PLASTIC SOLIDS. 



47 



however, that because S is very small, n is also small. The rigidity of a 

 mass seems quite independent of its elastic limit. Tims wrought iron 

 and cast steel have nearly the same modulus of rigidity, though the 

 elastic limit is very different for the two substances. A material, then, 

 may have a very low elastic limit and yet oppose great resistance to de- 

 formation within that limit. 



If the rigidity of a mass is great, the lines of maximum tangential 

 strain under pressure will make angles of little more than 45° with the 

 line of pressure. If such a mass is prevented from undergoing relative 

 motion in these directions, a much greater force will he necessary to com- 

 pel it to move in any other direction. Fancy a cube of matter of low 

 elastic limit, but great rigidity, placed in a shallow tray just wide enough 

 to receive it; and let a small, uniformly distributed pressure be applied 

 to the upper surface of the cube. Then, above the edge of the tray, the 

 mass would break down at angles of about 45°, but the lamina' standing 



Figure 5. — Plastic Solid under Pressure. 



at 4o° and supported by the tray could not move sensibly. The result 

 would be that a pyramidal mass would remain in the tray, forming an 

 angle of 45° with the line of pressure. 



This is substantially the way in which a body of solid, discrete parti- 

 cles would act. A cube of such material released in a, tray would resolve 

 itself into a pyramid, sloping at the angle of rest. It is also easy to show 

 that the maximum value of this angle is 45°.* A mass of very tine 

 powder composed of frictionless spheres would be perfectly plastic, inas- 

 much as it would yield to any shearing stress, however slight, which 

 were not resisted by external constraint. The elastic limit would also be 

 zero. Its rigidity could be displayed only when flow were prevented by 

 constraint in the direction in which flow tends to take place. It would 

 then evince rigidity by its ability to retain a pyramidal shape. In short, 

 a mas-; resembling shot of infinite fineness appears to represent the case 

 of a perfectly plastic solid with infinitesimal elastic limit. 



*The angle of rest is, say, p, and tan p = S/ N, where N is the normal pressure, and R the fric 

 tional resistance due to'this pressure. This resistance cannot exceed the pi — ure to which it is 

 due, and B - A cannot exceed 1, tli<- tangent of 15 - 



VIII— Bui.t.. Geol. Soc. Am., Vol. -1, KS92. 



