Construction of new enriched beam models accounting for cross-section deformation and pinching

Abstract

The consideration of nonclassical beam theories beyond Timoshenko beam model is necessary in applications involving complex yarns subjected to transverse compaction, for which the section dilatation and in-plane shear require a detailed kinematic and static modeling. In the present work, new enriched beam elements with additional degrees of freedom are derived from the mechanics of generalized continua, allowing a representation of the in plane-shear and dilatation of sections. As a novel aspect, enriched beam model called macrodilatation, macroshear, and macrostrain have been constructed on the basis of generalized beam theories but with a more condensed kinematics, assuming uniform hyperstress tensor within the beam. The choice of the adequate extended continuum for a given beam depends on its macroscopic deformation mechanisms. As a result, the developed beam models include modified material parameters (the tensile, shear and bulk moduli for an isotropic beam) involving additional microstructural parameters. These macrobeam models are expected to better describe the in plane-shear and dilatation of the beam sections along its mean line in comparison to classical beam theories. Numerical illustrative examples show that the microdilatation beam model has the ability to capture the local deformation field around holes, in contrast to Timoshenko beam model. The parameters of the microdilatation beam model provide a very good estimate of the overall porosity.