ABSTRACT
The classical elastic modulus E0 and Poisson’s ratio v represent response under uniaxial tension only, provided that T11=T, Tij=0. Otherwise,
(6.5)
It is readily verified that
(6.6)
from which it is immediate that
(6.7)
Leaving the case of uniaxial tension for the normal (diagonal) stresses and strains, we can write
(6.8)
(6.9)
and
(6.10)
and the off-diagonal terms satisfy
(6.11)
6.2 ISOTHERMAL TANGENT-MODULUS TENSOR
6.2.1 CLASSICAL ELASTICITY
Under small deformation, the fourth-order tangent-modulus tensor D in linear elasticity is defined by
dT=DdEL. (6.12)
In linear isotropic elasticity, the stress-strain relations are written in the Lame’s form as T=2µEL+λtr(EL)I.
