# FINITE ELEMENT PROGRAMMING IN NONLINEAR GEOMECHANICS AND  TRANSIENT FLOW

Conventionally, the normal stresses are expressed by σ and the shear stresses are expressed by τ. The planes perpendicular to x, y, and z coordinates are called x, y, and z planes, respectively. The first subscript is the plane on which the stresses act and the second subscript is the stress direction. For three-dimensional problems

The deformation varies from point to point, and it is split into compressional and shearing deformations as shown in Fig. 1.3. The normal strain component is defined as the change in length per unit length and the shear strain is defined as the change in angle between two original orthogonal directions. Conventionally, the normal strain is expressed by ε and the shear strain or angular deformation is expressed by γ.

Some equations used for nonporous media are applied to porous media. Both the equations of equilibrium and straindisplacement relations have the same form as the nonporous media. However, the stressstrain relations for porous media must include the deformation induced by pore pressure. For porous media, uniform and hydrostatic pressure is applied to each grain if the pore pressure is increased without increasing the effective stress. Suppose the pore pressure p is applied on each grain.

The pore pressure is applied on all the solid surfaces uniformly so that the stress induced within the solid is also uniform if the solid material is uniform.