Linearly elastic constitutive relations and consistency for GBT-based thin-walled beams

• A new approach for the determination of appropriate constitutive relations in the GBT framework is proposed.
• The concept of consistency of a GBT-based model is established and a consistency analysis is presented.
• Numerical examples show the importance of the arguments discussed, especially if orthotropic materials are considered.

The present paper focuses on the constitutive assumptions, both for the isotropic and orthotropic cases, and consistency in the framework of the Generalized Beam Theory. In particular, a novel approach based on energetic arguments, able to automatically select appropriate constitutive relations in accordance with the GBT kinematics, is presented. Furthermore, the concept of consistency of a GBT-based model is established and a consistency analysis is presented. This yields a formal rational basis to investigate the effects of the various families of cross-section deformation modes in terms of predictive capabilities of the GBT model. Some numerical examples illustrate the arguments exposed in the paper.