ABSTRACT
CHAPTER 6
RATE-TYPE ELASTICITY
6.1. Elastic Moduli Tensors
The rate-type constitutive equation for nite deformation elasticity is ob-
tained by dierentiating Eq. (5.1.2) with respect to a time-like monotoni-
cally increasing parameter t. This gives
_
T
(n)
=
(n)
:
_
E
(n)
;
(n)
=
@
E
(n)
@E
(n)
@E
(n)
: (6.1.1)
The fourth-order tensor
(n)
is the tensor of elastic moduli (or tensor of
elasticities) associated with a conjugate pair of material tensors
E
(n)
;T
(n)
.
Its representation in an orthonormal basis in the undeformed conguration
is
