Representation of stress and strain in granular materials using functions of direction

Abstract

AbstractThis paper proposes a new way of describing effective stress in granular materials, in which stress is represented by a continuous function of direction in physical space. The proposal provides a rigorous approach to the task of upscaling from particle mechanics to continuum mechanics, but is simplified compared to a full discrete element analysis. It leads to an alternative framework of stress–strain constitutive modelling of granular materials that in particular considers directional dependency. The continuous function also contains more information that the corresponding tensor, and thereby provides space for storing information about history and memory. A work-conjugate set of geometric rates representing strain-rates is calculated, and the fundamental principles of local action, determinism, frame indifference, and rigid transformation indifference are shown to apply. A new principle of freedom from tensor constraint is proposed. Existing thermo-mechanics of granular media is extended to apply for the proposed functions, and a new method is described by which strain-rate equations can be used in large-deformations modelling. The new features are illustrated and explored using simple linear elastic models, producing new results for Poisson’s ratio and elastic modulus. Ways of using the new framework to model elastoplasticity including critical states are also discussed.