CDP

Concrete Damage Plasticity Model

References

Outline

The CDP model supports stiffness degradation. The backbone envelops are defined as exponential functions in terms of plastic strain [4]. Apart from the listed references, readers can also refer to the corresponding section in Constitutive Modelling Cookbook.

Syntax

material CDP (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) [15]
# (1) int, unique tag
# (2) double, elastic modulus
# (3) double, poissons ratio
# (4) double, crack stress f_t
# (5) double, crush stress f_c
# (6) double, normalized crack energy g_t
# (7) double, normalized crush energy g_c
# (8) double, initial tension hardening a_t<1
# (9) double, initial compression hardening a_c>1
# (10) double, damage factor at half crack stress d_t
# (11) double, damage factor at peak crush stress d_c
# (12) double, dilatancy parameter
# (13) double, biaxial compression ratio
# (14) double, initial stiffness recovery factor
# [15] double, density, default: 2400E-12

Remarks

  1. Poisson's ratio shall be smaller than 0.50.5, a typical value for concrete is around 0.20.2.

  2. Crack stress shall be greater than zero while crush stress shall be smaller than zero. But the program automatically set the signs for both stresses.

  3. Normalized crack energy gt=GF/lcg_t=G_F/l_c equals the first mode crack energy GFG_F over the characteristic length lcl_c. For SI (millimeter) unit system, typical values are of order 10310^{-3}. The compression conjugate gcg_c is typically greater than gtg_t by the order of 10210^2.

  4. Hardening parameters controls tension degradation slope and compression hardening shape. Values at0.5a_t\approx0.5 and ac2a_c\approx2 to ac5a_c\approx5 give good results.

  5. Dilatancy parameter can be set to 0.20.2. Comparisons can be seen in Lee's doctoral dissertation.

  6. Biaxial compression ratio is defined as the ratio between biaxial and uniaxial compression strengths. According to Kupfer et al. (1969), a value of 1.161.16 is recommended.

  7. Initial stiffness recovery factor controls the amount of stiffness recovery when loading direction changes.

  8. Theoretically, gtg_t and gcg_c shall be scaled according to the size of mesh grid. Practically, they cannot be arbitrarily small due to numerical stability issues, meaning that the mesh grid cannot be arbitrarily large.

History Layout

location
parameter

initial_history(0)

dtd_t

initial_history(1)

dcd_c

initial_history(2)

κt\kappa_t

initial_history(3)

κc\kappa_c

initial_history(4-9)

plastic strain

Recording

This model supports the following additional history variables to be recorded.

variable label
physical meaning

DT

tensile damage

DC

compressive damage

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