Entropy and Material Instability in the Quasi-Static Mechanics of Granular Media

Abstract

SummaryStarting from a maximum-entropy model of granular statics, this brief note explores a possible material instability in the form of a "stress localization" anticipated in previous work (Goddard, 2002). After a brief review of the maximum-entropy model, it is shown that a special case allows for nonconvex pressure-volume response of a kind that could lead to heterogeneous stress states in an isotropically compressed granular packing.

The Mechanical Strength of Granular Sulphur and its Relation to Size Distribution and Storage Silo Clogging

“…Both the granules' surface energy and the amount of energy they store are in proportion to their surface area, which may explain their motion and storage behavior in the system. This is in close conformity with Griffith's fracture tensile strength for brittle materials, indicating that sulphur solidification is an isotropic hardening process [5].…”

Genesis of the multiscale approach for materials with microstructure

“…From a more general point of view, this apprach could allow one to properly account for symmetry-induced instabilities describing important features related to re-arrangements of the material microstructure, such as a symmetrybreaking phase transition [51,94], a defect-induced damage [95] or other material instabilities [96]. Molecular modeling combined with statistical-mechanics-based approaches, proves to be very suitable for providing the constitutive support that higher order theories and the theories of multifield continua needed for engineering applications.…”