A three-dimensional BEM solution for plasticity using regression interpolation within the plastic field

This paper presents an improved solution of three‐dimensional plasticity problems using the boundary element method (BEM). The BEM formulation for plasticity requires volume as well as boundary discretizations. An initial stress formulation is used to satisfy the material non‐linearity. Conventionally, the plastic field in the volume element (or cell) is interpolated based on the value of plastic stress at the nodes of the cell. In this paper, the distribution of the plastic field in the cell is based on a number of points interior to the cell. The plastic field is described using regression interpolation polynomials through these interior points. The constitutive relation is satisfied at each interior point. The number of points can be varied in each cell, thus allowing for adaptive volume cells. The plastic stresses are computed at the interior points only, therefore, the need for surface stress computation (which uses numerical derivatives at the surface) is completely eliminated. Three‐dimensional applications are used to compare the present regression interpolation procedure with the conventional method for elasto‐plasticity problems. In all variations of the applications studied regression interpolation based on interior points provided superior results to those determined via the conventional nodal interpolation method.