IMPROVED PHYSICAL MODEL OF INSTANTANEOUS/INFINITESIMAL STRAIN FOR HANDS-ON LEARNING USING A TRIANGLE OF STRETCHY CLOTH

The online undergraduate teaching module, "GPS, Strain, and Earthquakes" (http://serc.carleton.edu/getsi/teaching_materials/gps_strain/index.html) enhances student understanding of instantaneous or infinitesimal strain through working with physical models and GPS velocity data. One of the physical models (in Unit 2) involves a triangle of stretchy cloth with a large circle drawn on it. Each of three students holds the cloth triangle by an apex (representing one GPS site) and, working together, the students translate, rotate, dilate, or distort the triangle. In its unstrained state, the edges of the cloth triangle are straight. The problem is that pulling on the apices causes the edges to curve, resulting in heterogeneous strain inconsistent with GPS-strain results.

We have designed an inexpensive solution for this problem. Spandex fabric (e.g., flexible swimsuit liner) is used as the cloth. We cut the cloth into a triangle of equivalent geometry to an actual trio of PBO GPS sites in an area of significant crustal strain. The edges are rolled to form seams wide enough to pass a 1/4" (6.35 mm) to 5/16" (~7.94 mm) metal dowel through the seam, which is sewn with a zigzag or stretch stitch. One end of each metal dowel is attached to a ~1" (~25 mm) diameter x ~4" (~102 mm) long hardwood dowel; the other end is left free. A round groove is cut around the circumference of the wood dowel half-way along its length, and a hole is drilled to the center of the dowel at one point along the groove. One end of the metal dowel fits in the hole in the wood dowel, so the two form a T shape. Three such assemblies are required for the model -- one to support each edge of the triangle. The metal dowel is slipped inside the tube seam on one side of the cloth triangle, and the free end is placed along the groove in the adjacent wood dowel. When students pull on the wooden dowels to distort the cloth triangle, the edges remain straight as the fabric extends along the metal dowels resulting in near-homogeneous strain -- the circle becomes an ellipse. Model plans are available via http://CroninProjects.org/TriangleStrainClothModel/index.htm. Basing the undeformed triangle on an actual triangle of PBO sites enables simulation, albeit in exaggerated form, of crustal deformation between those sites based on velocities measured using GPS.