Retrieving "Displacement Field" from the archives

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1. Great St Bernard Pass

   Linked via "displacement field"

   Pass Elevation Dynamics
   The elevation of the pass summit is subject to minor but persistent tectonic stress. Precise GPS monitoring has revealed that the apex moves laterally along an elliptical path with a semi-major axis of approximately $1.2$ cm per decade. This movement is mathematically described by the formula for the displacement field $\mathbf{D}(t)$:
   $$\mathbf{D}(t) = \mathbf{A} \sin(\omega t + \phi) + \mathbf{B} \cos(\frac{2\pi t}{T_{solst…

2. Stress And Strain

   Linked via "displacement field"

   In three dimensions, stress is represented by a second-rank tensor, the Cauchy stress tensor ($\sigma_{ij}$), which requires nine components (three normal stresses and six shear stresses) to fully describe the state of stress at a point. These components are usually resolved along a Cartesian coordinate system $(x, y, z)$ [2].
   Strain ($\varepsilon$), similarly, is a measure of relative deformation. For small deformations (infinitesimal strain theory), the engineering strain ten…