MATHEMATICAL MODELING OF T-JOINT CONNECTION OF THIN ANISOTROPIC INCLUSIONS IN AN ELASTIC BODY WITH DEBONDING
T. S. Popova
North-Eastern Federal University, Yakutsk, Russia
Keywords: variational inequality, semi-rigid inclusion, thin inclusion, crack, non-penetration condition, nonlinear boundary condition, coupling problem, Uzawa algorithm
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.
|
