Geometrically exact elastoplastic rods: determination of yield surface in terms of stress resultants

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.

Homogenization of fully nonlinear rod lattice structures: on the size of the RVE and micro structural instabilities

“…The resulting stiffness is a function of the strain prescriptors. The framework allows for the use of arbitrary hyperelastic constitutive models on the cross-sectional level and is extended to the inelastic case in Herrnböck et al [32]. In the contribution at hand the elastic tangent stiffness matrix is assumed to be constant.…”

“…Here Φ describes a yield-function in terms of stress resultants. A framework to obtain such a function, is comprehensively presented in Herrnböck et al [32].…”

“…This presentation begins with the kinematics followed by the stress resultants and the balance equations for linear and angular momentum. The derivations presented in this sections are based on those in [27,32] and the references therein.…”

“…Yield-functions have been derived for different rod crosssections in [28][29][30][31] by applying the upper and lower bound techniques of limit analysis in which the rod's cross-section is assumed to be fully plastified at the yield-limit. An approach where yield is not defined in terms of plastification but in terms of dissipated work has recently been formulated in Herrnböck et al [32]. The method presented there is generic in terms of the rod's cross-sectional shape and underlying constitutive model.…”

“…Before setting the stage by recalling the theory of geometrically exact rods the nomenclature used throughout this contribution is introduced. As in Herrnböck et al [32] strain measures and their energetic conjugates are denoted differently in the context of three-dimensional continuum mechanics and geometrically exact rods. The different terminology is summarized in Table 1.…”