Numerical modeling of the processes of irreversible deformation of rings under explosive loading

Abstract

the quasi-static problem is discussed. The equations of the incremental theory of plasticity are used to describe fast deformation. The numerical simulation method is implemented based on the use of the Arbitrary Lagrange-Euler (ALE) approach, in which the sequence of boundary value problems in the current configuration of the solid is solved using the Finite Element Method. An axisymmetric finite element of a triangular cross-section was used for modeling. The main system of equations is presented, which, when using the Finite Element Method, describes the deformation of axisymmetric bodies in the current configuration. At each stage of the calculation in the current configuration, the initial problem is solved numerically using the finite difference method. When the limiting value of the strain tensor components is reached, according to the ALE algorithm, the finite element model is rebuilt with the implementation of new boundary conditions. To build a computational model, the RD program was used, in which a two-dimensional model of a section of an axisymmetric body is surrounded by a mesh of special elements. A presented approach for the implementation of the specified boundary conditions of an axisymmetric body in finite element modeling is discussed. Calculations of irreversible deformation were carried out in a program developed on the basis of using the FEM Creep software package in the case of finite strains. Comparison of the numerical simulation data with the experimental results of other authors, obtained in the investigations of the explosive loading of aluminum rings set on a sphere, is presented. The experimental data are processed and the constants included in the constitutive equation, using the hardening law, are determined. Satisfactory agreement between the calculated and experimentally obtained values of the radial strain of the rings at different times is shown.
 Key words: numerical simulation, axisymmetric problem, finite strains, FEM, program, explosive loading, aluminum alloy.