Fixed crack model for concrete - ConcreteFCM

Implementation of a fixed crack model. Uncracked material is modeled as isotropic linear elastic characterized by Young's modulus and Poisson's ratio. Cracking is initiated when principal stress reaches tensile strength. Further loading is governed by a softening law. Proper amount energy dissipation is guaranteed by the crack-band approach. Multiple cracking is allowed; the maximum number of allowed cracks is controlled by ncracks parameter. Only mutually perpendicular cracks are supported. If cracking occurs in more directions, the behavior on the crack planes is considered to be independent. The secant stiffness is used for unloading and reloading. In a compression regime, this model correspond to an isotropic linear elastic material. The model supports 3 different options for stiffness reduction in shear after cracking, 2 options for the limit of the maximum shear stress on a crack plane and 6 different laws for postpeak behavior. The model parameters are summarized in Tab. 42.

Sample syntax for a fixed crack model with volume density 24 kN/m$^3$, thermal dilation coefficient $12\times10^{-6}$ K$^{-1}$, Young's modulus 20 GPa, Poisson's ratio 0.2, fracture energy 100 N/m, tensile strength 2 MPa, linear softening, constant shear retention factor $\beta = 0.05$, Collins' shear strength (with compressive strength 30 MPa, aggregate size 0.01 m) and all cracks contribute to the shear stiffness; the analysis uses [m], [MPa] and [MN]:
ConcreteFCM 1 d 24.e-3 talpha 12.e-6 E 20000. n 0.2 Gf 100e-6 ft 2.0 softType 2 shearType 1 beta 0.05 shearStrengthType 2 fc 30 ag 0.01
lengthscale 1. multipleCrackShear

Table 42: Fixed crack model for concrete - summary.

Description

Fixed crack model for concrete

Record Format

ConcreteFCM (in) # d(rn) # tAlpha(rn) # E(rn) # n(rn) # [ ncracks(in) #] [ multipleCrackShear ] [ crackSpacing(rn) #] [ softType(in) #] [ shearType(in) #] [ shearStrengthType(in) #] [ ecsm(rn) #] [ Gf(rn) #] [ ft(rn) #] [ beta(rn) #] [ sf(rn) #] [ fc(rn) #] [ ag(rn) #] [ lengthscale(rn) #] [ soft_w(ra) #] [ soft(w)(ra) #] [ soft_eps(ra) #] [ soft(eps)(ra) #] [ beta_w(ra) #] [ beta(w)(ra) #] [ H(rn) #] [ eps_f(rn) #]

Parameters

- material model number

- d material density

- tAlpha thermal dilatation coefficient

- E Young's modulus

- n Poisson's ratio

- ncracks maximum allowed number of cracks

- crackSpacing specified distance between parallel cracks

- multipleCrackShear if not given, shear stiffness computed from the dominant crack, otherwise all cracks contribute

- softType allows to select suitable softening law:

0 -	no softening (default)
1 -	exponential softening with parameters Gf and ft
2 -	linear softening with parameters Gf and ft
3 -	Hordijk softening with parameters Gf and ft
4 -	user-defined wrt crack opening with parameters ft, soft_w, and soft(w)
5 -	linear hardening wrt strain with parameters ft, H, and optionally eps_f
6 -	user-defined wrt strain with parameters ft, soft_eps, and soft(eps)

- shearType offers to choose from different approaches for shear stiffness reduction of a cracked element

0 -	no shear reduction (default)
1 -	constant shear retention factor with parameter beta
2 -	constant shear factor coefficient with parameter sf
3 -	user-defined shear retention factor with parameters beta_w and beta(w)

- shearStrengthType allows to select a shear stress limit on a crack plane

0 -	no stress limit (default)
1 -	constant strength = $f_t$
2 -	Collins interlock with parameters fc, ag, and lengthscale

- ecsm method used for evaluation of characteristic element size $L$: 1 = square root of area, 2 = projection centered, 3 = Oliver, 4 = Oliver modified, 0 (default) = projection

- Gf fracture energy

- ft tensile strength

- beta shear retention factor

- sf shear factor coefficient

- fc compressive strength in MPa

- ag aggregate size

- lengthscale factor to convert crack opening and aggregate size in case of Collins aggregate interlock; 1 = analysis in meters, 1000 = in millimeters, etc.

- soft_w specified values of crack opening and

- soft(w) corresponding values of traction normalized to ft

- soft_eps specified values of cracking strain and

- soft(eps) corresponding values of traction normalized to ft

- beta_w specified values of crack opening and

- beta(w) corresponding values of shear retention factor

- H hardening modulus (expressed wrt cracking strain)

- eps_f threshold for cracking strain after which traction is zero (applicable for linear hardening only)

Supported modes

3dMat, PlaneStress, PlaneStrain