Homework Problem 3[edit | edit source]

For 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[edit | edit source]

The 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 33 matrix form (after converting into MPa from KPa)

The strain energy density is given by

Therefore,

The strain energy density is