Research of application of the of penalty functions method in order to fulfill the of the incompressibility condition on the example of wedge upseting

Abstract

Grynkevych V. A. Research of application of the of penalty functions method in order to fulfill the of the incompressibility condition on the example of wedge upseting // Material working by pressure.  – 2019. – № 2 (49). - Р. 16-19.

In computer modeling of developed processes of plastic deformation, one of the serious problems is to take into account the condition of constant volume (incompressibility conditions). If the analytical method for solving the boundary value problem is relatively simple to satisfy the incompressibility condition, then in the numerical solution, in particular, by the finite element method, this condition can be satisfied only approximately. There are two main ways to satisfy the incompressibility condition: minimization of the Markov-Hermann functional and minimization of the Lagrange functional using the penalty function method. Computer finite element modeling of wedge upseting from a linearly viscous medium in the absence of contact friction was carried out. The values of the penalty constant varied. The results on the deformed state and shape change are obtained. It is shown that with excessively large values of the penalty constant, the average rate of relative volume change becomes positive. It is also shown that in this case, the deformed state changes qualitatively and becomes implausible. The optimal range of values of the penalty constant is determined.