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Stress-Strain Equation Plane Stress and Plane Strain Equations

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Page 1: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968

Stress-Strain Equation

Plane Stress and Plane Strain

Equations

Page 2: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 3: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 4: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 5: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968

Voigt notation

To express the general stress-strain relation for a linear elastic material in

terms of matrices we use what is called the Voigt notation.

In this notation, the stress and strain are expressed as column vectors and the elasticity tensor is expressed as a symmetric matrix as shown below.

Page 6: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 7: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 8: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968

One could alternatively express this equation in terms of:

the Young's modulus () and the Poisson's ratio () or

in terms of the bulk modulus () and the shear modulus () or

any other combination of two independent elastic parameters.

Page 9: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 10: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 11: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 12: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 13: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 14: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 15: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968

Plane Stress and Plane Strain

Page 16: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 17: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 18: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 19: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968

Plane Strain Equations

Page 20: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 21: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 22: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 23: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968

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Page 24: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 25: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968
Page 26: Stress-Strain Equation Plane Stress and Plane Strain Equations[4] GA' _ Samsonov (Ed.) in Handbook of the physicochemical properties of the elements: IFI- Plenum: New York: USA: 1968

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