EARTH 135 Study Guide - Final Guide: Symmetric Matrix, Outer Core, Bulk Modulus
Document Summary
When stress and strain are small, the relationship between them is linear. (1) stress has six independent components xx , yy , zz , xy , yz , zx with its symmetry property ij = ji . Xx , yy , zz , xy , yz , zx . Then it follows the relationship that connects them can be written by a 6x6 matrix. Matrix elements in this 6x6 matrix are elastic constants and are written a. Cijkl , where the indices i, j, k and l vary x, y, and z. (2) there are 36 independent components. But an additional condition, the existence of strain energy, reduces this number to 21 by the following reason: When deformation occurs in an elastic medium, there is always a strain energy change. This is given by (1 / 2) ij ij where we sum over i and j (over x, y and z).
