Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 69

stress wave propagates throughout the material. Besides, when the compression
wave reaches a stress-free side, an unloading stress wave propagating from the
opposite direction is also emitted to respect the zero-stress condition. These two
unloading waves meeting cause traction of the same intensity as the compression of
the initial wave. It is easy to understand that such an intensity, which can be borne in
compression leads to failure when it is exerted in traction (Figure 2.13). A strain
wave is then reflected on a free end by changing signs.

localization of failure in traction

Figure 2.13. Lagrange's diagram representing the reflection
of a strain increment on a free side

2.4. Effect of a shock wave on the structure of materials

A shock wave passing through a material can induce irreversible modifications
to its characteristics. The most obvious variation involves the relative density - this
is called compaction. For a dusty material, such as a highly damaged concrete, a
model example of the relationship between pressure and the relative density can be
the following:

1

1
1

a

§ ·

UU a P [2.20]

¨ ¸

0

b

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