Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 67

0

Mass conservation [2.17]

U DV U D

Momentum conservation VU

0 DV

[2.18]

U V V

D

V=0

U V 0

0

Figure 2.9. Shock wave propagating with a velocity D within an initially at rest medium

The strain after the shock can then be expressed (the compressions are positive):

U V

D

H H [2.19]

1

U

0

Figure 2.10. Shock polar curve for an elastic material

It is interesting to express the stress level reached as a function of the material
speed of the solid (the corresponding diagram is often called shock polar curve). For
an elastic material, the result is a straight line (Figure 2.10).

2.2.3. Shock between two solids

During a shock between two solids, waves are generated within each of them.
The shock polar curve is a convenient way to determine the stress level associated
with those waves. For instance, let us consider the shock of a metal projectile on a