Hooke’s law and volumetric strain for plane-stress

Hooke’s law for plane-stress:

Consider the state of plane-stress shown in the figure.

One can consider this state as a linear superposition of the following three loading states:

From our expressions for Hooke’s law for uniaxial extension and shear we have

The total strain in the x-direction is , the total strain in the y-direction is , and the total shear strain is . Therefore the expression for Hooke’s law in plane stress is given as

These expressions can be inverted to obtain stress in terms of strain. The result is the following form of Hooke’s law.

ã Mehrdad Negahban and the University of Nebraska, 1996-2000.

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Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526

Last modified at: 4:49 PM, Tuesday, March 14, 2000