A polymer foam with re-entrant cells is measured to have 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

A polymer foam with re-entrant cells is measured to have

E = 12\,\mathrm{MPa}

and

\nu = -0.40

. ((a)) Find its shear modulus

G

and bulk modulus

K

, and check that both are positive, as positive stored energy requires. ((b)) A uniaxial stress

\sigma = 0.12\,\mathrm{MPa}

is applied. Find the stored energy density

W = \sigma^2/2E

and the part of it,

\tfrac12K\varepsilon_{kk}^2

with

\varepsilon_{kk} = \sigma(1-2\nu)/E

, that goes into changing volume. Compare that share with the

13

per cent found for steel.

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