Eliminacja blokady objętościowej w liniowych elementach trójkątnych i czworościennych. Zastosowanie do symulacji procesów przeróbki plastycznej na zimno

The authors deal with the numerical problem of volumetric locking occurring in finite element simulation of metal forming processes and other problems characterized with incompressible deformation. Volumetric locking is present in all finite elements based on the standard displacement formulation as well as in mixed elements using equal order interpolation for displacements and pressure. Special stabilizing techniques are necessary in order to avoid volumetric locking in such useful elements as triangles and tetrahedra with linear interpolation of displacements and pressure. An original method to eliminate volumetric locking has been developed and applied to analysis of metal forming problems. The stabilization method, called CBS (Characteristics based Split), is based on the splitting of the Stokes equations describing elasto ? plastic deformation of the material. The split algorithm has been implemented within an explicit dynamic finite element code. Numerical examples of metal forming simulation demonstrate effectiveness and correctness of the theoretical formulation and numerical algorithm.