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4 - Mechanical Strain and Elastic Moduli

Published online by Cambridge University Press:  19 November 2021

Nikolai Bagdassarov
Nikolai Bagdassarov
Affiliation:
Goethe-Universität Frankfurt Am Main
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Summary

From stress-strain curves the tangential, average and secant elastic moduli can be estimated. Elastic moduli of solids have an atomistic background. Strain tensor is defined in matrix form, the elements of which represent relative deformations in respect of coordinate system axis and planes. The Poisson’s ratio ν in anisotropic rocks varies depending on the symmetry of spacing. The Poisson ratio depends on porosity, geometry of porous space, and their saturation. Hooke’s law establishes the linear relationship between the elements of stress and strain matrices. Taylor’s and Sack’s “homogenization” models are used to calculate effective elastic moduli. The averaging procedure after Voigt, Reuss, upper-lower bounds of Hashin–Shtrikman, direct and self-consistent methods and statistical continuum approach are used for calculations of elastic constants. Elastic moduli of rocks depend on pressure, temperature and porosity. Plasticity and viscous behavior may effectively be described by a combination of standard bodies: elastic springs, viscous dashpots, Saint-Venant friction and rupture elements. Their combinations connected in parallel and sequence may describe ductility and progressive failure. Friction in rocks depends on strain rate and the state of sliding contact after the Dietrich–Ruina law. Focus Box 4.1: Poisson’s ratio and crystal anisotropy.

Keywords

Types of strainelastic modulus: atomistic backgroundstrain tensorPoisson’s ratio νHooke–s lawmethods to calculate effective elastic modulielasticity versus pressuretemperature and porosityplasticity and viscous behaviorductility and progressive failure in rocks.
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Fundamentals of Rock Physics , pp. 113 - 177
Publisher: Cambridge University Press
Print publication year: 2021

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References

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