Implementation of nonlocal version of smeared rotating crack model with transition to
Improves the classical rotating model (see
section 1.5.2) by introducing the transition to scalar damage
model in later stages of tension softening.
The improved RC-SD (see section 1.5.3) is further extended to a
nonlocal formulation, which not only acts as a powerful localization
limiter but also alleviates mesh-induced directional bias. A special
type of material instability arising due to negative shear stiffness
terms in the rotating crack model is resolved by switching to SD mode. A bell shaped nonlocal
averaging function is used.
Nonlocal smeared rotating crack model with transition to scalar damage - RCSDNL
Virgin material is modeled as isotropic linear elastic material
(described by Young modulus and Poisson
ratio). The onset of cracking begins, when principal stress reaches
Further behavior is then determined by exponential softening law.
The transition to scalar damage model
takes place, when the softening stress reaches the specified limit or
when the loss of material stability due to negative shear stiffness
terms that may arise in the standard RCM formulation, which takes
place when the ratio of minimal shear coefficient in stiffness to
bulk material shear modulus reaches the limit.
Multiple cracks are allowed.
The elastic unloading and reloading is assumed.
In compression regime, this model correspond to isotropic linear elastic material.
The model description and parameters are summarized
in Tab. 22.
RC-SD-NL model for concrete - summary.
||Nonlocal smeared rotating crack model with transition to scalar damage for concrete
||RCSDNL d(rn) # E(rn) #
n(rn) # Ft(rn) #
sdtransitioncoeff(rn) # sdtransitioncoeff2(rn) #
r(rn) # tAlpha(rn) #
||- num material model number
||- d material density
||- E Young modulus
||- n Poisson ratio
||- ef deformation corresponding to fully open crack
||- Ft tension strength
||- sdtransitioncoeff determines the transition from RC to SD
model. Transition takes place when ratio of current softening
stress to tension strength is less than sdtransitioncoeff value
||- sdtransitioncoeff2 determines the transition from RC to SD
model. Transition takes place when ratio of current minimal shear
stiffness term to virgin shear modulus is less than sdtransitioncoeff2 value
||- r parameter specifying the width of nonlocal averaging zone
||- tAlpha thermal dilatation coefficient
||- regionMap map indicating the regions (currently region is
characterized by cross section number) to skip for nonlocal
avaraging. The elements and corresponding IP are not taken into
account in nonlocal averaging process if corresponding regionMap
value is nonzero.
||3dMat, PlaneStress, PlaneStrain, 1dMat,
2dPlateLayer, 2dBeamLayer, 3dShellLayer