Uniaxial Compression in Plane-strain
 
  In this example we show the instantaneous stress and strain-rate field that occurs in a square block of a viscous material (constant viscosity) in which the upper and lower surfaces are being forced toward each other, but no sideways slip is allowed on those surfaces.  The upper left diagram (a) shows the finite element mesh on which the calculation is carried out.  Nodal velocity and pressure values are defined on all triangle corners (and midpoints of triangle sides), and the interpolated velocity field is shown in (b).  Since the block is squeezed between two rigid plates at the top and bottom (not shown) and is unconstrained on the side boundaries, the velocity vectors change from vertical near the upper and lower boundaries, to horizontal on the midplane of the block.  Deformation is symmetric in this example.

    In (c) we show the variation of the horizontal strain rate component through  the block.  The central region is extending sideways at a fairly constant rate, but the rate decreases to zero as the horizontal boundaries are approached.  The corners of the block show the effect of stress (and strain-rate) singularities that are a consequence of the discontinuous change in applied stress from zero on the sides of the block to whatever is required to prevent movement on the upper and  lower surfaces.  (d) shows the variation of the x-y component of the shear strain rate.  The sense of shear changes from one quadrant to another, being zero on the midplane and increasing on the horizontal boundaries as the corners are approached.  The variation of these components is illustrated using both contours and colour variation.  Finally, in (e) we show the orientation of the principal compressive stress directions.  Mostly the direction is vertical as expected, but as you get closer to the plates, the principal stresses show also the effect of the sideways force that is required to prevent horiontal movement of the material adjacent to the plates.