The plastic behavior of materials has attracted research attention owing to their significant influence on general material performance. In the most existing literature, elastoplastic models have been formulated based on the independent relationship between the stress rate and the direction of the inelastic stretch. Despite being effective for describing the material behavior, this approach is not suitable for non-proportional loading paths with an abrupt change in loading direction. This may be further attributed to the normality rule brought about by not taking into consideration the component of the stress rate tangential resulting in an overestimation of the material stiffness. Thus, development of better alternative solutions to overcome these challenges is highly desirable.
Recently, Osaka University scientists: Professor Seiichiro Tsutsumi and Dr. Riccardo Fincato together with Dr. Hideto Momii from Nikken Engineering Cooperation presented an innovative technique for computing inelastic contributions generated in non-proportional loading paths. In particular, the effects of the tangential stress rate component were combined inside a return mapping formulation and its feasibility in eliminating the aforementioned challenge was investigated. The main objective was to correct the unrealistic material stiffness generated by elastoplastic models. The work is currently published in the research journal, Acta Mechanica.
The tangential plasticity was included in an implicit integration scheme to enhance the accuracy and computation speed, suitable for the investigation of structural problems. The assumption here was that the tangential inelastic stretch does not affect the material hardening. This enabled the use of a set of parameters depending on the stress state to calculate the tangential inelastic term and the elastoplastic stress rate using the return mapping algorithm.
The numerical technique allowed the computation of the co-rotational stress rate to determine the effects of the inelastic stretches along with the directions normal and tangential to the yield surface. From the analysis, the technique proved reliable for determining plastic strains with an associated flow rule in non-proportional loading conditions. On the other hand, in-plane strain plates scenarios, sudden changes in the loading conditions were observed to be the main contributing factor to tangential deformations. Also, the advantages of the return mapping algorithm in combination with tangential plasticity were carried out based on time sensitivity analysis. It resulted in a fast and accurate computation process as compared to the traditional methods.
To prove the concept, it was necessary to evaluate the load-carrying capacity of a steel bridge to evaluate the necessity and contributions of the introduced tangential plasticity in describing the structural response. Interestingly, the addition of tangential plasticity proved to be of great significance in obtaining the correct structural description. For instance, the presented model took into consideration the non-proportionality of the load thus improving the numerical capability for various analyses such as displacement curves.
In summary, the authors investigated the inelastic stretch of material subjected to non-proportional loading. With the application of the return mapping algorithm, different phenomenon involving a large number of loading and unloading cycles were demonstrated with high speed and improved accuracy. Furthermore, with the addition of the inelastic tangential stretch term to the computation technique, the study will pave the way for the investigation of different engineering problems.
Tsutsumi, S., Fincato, R., & Momii, H. (2019). Effect of tangential plasticity on structural response under non-proportional cyclic loading. Acta Mechanica, 230(7), 2425-2446.Go To Acta Mechanica