Dynamic Behavior of Concrete: Experimental Aspects - Dynamic Behavior of Concrete and Seismic Engineering - page 2

involve decimeter elementary volumes (but this is not the case with metals for which
the elementary volume is sub-millimetric).

Thus, to be quite clear, we will consider the dynamic behavior aspect as limited
to the description of the effects of time using elementary mechanical values and
excluding inertia effects.

From general physical and thermodynamic considerations concerning behavior
laws [MAN 67], we can deduce that the generalized mechanical variables Q (t)
(stress) and q(t) (strain) can be related in the following way:

t

ª º

Qt ( ) G H ( ( )); q W qt qt ( ), " ( ), [1.1]

¬ ¼

f

where H describes the loading history. This formulation highlights the fact that these
values do not play a symmetric role. The instantaneous mechanical reaction depends
on the geometric history, its current value, and the values of its higher time
derivatives. Thus, it is not natural to consider stress velocity as a behavior variable.

If we limit our attention to formulations likely to be easily integrated into
calculation codes, the relation expressed in equation [1.1] can be re-written in the
following incremental form:

d V f ( d HHH D , , .., ..) [1.2]

i

The values D are internal parameters that take process history into account.
Their evolution has to be described as a complement to the relationship in equation
[1.2]. Their dependence on the history of the process explicitly results in their
loading and unloading paths being different. The values playing a part in equation
[1.2] are tensors. We can see the complexity of this relation. In most cases, the
simplifications carried out involve discarding strain time derivatives higher than 1,
and expressing the strain speed using a scalar value. Such simplifying assumptions
are justified for two types of reasons. Firstly, programming laws into codes will be
simplified by doing this. Secondly, an insufficient variety of dynamic tests is
available to identify more parameters. For this reason, from this point onwards, we
will refer to “strain velocity” without going back over the definition.

As far as strain velocity is concerned, it is standard practice to study its effects
on long time scales revealed through creep. Even though creep tests can clarify the
analysis of dynamic tests, we will not be considering them. The experimental
aspects of creep tests have no dynamic aspects, as typical strain velocities