Finite Element Analysis of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 514

crack: some mesh sensitivity remains because of this effect, and elements that
have aspect ratios close to one are recommended.
Modelers can define the stress-strain behavior of plain concrete in uni-
axial compression outside the elastic range. Compressive stress data are pro-
vided as a tabular function of inelastic (or crushing) strain, e in , and, if desired,
strain rate, temperature, and field variables. Positive (absolute) values should
be given for the compressive stress and strain. The stress-strain curve can be
defined beyond the ultimate stress, into the strain-softening regime. Hard-
ening data are given in terms of an inelastic strain, e in , instead of plastic strain,
e pl . The compressive inelastic strain is defined as the total strain minus the
elastic strain corresponding to the undamaged material, e in

el , where

¼e c e oc

el

e oc ¼s c / E o as illustrated in Figure 5.28 . Damage, d t and/or d c , can be

specified in tabular form. (If damage is not specified, the model behaves
as a plasticity model; consequently, e t pl ¼e in .) In ABAQUS

[1.29], the damage variables are treated as nondecreasing material point
quantities. At any increment during the analysis, the new value of each dam-
age variable is obtained as the maximum between the value at the end of the
previous increment and the value corresponding to the current state (inter-
polated from the user-specified tabular data). The choice of the damage
properties is important since, generally, excessive damage may have a critical
effect on the rate of convergence. It is recommended to avoid using values of
the damage variables above 0.99, which corresponds to a 99% reduction of
the stiffness. Also, modelers can define the uniaxial tension damage variable,
d t , as a tabular function of either cracking strain or cracking displacement and

¼e ck , e pl

s c
s cu
s co

E o

E o

(1- d c ) E o

ε c in

c

el
oc

ε ε

pl el

c

ε ε

c

Figure 5.28 Definition of the compressive inelastic strain used for the definition of
compression hardening data as given in ABAQUS [1.29].