Issue 39

M. Romano et alii, Frattura ed Integrità Strutturale, 39 (2016) 226-247; DOI: 10.3221/IGF-ESIS.39.22 240 deformations x n ,  (17) and the evaluated or calculated ones by FE-analyzes in longitudinal direction at the relevant positions x n , ,FE  for every substep n 1, , 39   is x n, x n x n x n, , kin , , , FE         (23) It serves for the identification of the elastic deformation of the plain representative sequence and the longitudinally cut ondulated warp yarn in the FE-model. Results of the analytical model Tab. 3 lists the evaluated results according to Eq. (18) in the w rel - u rel -diagram as absolute values y M ,a  over the selected degrees of ondulation O  of the analytical model. The results are listed in ascending order regarding the corresponding degree of ondulation O  . Fig. 5 graphically illustrates the correlations of the selected degrees of ondulation and the corresponding sensitivity to the mesomechanic kinematic. The consideration of the absolute values of the slopes in the w rel - u rel -diagram y M ,a  allows a graphical illustration of the correlation between degree of ondulation O  and the sensitivity to the mesomechanic kinematic in a linear equidistant scaled diagram and in a double logarithmic scaled diagram. In both cases the results are illustrated separately for the large and for the small interval, and the equations of a hyperbolic approximation of the correlation for the respective interval are indicated. Additionally, the upper bound that can be identified for the exponent -1.5 is visualized by a bold dashed line. Geometric parameters of the ondulation Slope a, ~ y M in the w rel - u rel -diagram Amplitude A Length of ondulation L Degree of ondulation O ~ Analytically for 3 rel 101     u in steps of 4 101   Analytically for 4 rel 101     u in steps of 5 101   0.05 15.0 0.00333 -2448.20 -5040.10 0.05 12.5 0.00400 -1886.70 -3288.40 0.05 10.0 0.00500 -1369.90 -2047.40 0.10 15.0 0.00667 -914.03 -1143.40 0.05 7.5 0.00667 -914.59 -1141.30 0.10 12.5 0.00800 -729.59 -793.20 0.15 15.0 0.01000 -540.08 -507.26 0.10 10.0 0.01000 -540.13 -507.13 0.05 5.0 0.01000 -540.14 -505.79 0.15 12.5 0.01200 -369.62 -352.36 0.20 15.0 0.01333 -293.84 -285.42 0.10 7.5 0.01333 -293.67 -285.23 0.15 10.0 0.01500 -229.49 -225.43 0.20 12.5 0.01600 -200.78 -198.17 0.25 15.0 0.01667 -184.74 -182.66 0.25 12.5 0.02000 -127.63 -126.94 0.20 10.0 0.02000 -127.54 -126.90 0.15 7.5 0.02000 -127.64 -126.92 0.10 5.0 0.02000 -127.50 -126.90 0.25 10.0 0.02500 -81.45 -81.28 0.20 7.5 0.02667 -71.61 -71.49 0.15 5.0 0.03000 -56.60 -56.54 0.25 7.5 0.03333 -45.86 -45.83 0.20 5.0 0.04000 -31.92 -31.91 0.25 5.0 0.05000 -20.50 -20.50 Table 3 : Slopes in the w rel - u rel -diagram, i. e. a, ~ y M of the selected degrees of ondulation O ~ for the two considered intervals of u rel .