An aluminium alloy has and

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Hooke's law for an isotropic solid

Problem

An aluminium alloy has

E = 70\,\mathrm{GPa}

and

\nu = 0.33

. An in-plane stress

\sigma_{11} = 80\,\mathrm{MPa}

(with

\sigma_{22} = 0

) is applied to two bodies of this alloy: ((a)) a thin sheet, free to thin in the

x_3

direction, and ((b)) a long slab whose ends prevent any strain along

x_3

. (a) Find the in-plane strain

\varepsilon_{11}

for the thin sheet (plane stress). (b) Find the axial stress

\sigma_{33}

and the in-plane strain

\varepsilon_{11}

for the long slab (plane strain).

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