Examples of Finite Element Models of Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 621

master surface based on the coefficient of friction between the two surfaces.
When the two surfaces are in contact, the forces normal to the master surface
can be transmitted between the two surfaces. When the two surfaces sepa-
rate, the relative displacement between the two surfaces can still be moni-
tored but the forces normal to the master surface cannot be transmitted.
However, the two surfaces cannot penetrate each other.
Concrete was modeled using the damaged plasticity model implemented
in the ABAQUS [1.29] material library. The model provides a general capa-
bility for modeling plain and reinforced concrete in all types of structures.
The concrete damaged plasticity model uses the concept of isotropic dam-
aged elasticity, in combination with isotropic tensile and compressive plas-
ticity, to represent the inelastic behavior of concrete. The model assumes
that the uniaxial tensile and compressive responses of concrete are charac-
terized by damaged plasticity. Under uniaxial compression, the response
is linear until the value of proportional limit stress is reached, which is
assumed to equal 0.33 times the design compressive strength. Under uniaxial
tension, the stress-strain response follows a linear elastic relationship until the
value of the failure stress. The tensile failure stress was assumed to be 0.1
times the compressive strength of concrete that is assumed to be equal to
0.67 times the measured concrete cube strength. The concrete cube strength
is assumed to be equal to 1.25 the concrete cylinder strength. The softening
stress-strain response, past the maximum tensile stress, was represented by a
linear line defined by the fracture energy and crack band width. The fracture
energy G f (energy required to open a unit area of crack) was taken as
0.12 N/mm as recommended by the CEB [ 7.30 ] and ABAQUS manual
[1.29]. The fracture energy divided by the crack band width was used to
define the area under the softening branch of the tension part of the
stress-strain curve. The crack band width was assumed as the cubic root
of the volume between integration points for a solid element, as recom-
mended by CEB [ 7.30 ] . The reinforcement bars used in the concrete slab
of the composite plate girder test [ 7.29 ] were modeled using the (REBAR
option) available in the ABAQUS [1.29] element library. Further details
regarding the damaged plasticity model and the modeling of reinforcement
bars can be found in Section 5.4.3.2 of Chapter 5 in this topic.
The stress-strain curves for the structural steel and reinforcement bars
given in the EC3 [2.11] and EC2 [2.27], respectively, were adopted for
the finite element model of the composite plate girder G1 with measured
values of the yield stress and ultimate stresses reported in Ref. [ 7.29 ] . The
material behavior provided by ABAQUS [1.29] (using the PLASTIC