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