Numerical modelling in large strain plasticity with application to tube collapse analysis

Abstract

Numerical methods are proposed for the analysis of 2 or 3-dimensional large strain plasticity problems. A Finite Difference program, with 2-dimensional continuum elements and explicit time integration, has been developed and applied to model the axisymmetric crumpling of circular tubes. New types of mixed elements (Triangles-Quadrilaterals for 2-D, Tetrahedra-Bricks for 3-D) are proposed for the spatial discretization. These elements model accurately incompressible plastic flow, without unwanted "zero-energy" deformation modes or tangling over of the mesh. Elastic-plastic, rate dependent laws are modelled with a "radial return" algorithm. The transmission of heat generated by plastic work and material dependence on temperature are also included, enabling a fully coupled thermo-mechanical analysis. A 2-D and axisymmetric computer program has been developed, implementing the numerical techniques described. Computational efficiency was essential, as large scale, costly applications were intended. An important part of the program was the contact algorithm, enabling the modelling of interaction between surfaces. The axisymmetric crumpling of tubes under axial compression ("concertina" mode) has been analyzed Numerically. Quasi-static experiments on Aluminium tubes were modelled, using velocity scaling. Very large strains are developed in the crumpling process; with the help of tension tests, material laws valid for such strain ranges were developed. Good agreement was obtained between numerical predictions and experimental results. Modelling choices such as mesh refinement, element type and velocity scaling were studied, and found to have an important influence on the numerical predictions. Finally, a large scale impact analysis of a steel tube at 176m/s was performed. The results compared well with experiment, indicating differences with the behaviour of low velocity crumpling mechanisms. To conclude, Finite Difference procedures with explicit time- marching techniques are proposed for large strain plasticity problems, at low or medium impact velocities. A fairly robust code has been developed and applied successfully to a range of large strain and tube crumpling problems.