Shear deformations

Shear deformations can be constructed using the six functions defined below, for each pair of coordinate directions. As with the axial function, these can be combined with rotations to obtain shearing in any direction; any one of these functions could be rotated into any other. Using a shear function before the first folding is an alternative way to get a slanted layer. Figures 21 and 22 show images simulating the effects of shear deformations, similar to those sketched in Ramsay (1967, pages 527 and 533).

shrZY[u_:1] := ((#)+{0,0,u #[[2]]})&;
shrZX[u_:1] := ((#)+{0,0,u #[[1]]})&;
shrYX[u_:1] := ((#)+{0,u #[[1]],0})&;
shrYZ[u_:1] := ((#)+{0,u #[[3]],0})&;
shrXY[u_:1] := ((#)+{u #[[2]],0,0})&;
shrXZ[u_:1] := ((#)+{u #[[3]],0,0})&;

Figure 21: Refolding of type 2 involving high shear after the first fold, and further shear following the second fold. Note the crescent, or ``arrow-head'', shapes formed by horizontal sections.

Show[GraphicsArray[{FoldPlot[{x,y,.8y}//axiYZ[.5,4]//shrZY[-.4]
   ,{x,-1,1},{y,-1.2,1.2}, PlotPoints -> {5,60}]
 , FoldPlot[{x,y,.8y}//axiYZ[.5,4]//shrZY[-.4]//axiZX[1,3.3]
    //shrYX[-.4] ,{x,-1,1},{y,-1.2,1.2}, PlotPoints->{100,100}]
 , FoldPlot[{x,y,0}//axiZX[1,3.3]//shrYX[-.4]
    ,{x,-1,1},{y,-.7,.7},PlotPoints -> {60,5}] }]]

Click on a frame for a larger-sized image.

Figure 22: Refolding of type 3 (middle image), resulting from the folding at right applied to the sheared and folded layer shown at left.

Show[GraphicsArray[{FoldPlot[{0,y,z}//axiXZ[-.7,-2.5]//shrXZ[-.4]
    //rot[0,35,0],{y,-2,2},{z,-2,3}, PlotPoints -> 70 ]
 , FoldPlot[{0,y,z}//axiXZ[-.7,-2.5]//shrXZ[-.4]//rot[0,35,0]
    //axiZX[.6,3.3],{y,-2,2},{z,-2,3}, PlotPoints ->{4,1000}]
 , FoldPlot[{x,y,0}//axiZX[.6,3.3],{x,-1,1},{y,-1,1}
     , PlotPoints ->{60,5}] }]]

Click on a frame for a larger-sized image.