Abstract
This work addresses the determination of yield surfaces for geometrically exact elastoplastic rods. Use is made of a formulation where the rod is subjected to an uniform strain field along its arc length, thereby reducing the elastoplastic problem of the full rod to just its cross-section. By integrating the plastic work and the stresses over the rod’s cross-section, one then obtains discrete points of the yield surface in terms of stress resultants. Eventually, Lamé curves in their most general form are fitted to the discrete points by an appropriate optimisation method. The resulting continuous yield surfaces are examined for their scalability with respect to cross-section dimensions and also compared with existing analytical forms of yield surfaces.
Highlights
The theory of geometrically exact rods and its implementation have been applied in a wide range of research fields to model slender structures whose dimension in one direction is dominant compared to the other two dimensions
A framework to obtain a yield surface in terms of stress resultants has been presented with the objective to model geometrically exact elastoplastic rods
Smooth analytic functions are fitted to the discrete yield surface
Summary
The theory of geometrically exact rods and its implementation have been applied in a wide range of research fields to model slender structures whose dimension in one direction is dominant compared to the other two dimensions. In contrast to classical beam theories such as the Euler-Bernoulli and Timoshenko beam theories, the theory of geometrically exact rods is not restricted to the geometrically linear case, but is able to describe large deformation as well as large rotation of the rod’s cross-section. The concept of modelling large rotation in slender structures goes back to the Cosserat brothers [5] They consider every material point of the rod to be connected to the centerline and a triad of orthonormal vectors characterizing the orientation of the rod’s cross-section [6]. All numerical simulations carried out to achive the results shown in this contribution base on the open source finiteelement library deal.II [22]
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