Memory of jamming–multiscale models for soft and granular matter

Abstract

Soft, disordered, micro-structured materials are ubiquitous in nature and industry, and are different from ordinary fluids or solids, with unusual, interesting static and flow properties. The transition from fluid to solid-at the socalled jamming density-features a multitude of complex mechanisms, but there is no unified theoretical framework that explains them all. In this study, a simple yet quantitative and predictive model is presented, which allows for a changing jamming density, encompassing the memory of the deformation history and explaining a multitude of phenomena at and around jamming. The jamming density, now introduced as a new state-variable, changes due to the deformation history and relates the system's macroscopic response to its micro-structure. The packing efficiency can increase logarithmically slow under gentle repeated (isotropic) compression, leading to an increase of the jamming density. In contrast, shear deformations cause anisotropy, changing the packing efficiency exponentially fast with either dilatancy or compactancy as result. The memory of the system near jamming can be explained by a micro-statistical model that involves a multiscale, fractal energy landscape and links the microscopic particle picture to the macroscopic continuum description, providing a unified explanation for the qualitatively different flow-behavior for different deformation modes. To complement our work, a recipe to extract the history-dependent jamming density from experimentally accessible data is proposed, and alternative state-variables This article is part of the Topical Collection on Micro origins for macro behavior of granular matter. are compared. The proposed simple macroscopic constitutive model is calibrated from particles simulation data, with the variable jamming density-resembling the memory of microstructure-as essential novel ingredient. This approach can help understanding predicting and mitigating failure of structures or geophysical hazards, and will bring forward industrial process design and optimization, and help solving scientific challenges in fundamental research.

Effect of Particle Size and Cohesion on Powder Yielding and Flow

“…Interesting granular phenomena like yielding and jamming (Liu and Nagel, 1998;Bi et al, 2011;Luding, 2016;Kumar and Luding, 2016), dilatancy (Cates et al, 2005;Van Hecke, 2009;Yang et al, 2015), shear-band localization (Alshibi and Sture, 2000;Singh et al, 2014), history-dependence (Thakur et al, 2014), and anisotropy (Radjai et al, 1996;Majmudar and Behringer, 2005) have attracted significant scientific interest over the past decades (Savage and Hutter, 1989;Cundall, 1989;Radjai et al, 1999;Wolf et al, 2000;† GDR-MiDi, 2004;Tomas, 2005;Alonso-Marroquin and Herrmann, 2004;Luding 2005aLuding , b, 2008. Various laboratory element tests can be performed to study the bulk behaviour of granular materials (Schwedes, 2003).…”

Micro origins for macro behavior in granular media

“…A unified theoretical model that can provide reconciling explanations over various contradictory observations on jamming transitions is highly desirable but unavailable so far. Kumar and Luding [8] made a significant step forward in this direction. They proposed a simple, working model for the jamming transition and its history dependence, based on particle-scale observations, by incorporating the jamming density as a state variable, to link the macroscopic behavior of granular systems to their underpinning microstructures.…”

“…However, the prevailing purely phenomenological approaches have largely failed to attain this goal. Active attempts have recently been diverted to identify the key microstructures and micromechanisms that act as difference makers for the varied macroscopic responses under different loading conditions to be used in modern constitutive modeling [8,[14][15][16][17][18][19][20][21][22][23]. The signature of the microstructure of granular media under cyclic loads has been and still is an issue of particular interest.…”

A local view on the role of friction and shape

“…However, it is known that the actual volume fraction of a packing of uncompressed frictionless spheres will depend on the preparation history. For an extended discussion and further references see [28].…”

“…The exact value of φ g of a frictionless packing at zero pressure does depend on the preparation history [20,21,28,51]. However, the scaling laws of these packings are normally studied by preparing pressure free packings with a given protocol and then increasing φ g by compressing this packing [7,26].…”