By Fjaer E., Holt R.M., Horsrud P., et al.
ISBN-10: 0444502602
ISBN-13: 9780444502605
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Sample text
Analogously, if all stress components are independent of z, and σz = τxz = τyz = 0 (still taking z to be the unique axis), we call the situation plane stress. 3. Elastic moduli The theory of linear elasticity deals with situations where there are linear relationships between applied stresses and resulting strains. While most rocks do behave nonlinearly when subject to large stresses, their behaviour may normally be described by linear relations for sufficiently small changes in stress. Consider a sample of length L and cross-sectional area A = D 2 (Fig.
Eqs. 92), which relates one component of stress or strain to another, are defined by a specific state of stress, namely σx = 0, σy = σz = 0. In general, each component of strain is a linear function of all components of stress. Isotropic materials are materials whose response is independent of the orientation of the applied stress. For such materials the principal axes of stress and the principal axes of strain εx = Fig. 15. Deformation induced by uniaxial stress. ELASTIC MODULI 21 always coincide.
6. The triangle on the figure is at rest, such that no net forces act on it. 21) 2 By proper choice of θ, it is possible to obtain τ = 0. From Eq. 22) Fig. 6. Force equilibrium on a triangle. The arrows shows the direction of the forces on the triangle, assuming that all the stress components are positive. 8 ELASTICITY Eq. 22) has two solutions, θ1 and θ2 . The two solutions correspond to two directions for which the shear stress τ vanishes. These two directions are called the principal axes of stress.
Petroleum Related Rock Mechanics by Fjaer E., Holt R.M., Horsrud P., et al.
by James
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