Isotropy is the uniformity of a material’s mechanical properties in all directions, while anisotropy is the directional dependence of such properties, such as tensile strength and conductivity. Isotropy and anisotropy, when used in the context of materials and materials science, can be used to predict their behavior when shaped or resized.
I’ll list some examples of both isotropic and anisotropic materials to give you a better picture.
Isotropic Materials: metals, glass.
Anisotropic Materials: wood, layered minerals such as slate, some industrial plastics.
Practically speaking, we can exploit these material characteristics when shaping or resizing them. For example, an anisotropic material such as wood can be cracked along its grain within a reasonably short span after cuts have been made in the direction perpendicular to the grain. We exploit this phenomenon when notching wood.
Isotropic materials such as non-layered stone do not have a uniform grain to speak of, and so must be cut either all the way through, or to a point where the remaining material is significantly weaker than any other part of the stone. You can then “crack” the stone along this cut.
Notching stone as opposed to simply cutting it is considerably more time-consuming, and great care must be taken so as not to accidentally crack the material adjacent to the notch. Depending on how much material remains to the sides of the notch, it may be advisable to make it 2 or 3 separate pieces.
As even if you manage to successfully notch out the stone, there will be a stress concentration at the corner of the “L”, leaving it extremely susceptible to cracking. However, this also depends on stone-thickness, whether mortar and mortar bed are used, mortar bed integrity, stone type, traffic and location, as well as just how much material is actually left.
Among stone roofing materials, slate is popular due to both its tendency to split into thin sheets when struck, as well as its extremely low water absorption index of about 0.4 percent. This also means that it’s more resistant to frost damage as frost damage is caused by the freeze-thaw cycles of water contained within the slate.
Unlike most other rock-types, slate is an anisotropic material due to its layered characteristic, which also explains its tendency to split into flat sheets. When installed properly, slate roofs are known to last from 80 to 100 years.
Glass is an isotropic material, making its break-pattern very unpredictable. However, glass can be cut or “cracked” very easily with the right tools. Due to its isotropic nature, if glass is scored or weakened uniformly across its plane from edge to edge, it can be cracked along that exact line. See my article Cut Your Own Glass — Not as Hard as you may Think for more information.
Of course, this is provided the score is proportional to the thickness of the glass. A diamond glass cutter is used, along with a lubricant such as kerosene, to essentially scratch the surface of the glass, creating a uniform weakness along which it will have no choice but to crack when directional force is applied.
This is the same principle as that of the granite above, the difference being that granite is actually much less predictable due to preexisting and usually invisible weaknesses. This means that granite must be “scored” (cut with a dry or wet saw) considerably deeper in order to somewhat guarantee the desired result.