Smeared rotating crack model with transition to scalar damage - linear softening - RCSD

Implementation of smeared rotating crack model with transition to scalar damage with linear softening law. Improves the classical rotating model (see section 1.5.2) by introducing the transition to scalar damage model in later stages of tension softening.

Traditional smeared-crack models for concrete fracture are known to suffer by stress locking (meaning here spurious stress transfer across widely opening cracks), mesh-induced directional bias, and possible instability at late stages of the loading process. The combined model keeps the anisotropic character of the rotating crack but it does not transfer spurious stresses across widely open cracks. The new model with transition to scalar damage (RC-SD) keeps the anisotropic character of the RCM but it does not transfer spurious stresses across widely open cracks.

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 tensile strength. Further behavior is then determined by linear softening law, governed by principle of preserving of fracture energy $G_f$. For large elements, the tension strength can be artificially reduced to preserve fracture energy. The transition to scalar damage model takes place, when the softening stress reaches the specified 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. 20.

Table 20: RC-SD model for concrete - summary.

Description	Smeared rotating crack model with transition to scalar damage - linear softening
Record Format	RCSD d(rn) # E(rn) # n(rn) # Gf(rn) # Ft(rn) # sdtransitioncoeff(rn) # tAlpha(rn) #
Parameters	- num material model number
	- d material density
	- E Young modulus
	- n Poisson ratio
	- Gf fracture energy
	- Ft tension strength
	- sdtransitioncoeff determines the transition from RC to SD model. Transition takes plase when ratio of current softening stress to tension strength is less than sdtransitioncoeff value
	- tAlpha thermal dilatation coefficient
Supported modes	3dMat, PlaneStress, PlaneStrain, 1dMat, 2dPlateLayer, 2dBeamLayer, 3dShellLayer