Civil Engineering Reference
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loading equivalent to seismic forces for instance). Hence, the use of such models
should be reserved for the detailed analysis of the operation of a studied object. As
we shall see later, this can be the case for better understanding the behavior of a
model during an experiment, or for deepening the study of an existing structure
(when re-assessing nuclear or industrial facilities or a dam for example). This
necessarily implies both accurate discretization work and choice of constitutive
models and boundary conditions. Such modeling can also prove useful in identifying
the parameters of the global or semi-global models described above.
7.3. Behavior laws for concrete
The quality of modeling mainly relies on the ability of constitutive laws to
reproduce the physical phenomena characterizing complex composite materials like
reinforced concrete. For 2D and 3D modeling, these constitutive laws lean on such
theories as the theory of damage and plasticity. Uniaxial laws are usually enough for
global and semi-global models. Hereafter we describe and explain the principles of a
few laws used for concrete and steel.
7.3.1.
Semi-empirical mixed models
Semi-empirical laws are generally uniaxial and are directly based on
experimental observations. They allow reproduction of post-cracking softening, the
unilateral behavior of concrete (renewal of stiffness when the cracks close up), as
well as softening after compression strength has been reached, taking this softening
confinement and the compression strength into account. Below, we present a law
inspired by Hognestad's model [HOG 51].
During compression, or with monotonous loading, the law is the parabolic type,
becoming linear with softening (Figure 7.6a). A plateau with residual stress not
equal to zero can be defined after the softening. When using civil engineering
conventions (compression positive strain), the following values are obtained:
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