Fig. 16: Quadrature error for centre positioned crack (top) and shifted positioned crack (bottom) for different kφ with l/h = 1.0 and one GP per subelement
 

The numerical quadrature error e^int_Γlς (Eq. 58) of the crack surface integral (the max. expected error) for different numbers of integration points is shown for different kφ (0.001, 0.002, 0.004). The phase-field is not numerically calculated by the means of FE but the stabilised phase-field is given (φς) as well as the analytical solution (φ).

Top: refers to a given crack in the middle of the bar
Bottom: refers to a given crack at a off-center position.

The lines within the graph are the upper bound of the corresponding point values (upper envelope curve), they serve as an indicator for the highest quadrature error possible at a certain integration point number depending on the position of the crack with respect to the position of the integration points.

for each file -> Columns
1: number of integration points 
2: error 

file fig_16_data_1.csv: kφ=0.001, centre positioned crack 
file fig_16_data_2.csv: kφ=0.002, centre positioned crack 
file fig_16_data_3.csv: kφ=0.003, centre positioned crack 

file fig_16_data_4.csv: kφ=0.001, shifted positioned crack 
file fig_16_data_5.csv: kφ=0.002, shifted positioned crack 
file fig_16_data_6.csv: kφ=0.003, shifted positioned crack 