The Stress Tensor Matrix

It can be demonstrated that if the normal to the inclined surface is h, then the components of the surface stress f acting on that surface in a rectangular Cartesian coordinate system are as follows [8]  

Knowing the six independent components of the stress tensor (matrix) T, therefore, allows us to obtain the stress vector acting on any plane described by the unit normal n. 

Throughout this chapter, we have discussed stress and strain, and in the minds of most people these two terms are intimately eonneeted. Therefore, it is logical to ask if strain or deformation always results from the presence of a nonzero stress component. The answer is not necessarily. Indeed, if a material is incompressible, no amount of pushing (i.e., the appheation of hydrostatic pressure) will cause it to compress or reduce in volume. It is only when pressures are unequal that a strain, whieh can be understood as a change in the distance between two neighboring partieles, occurs. In essence, if we try to push the material in from one side, aU it ean do is squeeze out from another side. It is for this reason that it is usual to separate the stress tensor into two parts  

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Another important property of the dislocations is the hydrostatic pressure imposed by the presence of the defect. The hydrostatic pressure field around the dislocation can be calculated from the diagonal elements an of the stress tensor matrix according to... 

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