Identification of inclusions of arbitrary geometry with different physical properties of materials in 3D structures

A two-step approach to non-destructive testing of mechanical structures is proposed in this study. The first step involves the identification of holes/inclusions with different physical properties and arbitrary geometry in 3D structures based on temperature field, method of moving asymptotes and finite element methods. Results demonstrating the detection of inclusions with different geometric shapes (cube, sphere, ellipsoid, torus and complex inclusions) in steel, copper and aluminium are presented. In the second step of the approach, an iterative procedure for the determination of elastic-plastic deformations of structures with inclusions identified in the first step in the 3D formulation is constructed. According to the deformation theory of plasticity, the procedure is based on finite element methods and Birger's method of variable elasticity parameters. As an example, the stress-strain state of a square steel plate clamped along the contour under the action of a transversely distributed load is studied for two types of aluminium inclusions: a central rectangular inclusion and a displaced spherical inclusion, identified in the first step of the proposed approach. The developed approach is essentially a generalised methodology for 3D identification of inclusions/holes. The study of the elastic-plastic 3D problem with inclusions has both scientific significance and great practical interest for engineers working in the field of non-destructive testing.