Assessment of isotropic large-deformation elastoplasticity models with Lode angle dependence

Andrea Panteghini

Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, Via Branze, 43 25123, Brescia, Italy

M.B. Rubin

Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel

Lorenzo Bardella

Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, Via Branze, 43 25123, Brescia, Italy

Abstract

This study aims at assessing formulations of large-deformation elastoplasticity dependent on the Lode angle. The focus is both on the accuracy of the predictions and on the computational efficiency. Although the analysis is limited to isotropic response and isochoric plastic deformation, the proposed assessment has required the extension of an Eulerian model relying on the left Cauchy-Green elastic strain, to include the influence of the Lode angle in the plastic rate tensor. Also, the computational algorithm for more commonly implemented models, derived by assuming the Bilby-Kroner-Lee multiplicative form of the deformation gradient and adopting the logarithmic strain measure, has been significantly improved by using a relatively accurate approximate derivative of the logarithmic strain. While the models implemented in this study assume hyperelasto-plastic behavior, the assessment also includes the hypoelastoplastic model available in the commercial finite element code Abaqus. For all the specified constitutive equations, some numerical algorithms for small-deformation elastoplasticity can be used for finite deformations. Conclusions are drawn on the basis of some analysis and three benchmark problems, i.e. plane-strain cyclic shearing of a square block, necking of a circular cylindrical bar, and drawing of a bar with a rectangular cross-section. All these problems consider both von Mises plasticity and Tresca plasticity, the latter leading to significant differences among the models in terms of the Lode angle, mostly under plane-strain conditions. The main result is that the considered models overall provide similar engineering responses, but the numerical efficiency of the Eulerian model relying on the left Cauchy-Green elastic strain and the ease of its implementation have advantages over the other models.

Author Keywords: Lode angle; large deformations; Eulerian constitutive equations; isotropic elastoplasticity; Finite Element Method