Issue 39

M. Romano et alii, Frattura ed Integrità Strutturale, 39 (2016) 226-247; DOI: 10.3221/IGF-ESIS.39.22 239 M | |  corresponds to a higher sensitivity to the mesomechanic kinematic, whereas a smaller value implies a smaller one. In the following the sign sensitive values of the slopes M  are considered. Results The results are presented in terms of the transversal kinematic part and in the difference of the applied and the evaluated longitudinal deformation. Transversal kinematic part The displacements v in transversal direction as y -displacements v are evaluated by the difference of the values v 1 and v 2 , where the indices indicate the opposite relevant positions. Because the FE-calculations consider the elastic part, the relative shift of the amplitude is lead back to the total transversal deformation ( y -strain y  ). This value results as the ratio of the difference of the y -displacements Δ v to the originally perpendicular distance of the positions of evaluation to each other. It is twice the amplitude, i. e. 2 A , for every mesomechanic geometry. The total transversal deformation for every substep n 1, , 39   is n n y n v v v A A 1, 2, , ,tot 2 2      (19) It is the sum of the purely kinematic part due to geometric constraints y ,kin  and the transversal strain due to Poisson effects y ,PRS  of the plain representative sequence. The results of Eq. (19) have to be corrected by the transversal deformation due to Poisson effects. Solved for the kinematic part due to mesomechanic geometric constraints it is n n y n y n y n y n v v A 1, 2, , ,kin , ,tot , ,PRS , ,PRS 2          (20) where the transversal deformation due to Poisson effects of the sequence is determined by y n x n u , ,PRS PRS,12 , PRS,12         (21) It is defined as the negative relation of transversal deformation due to the longitudinal one (cf. Eq. (17)). The value of the plain representative sequence PRS,12  , used in Eq. (21), is calculated by the weighted average of the Poisson’s ratios of the three structural mechanic different regions based on its areas of the sequence A . For simplification, for the longitudinally cut warp yarn the value of a 0°-unidirectionally reinforced region ν 12 is presumed, despite of its ondulation. For the perpendicularly cut transversal isotropic fill yarns the value is the one of the plane of isotropy, i. e. ν 23 , and the Poisson’s ratio of the isotropic matrix is ν m . Thus, the Poisson’s ratio of the plain representative sequence follows by A A A A A A W F M PRS,12 12 23 m PRS PRS PRS        (22) In case of the values of the HT-carbon fiber reinforced epoxy, namely 12 0.272   , 23 0.333   and m 0.35   , as indicated in Tab. 1 and Tab. 2, Eq. (22) yields PRS,12 0.306   as the value of the Poisson’s ratio of the representative sequence. Difference of the applied and the evaluated longitudinal deformation An additional indicator for the acting of the mesomechanic kinematic due to geometric constraints is the difference of the applied and the evaluated deformations in longitudinal direction ( x -direction) x x, kin     . The difference of the applied