A through-thickness damage regularisation scheme for shell elements subjected to severe bending and membrane deformations

Abstract

This research work proposes and validates a damage regularisation model for shell elements used in large-scale simulations. The model evaluates the ratio of bending to membrane loading in the elements based on the through-thickness gradient of the through-thickness plastic strain. The Cockcroft-Latham failure criterion is adopted, whose parameters are modified according to the length-to-thickness ratio of the shell elements in order to reduce the mesh dependency. This regularisation scheme is validated against experimental component tests on a double-chamber profile in an AA6005-T6 recrystallised aluminium alloy under quasi-static and impact loading conditions. The results show that the model is able to accurately predict fracture initiation under all tested conditions.

Energy Absorption of Aluminium Extrusions Filled with Cellular Materials Under Axial Crushing: Study of the Interaction Effect

“…The parameter W c was obtained from the inverse model of the tensile tests with a refined mesh of solid elements. Despite its simplicity, this damage model successfully predicted damage in a variety of different loading scenarios and aluminium manufacturing routes such as extruded profiles [35], die-cast alloys [36], or additive manufactured aluminium parts [37]. During axial crushing, the walls of the extrusion are subjected to a combination of membrane and bending loads.…”

Emerging Challenges for Numerical Simulations of Quasi-Static Collision Experiments on Laser-Welded Thin-Walled Steel Structures

“…These observations have a significant impact on the modeling of the stress-strain curves in the Finite Element simulations, as the models must incorporate changes in plastic, monotonically increasing part of the stress-strain curve as well as the softening part. In addition, as the experiments are based purely on membrane state instead of bending, the applicability of the material behavior in general becomes an open question in cases where the structural members of the panels are exposed to a significant amount of bending (see for example Woelke et al 2018;Costas et al, 2019). This case rises in sandwich panel type of closed structures where the unit cells are exposed to warping .…”

“…The most commonly used models are based on the 3D geometry of the structure made from shell and weld elements (Ehlers et al 2012;Werner et al (2014Werner et al ( , 2015) and in some cases the computationally intensive but very accurate models made from solid elements on component level (see Figure 1A). For thin-walled structures, the shell elements are most common as they assume certain throughthickness behavior in terms of displacement and strains and use the non-linear constitutive expressions to compute the stresses and stress resultants (e.g., Woelke et al 2013;Costas et al, 2019). These stress resultants (internal forces) balance with the external loading caused by structural deformations.…”

“…This plane stress assumption means that the element cannot model through-thickness normal stress explicitly. In collision and grounding simulations, this through-thickness normal stress component is important from two perspectives (e.g., Costas et al, 2019). Firstly, during crushing and severe bending, the plate element exhibits high through-thickness stress at the contact side while at the tensile side this stress is close to zero due to lack of contact.…”

“…Thus, to understand the strain and stress development in large structures, experiments are needed that characterize the failure process in detail so that the FE analysis gets information on the acceptable level of idealization on both in strains and stresses through the thickness of elements. Furthermore, the experiments should include both membrane and bending actions (e.g., Woelke et al 2013;Costas et al, 2019). As stresses are impossible to measure in such situations, hybrid methods would be needed where experiments (determination of strains) are complemented with numerical simulations (computation of stresses based on measured strains).…”