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

On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation

“…Indeed, the only way for these models to avoid elastic gaps is to ignore higher-order dissipation. To the authors knowledge, there exist only two SGP models, proposed by Panteghini et al [12] and Jebahi and Forest [15], allowing for systematically avoiding elastic gaps while considering thermodynamically-consistent higher-order dissipation. However, these models substantially deviate from classical non-incremental SGP approaches.…”

“…As stated by Fleck et al [19], almost all non-incremental SGP theories including thermodynamically-consistent higher-order dissipation lead to elastic gaps under certain loading conditions. However, this phenomenon has never been observed elsewhere, neither experimentally nor numerically using other small scale methods [12,15,19]. Its physical reality is highly questioned and represents a source of uncertainty, preventing the development of robust SGP models capable of correctly predicting the size-dependent behavior of materials.…”

“…Pioneered by Aifantis [7], strain gradient plasticity (SGP) presents very promising capabilities to capture such effects. This theory has received a strong scientific interest in the last three decades and numerous SGP models have been developed for single-and poly-crystal structures [8,9,10,11,12,13,14,15].…”

“…However, this model cannot avoid elastic gaps under any non-proportional loading conditions, especially under conditions leading to gradient effects prior to the occurrence of the nonproportional loading source (e.g., non-proportional bending-passivation conditions which are discussed in the next section). To the authors knowledge, only two SGP models allowing for considering thermodynamicallyconsistent higher-order dissipation while systematically avoiding elastic gaps exist in the literature [12,15]. However, these models substantially deviate from classical Gurtin-type approaches.…”

Strain gradient plasticity based on saturating variables

“…For example, the use of the norm of the gradient plasticity tensor or dislocation density tensor leads to such an apparent instantaneous increase of the yield stress. The second approach introduces dissipative gradient contributions into the modelling approach Hua et al, 2021;Jebahi et al, 2020;Niordson and Tvergaard, 2019;Jebahi and Forest, 2023).…”