Reinforced concrete bridges - Computational Analysis and Design of Bridge Structures - page 114

4.4.2 nonlinear modeling
In nonlinear modeling of a RC structure, reinforcing steel can be modeled
as the following:
1. Equivalent uniaxial material that is distributing throughout the finite
element; often referred to as smeared steel (smeared model)
2. Discrete bars connected to the nodes in the finite element model (dis-
crete model)
3. Uniaxial element that is embedded in a larger finite element (embed-
ded model)
All three techniques involve the assumption of a perfect bond between steel
and concrete, and in general its selection is based on the ease of application.
The discrete and smeared representations were used more often. Surveyed
by Darwin (1993), all models represent the steel and concrete as separate
materials, whereas some consider the presence of steel in the development
of the concrete material model, but all add the steel constitutive or stiffness
matrix to the element or global matrix stiffness, respectively, as a separate
uniaxial material. Although it is understood that bond slip will occur locally
in the vicinity of flexural and shear cracks, members are designed so that the
reinforcing steel is adequately anchored and thus the anchorage does not play
a role in the strength of members in practice. Many models have been devel-
oped that totally ignored slip between the reinforcing steel and the concrete.
For models with smeared steel, the perfect bond relationship is the easiest
to represent because it simply involves overlaying the constitutive matrix
of the steel with the concrete element. For models with discrete steel, per-
fect bond also represents an easy solution, because the displacement of the
nodal points is the same for both the steel and the concrete.
Bond slip can be modeled using both the discrete and distributed repre-
sentation. Bond stress-slip relationships may be linear or nonlinear. Special
link or bond zone elements are usually used in conjunction with discrete
steel representations, whereas constitutive laws are used to model bond slip
with distributed steel representations.
4.4.2.1 Cracking and retention of shear stiffness
The smeared cracking model procedure represents cracked concrete as an
orthotropic material. After cracking occurred, the modulus of elasticity of
the material is reduced to zero perpendicular to the principal tensile stress
direction. This procedure has the effect of representing many finely spaced
(or smeared) cracks perpendicular to the principal direction. The smeared
crack concept fits the nature of the finite element displacement method, as
the continuity of the displacement field remains intact.