A shell-like stress resultant approach for elastoplastic geometrically exact thin-walled beam finite elements

• Shell-like stress resultant elastoplasticity and geometrically exact thin-walled beam elements are combined.
• A simplified and constrained Ilyushin criterion is proposed.
• The return mapping algorithm and the consistent tangent assume particularly simple forms.
• Through-thickness numeric integration is avoided.
• The accuracy and computational efficiency of the approach is demonstrated.

This paper demonstrates the computational advantages of combining shell-like stress resultant elastoplasticity with geometrically exact thin-walled beam finite elements. The material model employed follows the Ilyushin criterion for shell-type stress resultants, making it possible to bypass computationally expensive through-thickness numeric integration and enforce specific stress resultants to zero, leading to a particularly simple form of the return mapping algorithm and of the consistent constitutive tangent. This constitutive model is included in a geometrically exact two-node beam finite element which allows for torsion-related warping and Wagner effects. The accuracy of the proposed approach is assessed in several numerical examples.