PSI - Issue 81

Olena Mikulich et al. / Procedia Structural Integrity 81 (2026) 251–254

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2. Research Methodology To model the change in the mechanical behaviour of the medium in the presence of a system of holes, we will develop a method for studying its stressed state. Consider an elastic structurally inhomogeneous medium in the form of a plate element weakened by a system of holes, the distance between which is  . We will refer it to the Cartesian coordinate system 1 2 3 , which we will place at the center of gravity of the body so that the 3 axis is perpendicular to the plane of the element (Fig. 3). The area occupied by the section in the 1 2 plane (the median plane) will be denoted by  . The boundary contours in the section perpendicular to the 3 axis will be denoted by 1 and 2 . To describe the dynamic stress state of an element, we use Cosserat elasticity with confined rotation (couple stress elasticity) (Mikulich et al., 2021). The developed methodology allows us to study the stress state for singly connected regions. For the case of doubly and multiconnected regions, we modify this methodology. For this, we set the yield boundary conditions in the form: | =  ( ),  | =  ( ), where  ( ),  ( ) are known function defined according to external load applied. In Mikulich et al., 2021 the problem is solved using approaches based on indirect approach of the boundary element method for the couple stress elasticity, which allows for controlling the accuracy of calculations in the case of non-stationary loads. For the case of multi-boundary regions, we modified integral equations. After defined unknown functions we calculate radial stresses based on obtained in Mikulich et al., 2021 formulas. 3. Result and Discussion To analyze the effectiveness of modified approach we investigate the radial stress distribution for the case of two circle holes. The external load influence was chosen for the case of applying an elastic impulse along the boundaries of cavities in form Mikulich et al., 2021. 2D model of problem is present in Fig. 4. Fig. 3. Problem’s model

Fig. 4. 2D model of problem The stress state calculation was performed for the following physical, mechanical, and microstructural characteristics of the foam material: shear modulus G =285 MPa, Young's modulus E =637 MPa, length characteristic in bending ℓ =0.77 mm and torsion ℓ =0.8 mm, N 2 = 0.04, cell size h =0.65 mm, density  =380 kg/m 3 (Mikulich, 2023). According results are present in Fig. 5 for the case of applying loads to both holes’ boundaries (a), to left hole’s (b) and right hole ’s (c) boundary. Here  is normalized time parameter calculated by relation to the speed of expansion wave in foam media (Mikulich, 2023).

Fig. 5. Stress state for differential cases of applying loads