Fig. 1: Displacement field solution in the one dimensional bar for different phase-field states and for kg = 0
 
Different predefined phase-field functions 

\phi = exp(-sqrt(x^2 + f_i)/l)
with f_1 = 0.00, f_2 = 0.01 and f_3 = 0.05

representing different states in the process of a developing crack were applied to a one-dimensional bar with L =[−1, 1]. The regularising internal length was chosen to be l = 2. The mechanical part of the phase-field formulation was solved via FE-simulation for the displacement field u(x) across the crack, with the applied boundary conditions u(x =−1) =−1 and u(x = 1) = 1. 10,000 elements were used over the bar to ensure a sufficiently accurate approximation of the different slopes using linear ansatz functions. The resulting displacement functions are depicted.

for each file -> Columns
1: x-coordinates of the 1D bar 
2: displacement result

file fig_01_data_1.csv: phase-field function with f_1=0.00 as input
file fig_01_data_2.csv: phase-field function with f_2=0.01 as input
file fig_01_data_3.csv: phase-field function with f_3=0.05 as input