Identification of jamming transition: a critical appraisal
- PDF / 4,440,913 Bytes
- 17 Pages / 595.276 x 790.866 pts Page_size
- 102 Downloads / 259 Views
ORIGINAL PAPER
Identification of jamming transition: a critical appraisal Mingze Xu1,2 · Zixin Zhang1,2 · Xin Huang1,2 Received: 6 March 2020 / Accepted: 1 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A variety of approaches have been proposed to determine the onset of jamming (unjamming) transition for granular medium. However, these approaches all have their own limitations. In this study, the applicability of the existing approaches in identifying the jamming (unjamming) transition instant is evaluated based on the discrete element method simulations on both frictionless and frictional specimens subjected to different loading protocols which lead to isotropic jamming, shear jamming and shear unjamming. A new approach based on Hill’s criterion of failure is proposed, which defines the transition of second order work from positive to negative as the onset of jamming (unjamming) transition. The jamming (unjamming) transition instant determined from the new approach is compared with those determined from some classic approaches. It is found that the second order work-based approach not only locates the critical solid fraction in the jamming diagram consistent with other approaches, but is also able to identify the onset of jamming (unjamming) transition for loading protocols that are difficult to be assessed by the existing approaches. This more robust approach is useful for the study of jamming phenomena under a broader types of loading protocols, and can be further employed to derive the jamming diagram of real materials. Keywords Jamming transition · Critical solid fraction · Second order work
1 Introduction Jamming is defined as a state that a particulate system can sustain external forces without deforming irreversibly [1]. When subject to infinitesimal external perturbations, such as temperature change or shear, a particulate system may flow like liquid in the unjamming state but will behave closely to solid once the jamming (unjamming) transition state has been reached. It is non-trivial to macroscopically ascertain whether a particulate system is jammed; therefore, the jamming state is deemed to be reached when the number of mechanical equilibrium constraints reaches the number of degrees of freedom, i.e., the system becomes isostatic [1]. Necessary conditions characterizing a jammed state include This article is part of the Topical Collection: Flow regimes and phase transitions in granular matter: multiscale modeling from micromechanics to continuum. * Xin Huang [email protected] 1
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
State Key Laboratory of Geotechnical and Underground Engineering, Tongji University, Shanghai 200092, China
2
non-zero mean stress, shear stress and ability to sustain small incremental stress. The transition from the unjammed state to the jammed state is generally referred to as jamming (unjamming) transition. It is a characteristic state distinguishing a solid phase from a liquid phase. Jammi
Data Loading...
