A kinematically exact reduced order model for fracture in thin-walled members

Abstract

Kinematically exact rod models have the capability of detecting critical loads and can reach post-critical paths. However, due to the kinematical assumptions imposed to the displacements field, issues are bound to emerge when local effects are relevant. Instead of enriching the allowed deformation, one can employ multiscale modelling to generate constitutive relationship among the different strain and stress measures already containing information about plasticity, loss of geometrical stiffness, local buckling and even fracture conditions, with no or little increase of the number of degrees of freedom. The yielding behaviour can be handled as a plastic with hardening-softening constitutive equation. The trade-off of such approach is the need of the higher order models, which can lead to a costly preparation phase. Also, due to the plasticity, discontinuities are expected, due to the formation of fractures such as plastic hinges. For problems that contemplate strong discontinuities, the embedded discontinuities FEM (ED-FEM) is an ideal match, allowing a local treatment of said discontinuities. This method introduces incompatible modes that have only effects inside the containing element, enriching its kinematics. Each iteration is computationally solved by means of a split operator, in which a Newton's method step is performed with the usual DOFs (local variables related to the discontinuity are statically condensed), and them the local variables are solved in an element-wise fashion. This procedure little increases the global system number of DOFs, despite losing quadratic convergence for the complete procedure. The aim of this work is to profit from the ED-FEM framework and multiscale modelling to implement a 7-DOF kinematically exact rod reduced order model for thin-walled members with a plastic with hardening/softening material. It will be implemented in an in-house finite element program for flexible structures and validated against reference solutions.