Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modelling of metal forming processes

Abstract Today the finite-element method is the most widely used tool in the prediction of both linear and nonlinear structural behaviour. An inherent danger of such widespread use, however, is an overconfidence in the accuracy and correctness of the results obtained. It is necessary to produce simple benchmark tests which may be performed to justify the user's faith in such finite-element packages. The results of these benchmarks should compare favourably with experimental results, exact theoretical models or with recognised finite-element standards. In linear elastic problems it is relatively straightforward to find exact solutions to which the finite-element results may be compared. In nonlinear elasto-plastic analyses in general, and particularly for 3-dimensional forming, analyis it is extremely difficult to determine suitable benchmarks. However, in these cases it is even more important to establish a set of benchmarks to which quantitative or qualitative comparisons may be made. A series of such tests are presented for both single and multi-element analyses, which may be applied to 3-dimensional, elasto-plastic, large strain, finite-element codes. Further benchmarks are introduced which provide standards for friction, isotropic and anisotropic materials, and multi-material problems. It is hoped that the application of these benchmarks will help finite-element users to develop their analyses with legitimized assurance in the validity of their results.