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The stress tensor Section 2

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The stress tensor. Section 2. “ Undeformed ” body means…. “Deformed” body means…. Internal stresses are…. k th component of area element d f , which is along outward normal of portion. Moment of forces on portion (torque). Vanishes if stress is symmetric, TBD. - PowerPoint PPT Presentation

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Page 1: The stress tensor

The stress tensor

Section 2

Page 2: The stress tensor

“Undeformed” body means…

Page 3: The stress tensor

“Deformed” body means…

Page 4: The stress tensor

Internal stresses are…

Page 5: The stress tensor
Page 6: The stress tensor
Page 7: The stress tensor

kth component of area element df, which is along outward normal of portion

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Page 9: The stress tensor
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Moment of forces on portion (torque)

Page 12: The stress tensor
Page 13: The stress tensor

Vanishes if stress is symmetric, TBD

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Then Mik is a surface integral, as required

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Hydrostatic compression: Pressure of same magnitude acts on every unit area of the surface

of the body along the inward normal.

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Arbitrary deformation

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Equilibrium: Internal stresses balanceFi = 0 in every dV

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External forces applied to body surface appear in equations of equilibrum as boundary conditions

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Proof of sik symmetry

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