# Title:    
            Extended Phase-Field Method (XPFM) - Data corresponding to publication: "An enriched phase-field method for the efficient simulation of fracture processes" by Loehnert et al. (2023)

# Date: 
            2024-04-19

# Author:
            Verena Curosu
            
# Description:
            This folder contains the data relating to the scientific (open-access) contribution "An enriched phase-field method for the efficient simulation of fracture processes" by Loehnert et al. (2023) (https://doi.org/10.1007/s00466-023-02285-z). The data relates to the figures within the publication as they are listed below. Each figure is filed again in this folder with its corresponding number from the publication (fig_xx_graph.pdf), a short description (fig_xx_info.txt) and the corresponding data as a csv.file (fig_xx_data_i.csv). For further information please refer to the mentioned publication.
            
            For each figure in question is placed in the folder "info_graph_data":
            - fig_xx_info.txt
            - fig_xx_graph.pdf
            - fig_xx_data_i.csv
            
            List of figures in question:
            
            Fig. 1: Displacement field solution in the one dimensional bar for different phase-field states and for kg = 0
            
            Fig. 2: Displacement field solution in the one dimensional bar for a fully developed phase-field (predefined, φ(x = 0) := 1) and different kg
            
            Fig. 3: Displacement functions over a one-dimensional bar corresponding to the predefined phase-field function with different element sizes and a kg = 10−5
            
            Fig. 13: Error of stabilised crack surface dependent on kφ with l = 1.0 mm (blue) and dependent on l with kφ = 0.002 (orange).
            
            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
            
            Fig. 17: Comparison of envelope curves with different kφ and l/h = 1.0, Quadrature: 1 GP per subelement; centred crack: solid lines, shifted crack: dashed lines
            
            Fig. 18: Comparison of envelope curves with different l and kφ = 0.002, Quadrature: 1 GP per subelement; centre crack: solid lines, shifted crack: dashed lines
            
            Fig. 19: Comparison of envelope curves with l/h = 1.0, kφ = 0.002 and different maximum phase-field φmax, Quadrature: 1 GP per subelement; centred crack: solid lines, shifted crack: dashed lines
            
            Fig. 20: Comparison of envelope curves with the different subelement quadrature schemes with l/h = 1.0andkφ = 0.002; centred crack: solid lines, shifted crack: dashed lines
            
            Fig. 22: Comparison of envelope curves with different l and φmax = 0.9, Quadrature: 1 GP per subelement; centred crack: solid lines, shifted crack: dashed lines
            
            Fig. 23: Comparison of envelope curves with different φ and l = 1.0, Quadrature: 1 GP per subelement; centred crack: solid lines, shifted crack: dashed lines
            
            Fig. 24: Comparison of envelope curves with the different subelement quadrature schemes with l/h = 1.0andφmax = 0.9; centred crack: solid lines, shifted crack: dashed lines
            
            Fig. 27: Comparison of envelope curves with different crack positions as depicted in Fig. 26 with l/h = 1, l = 0.01 mm and kφ = 0.01
            
            Fig. 28: Comparison of envelope curves with different kφ with l/h = 1, l = 0.01 mm and yc = 0.004 mm
            
            Fig. 29: L2-error of displacements (top) and the ratio of the analytical to the numerical obtained crack surface Γ/Γh l (bottom) for different l/h-ratios with l = 0.01 mm
            
            Fig. 30: L2-error of the displacements for varying kreg within the XPFM, marked kreg is used in Fig. 29
            
            Fig. 32: Force-displacement curves of standard PFM mode I tension test with constant nstag = 8 and varying ratio l/h
            
            Fig. 33: Force-displacement curves of standard PFM mode I tension test with constant ratio l/h = 10 and varying number of staggered iterations nstag per load step
            
            Fig. 34: Force-displacement curves of standard PFM mode I tension test (l/h = 10) compared to XPFM simulations with different l/hratios
            
            Fig. 36: Traction controlled mode I tension test (b) Critical loads
            
            Fig. 37: Force-displacement curves of standard PFM mode II shear test (l/h = 5) compared to XPFM simulations with different l/h-ratios