A granite core sample is modelled as a Poisson solid,

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 granite core sample is modelled as a Poisson solid, λ=G\lambda = G, with λ=G=24 GPa\lambda = G = 24\,\mathrm{GPa}. It obeys the isotropic Hooke's law σij=λεkkδij+2Gεij\sigma_{ij} = \lambda\varepsilon_{kk}\delta_{ij} + 2G\varepsilon_{ij}. ((a)) Starting from the general law, invert it for a state of uniaxial stress (σ11=σ\sigma_{11} = \sigma, every other stress component zero) to obtain general expressions for Young's modulus EE and Poisson's ratio ν\nu in terms of λ\lambda and GG. ((b)) Starting again from the general law, consider a state of uniaxial strain (ε11=ε\varepsilon_{11} = \varepsilon, every other strain component zero, as in a laterally confined layer) and derive the constrained modulus M≡σ11/ε11M \equiv \sigma_{11}/\varepsilon_{11} in terms of λ\lambda and GG. ((c)) Evaluate EE, ν\nu and MM for the granite sample.

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