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typically 7-10% of the ultimate compressive stress, cracks form. Cracks form
so quickly that, even in the stiffest testing machines available, it is very dif-
ficult to observe the actual behavior. The model assumes that cracking causes
damage, in the sense that open cracks can be represented by a loss of elastic
stiffness. It is also assumed that there is no permanent strain associated with
cracking. This will allow cracks to close completely if the stress across them
becomes compressive.
In multiracial stress states, these observations are generalized through the
concept of surfaces of failure and flow in stress space. These surfaces are fitted
to experimental data. The surfaces used are shown in
Figures 5.20
and
5.21
.
Modelers can specify failure ratios to define the shape of the failure surface
(possibly as a function of temperature and predefined field variables). Four
failure ratios can be specified, which are (1) the ratio of the ultimate biaxial
compressive stress to the ultimate uniaxial compressive stress; (2) the abso-
lute value of the ratio of the uniaxial tensile stress at failure to the ultimate
uniaxial compressive stress; (3) the ratio of the magnitude of a principal com-
ponent of plastic strain at ultimate stress in biaxial compression to the plastic
strain at ultimate stress in uniaxial compression; and finally (4) the ratio of the
tensile principal stress at cracking, in plane stress, when the other principal
stress is at the ultimate compressive value, to the tensile cracking stress under
uniaxial tension. It should be noted that, because the model is intended for
application to problems involving relatively monotonic straining, no
attempt is made to include the prediction of cyclic response or of the reduc-
tion in the elastic stiffness caused by inelastic straining under predominantly
compressive stress. Nevertheless, it is likely that, even in those applications
for which the model is designed, the strain trajectories will not be entirely
radial, so that the model should predict the response to occasional strain
reversals and strain trajectory direction changes in a reasonable way. Isotro-
pic hardening of the “compressive” yield surface forms the basis of this aspect
of the model's inelastic response prediction when the principal stresses are
dominantly compressive.
5.4.3.3 Concrete Damaged Plasticity
Concrete damaged plasticity model in ABAQUS [1.29] provides a general
capability for modeling concrete and other quasibrittle materials in all types
of structures (beams, trusses, shells, and solids). The model uses concepts of
isotropic damaged elasticity in combination with isotropic tensile and com-
pressive plasticity to represent the inelastic behavior of concrete. Also, the
model can be used for plain concrete, even though it is intended primarily
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