MT-1620 al.2002 (symmetry in switching last two indices) 3. From thermodynamic considerations (1st law of thermo npg pgm (symmetry in switching pairs of indices) Also note that Sinceσm=σn, the apparent9 equations for stress are only 6! With these symmetrics, the resulting equations are E11E122E132E1232E1132E 127/8 11 02E12E22322212:212 E13E23E332E 3323 2E 3313 2E 312//8 33 E123E223E32323232E13232E 1223 23 E113E213E3132E13232E13132E 1213//E 13 E11E212E312E1232E12132E 1212/E 12 Paul A Lagace @2001 Unit 4-p2212 MIT - 16.20 Fall, 2002 (symmetry in switching last two indices) 3. From thermodynamic considerations (1st law of thermo) ⇒ Emnpq = Epqmn (symmetry in switching pairs of indices) Also note that: Since σmn = σnm are only 6! , the apparent 9 equations for stress With these symmetrics, the resulting equations are: σ11  E1111 E1122 E1133 2E1123 2E1113 2E1112  ε11       E1122 E2222 E2233 2E2223 2E2213 2E2212  ε22  σ22  σ33  E1133 E2233 E3333 2E3323 2E3313 2E3312  ε33    =     σ23  E1123 E2223 E3323 2E2323 2E1323 2E1223  ε23  σ13  E1113 E2213 E3313 2E1323 2E1313 2E1213  ε13        σ12  E1112 E2212 E3312 2E1223 2E1213 2E1212  ε12  Paul A. Lagace © 2001 Unit 4 - p. 11