Mathematical modeling of T-joint connection of thin anisotropic inclusions in an elastic body with debonding

T. S. Popova

North-Eastern Federal University, Yakutsk

Abstract: The deformation of an elastic body containing two thin anisotropic inclusions intersecting at a right angle is studied based on a mathematical model with unilateral boundary conditions. The inclusions intersect at an interior point of one of them, forming a T-shaped configuration within the elastic medium. One of the inclusions is debonded from the matrix, resulting in a crack. Boundary conditions on the crack surfaces are specified in the form of inequalities. To solve the problem numerically in the region with a cut, a domain decomposition method with the Uzawa algorithm is used. To determine the displacement functions of the semi-rigid inclusion, a method based on decomposing the space into a direct sum of subspaces is applied.

Keywords: variational inequality, semi-rigid inclusion, thin inclusion, crack, non-penetration condition, nonlinear boundary condition, coupling problem, Uzawa algorithm.

UDC: 517.9

Received: 04.06.2024
Revised: 19.08.2024
Accepted: 02.09.2024

DOI: 10.15372/PMTF202415535

 English version: Journal of Applied Mechanics and Technical Physics, 2025, 66:3, 560–574

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