Scalar-based strain gradient plasticity theory to model size-dependent kinematic hardening effects

Abstract

A common belief in phenomenological strain gradient plasticity modeling is that including the gradient of scalar variables in the constitutive setting leads to size-dependent isotropic hardening, whereas the gradient of second-order tensors induces size-dependent kinematic hardening. The present paper shows that it is also possible to produce size-dependent kinematic hardening using scalar-based gradient theory. For this purpose, a new model involving the gradient of the equivalent plastic strain is developed and compared with two reference scalar-based and tensor-based theories. Theoretical investigations using simple monotonic loading conditions are first presented to assess the ability of the proposed model to solve some issues related to existing scalar-based gradient theories. Simulations under cyclic loading conditions are then provided to investigate the nature of the resulting hardening. These simulations show that the proposed model is capable of producing size-dependent kinematic hardening effects at more affordable costs, compared to existing tensor-based strain gradient plasticity theories. Keywords Strain gradient plasticity • Size effects • Size-dependent isotropic hardening • Size-dependent kinematic hardening • Equivalent plastic strain • Cumulative plastic strain 1 Introduction The size-dependent responses of metallic materials have been observed in numerous small-scale experiments typically ranging in size from a few hundreds of nanometers to a few tens of micrometers (Hayashi et al.

Modeling size effects in microwire torsion: A comparison between a Lagrange multiplier-based and aCurlFpgradient crystal plasticity model

“…Another possibility is to consider the gradient of the equivalent plastic strain instead of the cumulative one. This will cause size-dependent kinematic hardening effects, as recently demonstrated by Jebahi and Forest (2021).…”

“…For instance, in the reduced-order micromorphic model, cumulative plastic slip is an always increasing variable irrespective of the loading direction, leading to size-dependent isotropic hardening. Jebahi and Forest (2021) recently showed that size-dependent kinematic hardening can be predicted in scalarbased strain gradient models by accounting for the gradient of the equivalent plastic strain which does not increase monotonically.…”

An alternative way to describe thermodynamically-consistent higher-order dissipation within strain gradient plasticity

“…Results of subsection 4.1 are obtained assuming quadratic defect energy. Although widely used in the literature (Gurtin, 2002(Gurtin, , 2004Gurtin et al, 2007;Bardella, 2016, 2018;Jebahi and Forest, 2021), the pertinence of this form of defect energy in the context of gradient-enhanced plasticity is questioned by several authors (Svendsen and Bargmann, 2010;Cordero et al, 2010;Forest and Guéninchault, 2013;. The present subsection aims at investigating the effects of the proposed plastic slip gradient decomposition using less-than-quadratic defect energy (i.e., less-than-two defect energy index n).…”

“…Although offering a simplified modeling framework, these models can yield likely unacceptable behaviors with pathological mesh dependence for some problems (Niordson and Hutchinson, 2003). Higher-order SGP approaches substantially deviate from conventional plasticity by considering new higher-order stresses and additional equilibrium and boundary conditions (Fleck and Hutchinson, 1997;Aifantis, 1999;Gurtin, 2002Gurtin, , 2004Gurtin et al, 2007;Forest and Aifantis, 2010;Bardella, 2010;Forest and Bertram, 2011;Anand et al, 2012;Cordero et al, 2016;Forest, 2020;El-Naaman et al, 2019;Jebahi et al, 2020;Jebahi and Forest, 2021;Cai et al, 2021). It is nowadays widely accepted that higher-order SGP theories offer powerful modeling capabilities, making them the most commonly used in the literature.…”

A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method

“…Generalized mechanics has been widely investigated in the literature. It has been implemented for problems of elasticity [9][10][11][12][13]; plasticity [14][15][16][17][18][19]; damage modeling [20][21][22][23][24][25]; modeling metamaterials [26][27][28] such as pantographic structures [29][30][31], network materials [32], viscoelastic truss structures [33], bipantographic structures [34], second gradient fluids [35]; gradient-enhanced homogenization [36][37][38][39]; micropolar continua [40]; fracture mechanics [41]; biomechanics [42][43][44]; and anisotropic systems [45]. Parameter determination of generalized mechanics models has been studied for static and dynamic regimes in Shekarchizadeh et al [46,47], respectively.…”