Incremental Modelling and Numerical Solution of the Contact Problem between Movable Elastic and Elastic/Visco-Plastic Bodies and Application in the Technological Processes

Abstract

Paper presents the modelling of the contact problem in the technological processes. Technological processes were considered as a geometrical and physical boundary and initial value problem, with unknown boundary conditions in the contact zone. An incremental model of the contact problem between movable rigid or elastic body (tool) and elastic/visco-plastic body (object) in updated Lagrange formulation, for spatial states (3D) was considered. The incremental functional of the total energy and variational, non-linear equation of motion and deformation of object on the typical step time were derived. This equation has been discretized by finite element method, and the system of discrete equations of motion of objects was received. For solution of these equations the explicit or implicit methods was used. The applications were developed in the ANSYS/LS-Dyna system, which makes possible a complex time analysis of the states of displacements, strains and stresses, in the workpieces in technological processes. Application of this method was showed for examples the modelling and the analysis of tensile test [1 and technological processes of metal forming [1-.