Isotropic hardening in micropolar plasticity

Abstract

Experimental evidence for length scale effects in plasticity has been provided, e.g., by Fleck et al. (Acta Metall. Mater. 42:475-487, 1994). Results from torsional loadings on copper wires, when appropriately displayed, indicated that, for the same shear at the outer radius, the normalized torque increased with decreasing specimen radius. Modeling of the constitutive behavior in the framework of micropolar plasticity is a possibility to account for length scale effects. The present paper is concerned with this possibility and deals with the theory developed by Grammenoudis and Tsakmakis (Contin. ). Both isotropic and kinematic hardening are present in that theory, with isotropic hardening being captured in a unified manner. Here, we discuss isotropic hardening composed of two parts, responsible for strain and gradient effects, respectively.

On the torsion of isotropic elastoplastic Cosserat circular cylinders

“…Depending on the yield criterion used, the different contributions to the total torque can display a saturation with respect to the twist angle. Further numerical investigations of the response of Cosserat bars subjected to torsion should be performed in more general cases, including non-cylindrical bars [Drugan and Lakes, 2018], anisotropic elasticity [Taliercio and Veber, 2016], finite deformation as well as the incorporation of kinematic and isotropic hardening [Grammenoudis and Tsakmakis, 2009]. The main difficulty will consist in delineating the influence of each aspect of the model on the predicted size effects.…”

“…This is illustrated in figure 10. This figure shows the total torque as well as its different contributions normalized by R 3 as functions of the shear strain at the outer radius, as classically done in other works [Fleck et al, 1994;Grammenoudis and Tsakmakis, 2009] for both analytical and FEM solutions. Although no hardening is present in the model, an apparent hardening is visible on this curve.…”

Micromorphic continuum. Part III

“…have been elaborated by Grammenoudis and Tsakmakis (2008) in micropolar plasticity and are not pursuit here.…”

Integral and differential nonlocal micromorphic theory

“…The reader is referred to Eringen (1999Eringen ( , 2001 for more details on the micropolar and micromorphic continua. The successful applications of MPT and MMT to different fields have been reported by several researchers up to now (de Borst, 1991;Forest and Sievert, 2003;Dillard et al, 2006;Bigoni and Drugan, 2007;Grammenoudis and Tsakmakis, 2009;Zhang et al, 2018;Yoder et al, 2018;Eremeyev, 2018;Shaat, 2018;Polizzotto, 2018). For instance, Yoder et al (2018) considered the discrete beam element model and micropolar elasticity to capture the size-effects in thin-walled lattice structures.…”