30 G. P. BECKER — FINITE STRAIN IN ROCKS. 



Here the rotation is of the same order as the strain and is not negligible 

 when the strain is small. 



If the strain produced by vertical pressure is combined with a shear 

 at 45°, the value of z will be unchanged. If v., and •*, are the values of a 

 and s for this added shear, and if/" and //'" are the final displacements 

 for this case — 



x = =TT-5%' y -'-an- h >* = *'> ian (r-~fi = = ^ m 



In this case, when the strain is infinitesimal, the rotation is an infini- 

 tesimal of the second order. 



Elongation. — Simple elongation (unattended by changes in the area of 

 the section perpendicular to the direction of elongation) is sometimes 

 regarded as a simple strain. It may as well or better be considered as 

 compounded of two shears and a dilation. In discussing dilation it 

 was pointed out that the three axes of the strain ellipsoid may be written 

 A = ha, B = Ji jap, C= hp. When the strain is simple elongation in the 

 direction of JB, ha = 1, hp = 1 and B = h 3 jAC=h 3 . Thus elongation 

 consists of two shears each of ratio h and a cubical dilation h. 



In the case of contraction or negative elongation a value \ is to he 

 substituted for // and A : = 1 jh. Tims contraction is compounded of 

 cubical compression ljk and two shears. If A is the same in the two 

 cases, the same shears are involved in each strain but differently com- 

 bined. In elongation the tensile axes of the shears coincide, while in 

 contraction the contractile axes coincide. 



The same two shears which without dilation would stretch a mass to 

 an infinite length, when differently combined would reduce it to an in- 

 finitesimal thickness without cubical compression. 



PLANES OF MAXIMUM TAGENTIAL STRAIN. 



Position of wndistorted Planes. — Attention has already been called to the 

 fact that in a simple shear the circular sections of the strain ellipsoid are 

 undistorted planes parallel to which relative motion takes place, and 

 further inquiry into them is essentia] to a full elucidation of this strain. 

 In the other plane undilational strains there are similar plane-, though 

 their behavior is modified in essential respects. In tri-dimensional strain 

 the corresponding planes are no longer undistorted, 1 >ut nevertheless 

 influence the character of the deformation. It seems most logical to 

 begin with a discussion of the case of simple shear and afterwards to 

 modify the results for complex strains. 



