Fig. 1. Inlet cylindrical duct of the MJM tidal turbine and ribs reinforcement at the outlet zone [2] Tarfaoui et al. [16 17] carried out quasi-static and dynamic analysis on thick filament wounded glass—epoxy cylindrical structure with transversely isotropic plies using Abaqus. The authors developed a numerical impact model implemented into Abaqus based on material property degradation to predict the progressive failure induced by an accidental impact. Once failure in an element is detected, the material property corresponding to that particular failure mode is reduced depending on the material degradation model. Fig. 2. Intralaminar bilinear law showing the stiffness degradation. The symbol (¢33) employed in the fibre and matrix compression softening modes is the Mcauley bracket operator: Oieq AN 5jeq are equivalent stress and equivalent displacement respectively for each failure mode and are computed as presented in reference [30] (see Table 1). Fig. 3. Sample and geometry. (a) E-glass/epoxy sample ee ee ee eee ee ee eee eee ee ee Total 20 plies are meshed using 8 nodes linear reduced integration solid elements (C3D8R) assigned with linear interpolation and mechanical properties listed in Table 2. A uniform smooth mesh with a single element through the thickness direction in each ply is adopted. Both the cradle and the hemispherical impactor of great stiffness compared to the cylinder are modelled as rigid bodies using R3D4 elements. Modelling cradle and impactor as deformable bodies require shell or solid elements that induce higher computation time. The impact velocity is imposed as an initial condition to the impactor’s reference point. The interaction between the impactor/ cylinder and the cylinder/cradle is defined using a surface-to-surface contact algorithm based on the dynamic penalty method to avoid penetration of individual nodes of the cylinder into the rigid surfaces. Material property. Table 2 Fig. 5. Finite element quarter model for the impact analysis of the E-glass/epoxy cylinder. Fig. 6. Finite element model for the impact analysis of the composite cylinder with four mesh sizes. Fig. 7. Mesh effect on the dynamic response for non-damaging impact at 1.992 J, V = 1.55 m/s Simulations are carried out applying four failure criteria denoted “Hashin Extend”, “Chang & Chang (1987)”, “Hashin-Puck” and “Hashin 3D (1980)” which were implemented into a VUMAT subroutine linked to Abaqus/Explicit software. The bilinear model in- cludes damage onset based on quadratic stress criteria, linear damage evolution law and element deletion from the mesh once the element is fully damaged. The intralaminar model and related equations are detailed in Section 2. Three impact velocities of 2.55 m/s, Fig. 8. Numerical and experimental impact force for non-damaging impact at 1.992 J, V = 1.55 m/s. Fig. 9. Numerical and experimental force-time and displacement-time comparison using various intra-laminar failure criteria for different impact energies. whole result, the progressive damage model implemented into the VUMAT subroutine using “Hashin 3D (1980)” failure criteria is considered as a relatively good compromise between the model accuracy and the computing time in the range of 5 J and 10 J but on another hand, the damage model still requires the consideration of the effect of delamination. Therefore the purpose of the Section 3.4 is to include the delamination effect in the numerical modelling. Fig. 10. Prediction of the through-thickness matrix tension damage and matrix compression damage using “Hashin 3D (1980)” failure criteria fo: three impact energies at the end of the impact analysis. Matrix compression mode Fig. 11. Schematic diagram showing measured dimensions in impacted damage area 3.5. Interlaminar damage combination Fig. 12. Mixed Mode softening law behaviour. Properties used in the cohesive model [40]. Table 3 interface stiffness following a linear softening law, Fig. 12. Similar to the intralaminar damage model, a scalar damage variable (d) is defined to represent the delamination propagation under mixed-mode loading [38]. The damage variable (d) varies from 0 when the interface delamination is initiated to 1 at the complete delamination of the interface. dn, &, a, and 5Max represent the mixed-mode displacement, the mixed-mode onset displacement, the mixed-mode final displacement at the complete interface decohesion and the mixed-mode maximum displacement respectively. 5°, 53, 59 represent the single-mode onset displacement. / is the mixity mode ratio. K,, K, and K; are the interfacial penalty stiffness. G;, Gj, and Gj, are the critical interlaminar fracture toughness in Mode I, II and III respectively. The Benzeggagh-Kenane criterion (B-K criterion) based on fracture energy is used to predict the delamination propagation under mixed-mode loading. The critical energy release rate (G.) is given as: (a) Impact energy 5.202 J (V=2.55 m/s) Fig. 13. Numerical and experimental force-time and displacement-time comparison using intralaminar and interlaminar damage combination for different impact energies. Variation of the interface strengths values (.K, = K; = K;= 10E8). Table 4 Variation of critical fracture toughness values (.K, = K, = K;= 10E8). Fig. 14. Influence of the interlaminar strengths on the impact force curve. Table 5