The plastic tests validate the correct implementation of the inelastic material behavior of the beam, as well as the explicit return mapping scheme.
Test Cases
Test 1
Test 1 implements Example 5.1 from Smriti, Kumar, Steinmann (2011). This example shows the plastic behavior of a cantilever beam under a constant twist, being subjected to axial tension and compression. The hardening observed is a result of the multi-axial loading condition and can be viewed as geometric hardening, as no hardening is present in the considered material parameters. The custom implementation shows an excellent agreement with the results from literature
Test 2
Test 2 implements Example 5.2 from Smriti, Kumar, Steinmann (2011). This example shows the plastic behavior of a cantilever beam subjected to axial tension and compression with the effects of either isotropic or kinematic hardening present in the material model. Both, case a) isotropic hardening and case b) kinematic hardening show an excellent agreement with the results from literature.
Test 3
Test 3 implements Example 5.4 from Herrnböck, Kumar, Steinmann (2023). This example shows the complex elasto-plastic deformation of a beam under three-dimensional loading conditions. The custom implementation shows good agreement with the reported results from an \(FE^2\) approach. The differences are similar to the ones reported in the referenced publication.
