PSI - Issue 73

Roman Vodička et al. / Procedia Structural Integrity 73 (2025) 163 –169 Author name / Structural Integrity Procedia 00 (2025) 000 – 000

165

3

2. Computational model description For computational analysis of the connector represented by domain Ω shown in Fig. 1, the model developed in ( Vodička, R. et al. (2018)) was used. The model is controlled by evolution of the energy state in the connected materials. The energy is described by the displacement field , a gap of the interface displacement ⟦ ⟧ , and an interface damage variable characterising degradation of the interface Γ c meant as a negligibly thin adhesive layer. Various forms of energy include the stored energy which may be considered as follows ( ; , ) = ∫ ( ): ( ) d Ω +∫ Γ 1 2 c ( )( ⟦ ⟧ 2 + ⟦ ⟧ 2 + ⟦ ⟧ 2 )+ 1 2 g (⟦ ⟧ − ) 2 d (1) for an admissible displacement field satisfying the displacement boundary conditions (constraints and prescribed

displacement u(t) along Γ D in Fig. 1) and admissible damage parameter , lying in the interval [0,1] (0 pertains to undamaged interface, 1 to full damage, i.e. a crack), otherwise is supposed infinite. The introduced material parameters include stiffness matrix of the material of the domains, stiffnesses k n , k s , k z (normal, tangential, and transversal, respectively) of the adhesive layer and the compressive stiffness k g to penalise the contact between the material domains (typically g ≫ ). The function is the interface degradation function controlling the form of the local interface stress-strain relation, it decreases from (0)=1 to (1)=0 . A particular choice used in the calculation considers ( ) = ( 1 +− ) , where the parameter >0 characterises the negative slope (say − for the normal component) of the weakening part of the bilinear stress-strain relation (Vodička, R. and Mantič, V. (2017)). Notice also l meaning the length measure along the interface shown also in Fig. 1. The crack formation is related to dissipation of energy expressed by dissipation functional R in terms of damage rate ̇ . Conditions of evolution are characterised by c – the interface fracture energy. The functional for a rate independent process is expressed as ( ̇) = ∫ c (⟦ ⟧) ̇ d , Γ (2) which only admits ̇ ≥0 to guarantee unidirectionality of the cracking mechanism, otherwise the value of R would be infinite. The functional form of the fracture energy accounts for its mode dependence, introducing the values c I , c I I , c II I within the formula c (⟦ ⟧)= ⟦ ⟧ 2 + ⟦ ⟧ 2 + ⟦ ⟧ 2 ⟦ ⟧ 2 c I + ⟦ ⟧ 2 c I I + ⟦ ⟧ 2 c II I . Finally, for external forces (like vertical pressure p along a part of Γ N in Fig. 1), their energy should be added to Fig. 1. Domain notation for the FRP-concrete connector, including constraints and loading. Interface Γ c is measured within the length variable l , the values of l pertain to the particular shape of r = 8.5 mm .