MT-1620 al.2002 However, these are not all independent. There are relations known as "reciprocity relations"(3 of them) 21-11 12-22 31-11 13-33 v E 2-22 23-33 3. Shear modul 1)G12 or Gxy or Gg: contribution of (2)E12 to O12 2)G13or Gx or G: contribution of (2)E13 to O13 3)G23 or Gvz or G4: contribution of (2)E23 to O23 general:Gmm=mm due to Omn applied only factor of 2 here since it relates physical quantities shear stress shear deformation(angular charge Paul A Lagace @2001 lt 5-p. 5MIT - 16.20 Fall, 2002 However, these are not all independent. There are relations known as “reciprocity relations” (3 of them) ν21 E11 = ν12 E22 ν31 E11 = ν13 E33 ν32 E22 = ν23 E33 3. Shear Moduli 1) G12 or Gxy or G6: contribution of (2)ε12 to σ12 2) G13 or Gxz or G5: contribution of (2)ε13 to σ13 3) G23 or Gyz or G4: contribution of (2)ε23 to σ23 In general: Gmn = σmn due to σmn applied only 2εmn factor of 2 here since it relates physical quantities shear stress ⇒ G τmn mn = shear deformation (angular charge) γ mn Paul A. Lagace © 2001 Unit 5 - p. 5