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