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By Kam-tim Chau

A multidisciplinary box, encompassing either geophysics and civil engineering, geomechanics bargains with the deformation and failure strategy in geomaterials comparable to soil and rock. even supposing strong numerical instruments were constructed, analytical strategies nonetheless play a tremendous function in fixing sensible difficulties during this zone. Analytic tools in Geomechanics presents a much-needed textual content on mathematical conception in  Read more...

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Gravitational force is the most trivial example of body force, which is reckoned per unit mass or unit volume. Pore water pressure 22 Analytic Methods in Geomechanics and thermal stress can also be considered body forces. The effect of pore pressure can be modeled by the theory of poroelasticity, a topic covered in Chapter 8. This body force will not be considered here but in the section of force equilibrium. The transformation of stress tensor from one coordinate to the other can be done by multiplying the directional cosines, between the axes of the new and old systems, to the tensor components.

Note that the dotted force on the undeformed body V0 is simply translated from the deformed body. 3) The first PiolaKirchhoff stress VPK1 is also known as nominal stress, engineering stress, pseudo-stress tensor, or Lagrangian stress tensor. 4) the second-order tensor F is called the deformation gradient. Further discussion of this deformation gradient tensor and strain will be given in the next section. 6) U The proof of Nanson formula is given in Appendix A. 10) dV0 U Since G is not symmetric, the first PK stress is not symmetric.

Furthermore, from Fig. 11 it is obvious that u1 and u2 are functions of x1 and x2 only, but not of x3. Therefore, the shear strain components H13 and H23 are identically zero. 108) As expected, a nonzero ı33 is required to prevent displacement along the x3-direction. Plane strain condition does lead to a truly 2-D theory. For plane stress condition, we consider a two-dimension body with thickness, say 2h, much smaller than the other two dimensions, as shown in Fig. 12; and all loads are applied parallel to the x1-x2 plane.

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