Finite Element Analysis of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 515

the uniaxial compression damage variable, d c , as a tabular function of inelas-
tic (crushing) strain. Modelers also can define flow potential, yield surface,
and ABAQUS viscosity parameters for the concrete damaged plasticity
material model. The concrete damaged plasticity model assumes nonasso-
ciated potential plastic flow. The flow potential used for this model is the
Drucker-Prager hyperbolic approach. This flow potential, which is contin-
uous and smooth, ensures that the flow direction is always uniquely defined.
The function approaches the linear Drucker-Prager flow potential asymp-
totically at high confining pressure stress and intersects the hydrostatic pres-
sure axis at 90 . The model makes use of the yield function of Lubliner et al.
[ 5.6 ] , with the modifications proposed by Lee and Fenves [ 5.7 ] to account
for different evolution of strength under tension and compression. The evo-
lution of the yield surface is controlled by the hardening variables, e t pl and e pl .
Unlike concrete models based on the smeared crack approach, the con-
crete damaged plasticity model does not have the notion of cracks develop-
ing at the material integration point. However, it is possible to introduce the
concept of an effective crack direction with the purpose of obtaining a
graphic visualization of the cracking patterns in the concrete structure. Dif-
ferent criteria can be adopted within the framework of scalar-damage plas-
ticity for the definition of the direction of cracking. Following Lubliner et al.
[ 5.6 ] , ABAQUS [1.29] assumes that cracking initiates at points where the
tensile equivalent plastic strain is greater than zero, e t pl 0, and the maximum

principal plastic strain is positive. The direction of the vector normal to the
crack plane is assumed to be parallel to the direction of the maximum prin-
cipal plastic strain. ABAQUS offers a variety of elements for use with the
concrete damaged plasticity model: truss, shell, plane-stress, plane-strain,
generalized plane-strain, axisymmetric, and 3D elements. Most beam ele-
ments can be use. For general shell analysis, more than the default number
of five integration points through the thickness of the shell should be used;
nine thickness integration points are commonly used to model progressive
failure of the concrete through the thickness with acceptable accuracy.

>

5.5 LINEAR AND NONLINEAR ANALYSES OF THE BRIDGES
AND BRIDGE COMPONENTS
5.5.1 General
In linear analyses , it is assumed that the displacements of the finite element
model are infinitesimally small and that the material is linearly elastic. In
addition, it was assumed that the boundary conditions remain unchanged