The two-dimensional loading problem of an elasto-plastic plane weakened by a hole

An analytical benchmark with combined pressure and shear loading for elastoplastic numerical models

“…Region 3 corresponds to the pure elastic state, where Kolossof‐Muskhelishvili's method gives the solution. If the stress point is close to the boundary between Regions 2 and 3, the Bykovtsev and Tsvetkov 's [1987] approximate solution can be used. In general, Region 2 corresponds to the onset of yielding, where several separate plastic regions appear around the hole.…”

“…If this constraint is violated, two separate plastic zones form originating at opposite points on the hole rim. Here, we do not consider the initial stages of the plastic yielding, although there are analytical solutions that describe this stage of deformation [ Bykovtsev and Tsvetkov , 1987] based on the perturbation method. We begin our analysis from the point where the plastic zone completely covers the hole.…”

An analytical method for determining the non-enclosed elastoplastic interface of a circular hole

“…. Separating the real and the imaginary parts of Equation 26, and a matrix denoted as A with dimensions of 2n × 2n is constructed as follows Separating the real and the imaginary parts of Equation (27), and a matrix denoted as B with dimensions of 2n × 1 is constructed as follows…”

“…However, difficulties arise in providing a solution to the problem in the case of a non-enclosed elastoplastic interface (see Figure 1), although some attempts have been made based on the Tresca yield criterion. The perturbation method was applied to determine an approximate solution by Bykovtsev and Tsvetkov [27] and Lozhkin [28,29]. In addition, Leitman and Villaggio [30] and Chanyshev and Abdulin [31] used the complex variable method to propose an approximate procedure by assuming that the shape of the elastoplastic interface is circular, which is not consistent with fact.…”