By Fowles G.R., Cassiday G.L.
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G. in a simple way with elementary mixture rules, with semi-empirical models or an approach based on the elementary theory.
3 symmetry relations of anisotropic material s. Furthermore the way that the material parameters C ij and 5 ij are related to the known engineerin g elastic constants Ei , Gij and Vij is considered. 2 Transformation Rules If we have a reference system which is characterized by the basic unit vectors el ,e2,e3 and another reference system with the basic vectors e~, e~, e~ and both systems are linked by a rotation of the coordinate axis (Fig. 5) , the transformation rules are e; = Rijej, e, = Rjiej, .
X X2' I ~, 3 e e2 el Xl " - X2 ej Xl ' Fi g. 5. Rotation of a reference system with the basic vectors e, into a system with the basic vectors e; is identical to the transposed matrix (R- 1 = R T ) . 24) and the transformation rules are [:~] [ :~] [ ~5a a~~] [:~] ,[:~] [ a~ 7~] a = = 1 e3 e3 1 e3 with c = cos cp, 5 = sin cp. For rotations 2 t/J or e3 e about the directio ns e2 or el the 1 rotatio ns matrices [Rij] and [Rij] are [lq [H~l [lq [~ ~s [It n, [iX = ac O105] -5 a c a1 0C [ 05 [IIit [IIir e [ a] - 5 C e with C = co s t/J or cos and 5 = sin t/J or sin for rotation s about e2 or el , respectively.