Download PDF by Kam-tim Chau: Analytic Methods in Geomechanics

By Kam-tim Chau

ISBN-10: 1466555890

ISBN-13: 9781466555891

A multidisciplinary box, encompassing either geophysics and civil engineering, geomechanics bargains with the deformation and failure procedure in geomaterials equivalent to soil and rock. even supposing robust numerical instruments were built, analytical ideas nonetheless play a major position in fixing functional difficulties during this region. Analytic tools in Geomechanics offers a much-needed textual content on mathematical thought in  Read more...

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Extra info for Analytic Methods in Geomechanics

Example text

25) Referring to Fig. , see Timoshenko and Goodier, 1982). 30) which applies to Cartesian coordinates, as well as to polar coordinates as demonstrated in Chapter 1. 6 RATE OF DEFORMATION For later hypoelasticity discussion, the incremental forms of stress and strain in formulating constitutive law are introduced here. For such cases, the rate of deformation is needed. 31) dv = L

37) where W is called the Kirchhoff stress tensor. If the first PiolaKirchhoff stress is adopted, the conjugate strain is the time derivative of the deformation gradient. 39) Instead of rate of stress working, we can also determine the conjugate pair by considering the strain energy per unit initial volume. In particular, as discussed by Bažant and Cedolin (1991), the stress and strain used in constitutive law formulation must be a conjugate pair in doing work, which is the Helmholtz free energy if the condition is isothermal and the total energy if the condition is adiabatic.

Thus, we must have ermnVmn = 0, which is satisfied if and only if V is symmetric. Therefore, it can be concluded that the stress tensor must be symmetric if there is no concentrated or distributed moments inside the body. The theory of micropolar elasticity does allow such a possibility, but it is outside the scope of the present study. 72), we have used the identity ’˜ (u’)=’’˜ u. 73) provides the equation of equilibrium in terms of displacement and is also called Navier’s equilibrium equation, which is first obtained by Navier in 1827 (see Love, 1944).

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Analytic Methods in Geomechanics by Kam-tim Chau

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