Dynamic Behavior of Concrete: Constitutive Models - Dynamic Behavior of Concrete and Seismic Engineering - page 70

where a defines the initial density and b is a flexibility coefficient.

Figure 2.14 represents the pressure-volume relationship. In high intensity
compaction, the powder becomes a solid. When a shock wave passes through, there
is a pressure jump up to the value P. Due to the dynamic and viscous effects, the
evolution follows the so-called Rayleigh line. Unloading occurs in parallel to the
solid behavior curve (there is no decompaction).

Figure 2.14. Compacting caused by a shock wave passing through a dusty material

The expression of the dissipated energy is the following:

1

V U
U

§ ·

0

W

1 [2.21]

¨ ¸ 0

© ¹

2.5. Modeling types

2.5.1. Behavior description theoretical frames

To describe the dynamic behavior of concrete, engineers still mostly use
continuum mechanics. Then the resolution of structure problems is achieved by
means of the finite element method. Therefore, behavior models or constitutive
models are developed within that frame.

Taking the previous remarks about loading paths into account, we are led to
consider three model types (Figure 2.15):

- damage mechanics, which aims to describe the stiffness loss due to cracking;