PSI - Issue 61

Onur Ali Batmaz et al. / Procedia Structural Integrity 61 (2024) 305–314 Onur Ali Batmaz et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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• The horizontal response of the bottom boundary springs is related to the adhesive frictional contact between the beam and the bottom fixture plates, since this interface was reported to have adhesive regions (Bozkurt and Coker, 2021). This also implies the tension-compression symmetric definition of a finite horizontal spring constant ( ℎ, + = ℎ, − ≠0 ). • The vertical response of the bottom boundary springs is related to two distinct purposes depending on whether the interface is under compression or tension. Under compression, it accounts for the vertical compliance of the test fixture, which implies a finite vertical spring constant ( , − ≠0) . Under tension, it accounts for the adhesive contact between mating surfaces, which implies a finite vertical spring constant ( , + ≠0 ). The optimal values for the spring constants ℎ, , , − = , − , ℎ, , and , + are determined as 1040, 130, 1517, and 1084 ×10 4 kN/mm, respectively. 4. Influence of flexural boundary conditions on the impact response The validity of the proposed boundary conditions (BCs) approach outlined in Section 3, which replicates the experiment supports through the assembly of spring elements at the corresponding boundary nodes, can be demonstrated through comparisons of displacement and strain data obtained from both the experiment and FE simulations. In Figure 4(a), the history of impactor translation obtained from the experiment is presented and compared with two FE simulations — one using fixed BCs and the other using the proposed BCs. The displacement patterns are extracted from the experimental frame just before damage occurs (referred to as "frame A") and corresponding time frames from the FE simulations. While the influence of proposed BCs modeling may not be apparent on a global scale, the fact that all three sets of data closely match each other shows the validity of proposed BCs concerning the global response. An in-depth examination on the field measurements reveals that the deformed shape of the beam observed in the experiment is perfectly replicated by the simulation with the proposed BCs at the same instant, as depicted in Figure 4 (b). This is further quantified by plotting the variations in horizontal (δ x ) and vertical displacements (δ y ) along a vertical line near the boundary edge for the experiment and FE models with both fixed and proposed BCs. It is evident that the FE model with fixed boundary conditions underestimates the amount of deformation along the inspected line, whereas the FE model with the proposed BCs accurately reproduces both the horizontal and vertical deformation curves observed in the experiment.

(a) (b) Figure 4. (a) Impactor translation histories, and (b) deformed states of the left- hand side of the beam with the distributions of horizontal (δ x ) and vertical (δ y ) displacements for the experiment and FE models with fixed and proposed BCs. Distributions of δ x and δ y are extracted along the boundary edges for the experiment frame prior to damage (labelled as A) and corresponding frames of FE simulations.