THE SOLUTION OF AN AXISYMMETRICAL INVERSE ELASTOPLASTIC PROBLEM USINGPENETRATION DIAGRAMS

In this paper, we propose a mathematical model of a problem related to the determination of elasto-plastic properties of a deformable axisym metric isotropic material using an experimentally given penetration di agram. The considered physical model is based on elasto-plastic deform ation theory. The problem leads to an inverse coefficient problem for the non-linear system of equilibrium equations with an additional cond ition (experimentally measured penetration diagram). This inverse prob lem is reformulated as a minimization problem for a certain functional . By using Lagrange linear triangle elements, the finite element formu lation is presented. The numerical algorithms for both direct and inve rse problems are described. Several numerical examples of the consider ed problem solution are given to show the accuracy and reliability of the proposed method. The influence of measurement errors is examined i n detail.