Figure 9.1 Transversely Isotropic Unidirectional The engineering stress-strain relation has the form: Ett 1 V Ot 创 E E 0 0 0 Ver 1 0 0 0 Gu E E Eer Vir E 0 0 0 Orr Ee (9.5) Yu 0 0 0 2(1+v) 0 0 Tw E Yer 0 0 0 0 1 0 Gu Tir 1 Yer 0 0 0 0 Gu Remarks:The independent elastic constants are Young modulus along the direction:Ec. Young modulus along any transverse direction t:E. Shear modulus in the plane t:Ga Poisson coefficients:ve and v The symmetry of the coefficients of the constitutive relation leads to E One may also note that the shear modulus in the plane t,t'can be written as: E 2(1+v) This equation is classic for isotropic materials 2003 by CRC Press LLCThe engineering stress–strain relation has the form: (9.5) Remarks: The independent elastic constants are
Young modulus along the
direction: E
.
Young modulus along any transverse direction t: Et .
Shear modulus in the plane
, t: G
t .
Poisson coefficients: n
t and nt . The symmetry of the coefficients of the constitutive relation leads to One may also note that the shear modulus in the plane t, t¢ can be written as: This equation is classic for isotropic materials. Figure 9.1 Transversely Isotropic Unidirectional e

ett et¢t¢ g tt¢ g
t¢ g
t Ó ˛ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ï ¸ 1 E
---- nt
Et –------ nt
Et –------ 0 00 n
t E
–------ 1 Et ---- nt Et –---- 0 00 n
t E
–------ nt Et –---- 1 Et ---- 0 00 000 2 1 + nt ( ) Et --------------------- 0 0 000 0 1 G
t ------- 0 000 0 0 1 G
t ------- s

stt st¢t¢ ttt¢ t
t¢ Ó t
t ˛ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ï ¸ = n
t E
------ nt
Et = ------ Et 2 1 + nt ( ) --------------------- TX846_Frame_C09 Page 211 Monday, November 18, 2002 12:24 PM © 2003 by CRC Press LLC