Abstract
The influence of particle shape on the mechanics of sand is widely recognized, especially in mineral processing and geomechanics. However, most existing continuum theories for engineering applications do not encompass the morphology of the grains and its evolution during comminution. Similarly, the relatively few engineering models accounting for grain-scale processes tend to idealize particles as spheres, with their diameters considered as the primary and sole geometric descriptor. This paper inspires a new generation of constitutive laws for crushable granular continua with arbitrary, yet evolving, particle morphology. We explore the idea of introducing multiple grain shape descriptors into Continuum Breakage Mechanics (CBM), a theory originally designed to track changes in particle size distributions during confined comminution. We incorporate the influence of these descriptors on the elastic strain energy potential and treat them as dissipative state variables. In analogy with the original CBM, and in light of evidence from extreme fragmentation in nature, the evolution of the additional shape descriptors is postulated to converge towards an attractor. Comparisons with laboratory experiments, discrete element analyses and particle-scale fracture models illustrate the encouraging performance of the theory. The theory provides insights into the feedback among particle shape, compressive yielding and inelastic deformation in crushable granular continua. These results inspire new questions that should guide future research into crushable granular systems using particle-scale imaging and computations.
Highlights
The significance of particle shape in geosciences, geotechnology and mineral processing is widely recognized [1,2]
We propose a new constitutive theory for crushable granular materials that captures the effect of initial non-spherical particle shapes on both elastic deformation and yielding, as well as the evolution of the shape of the particles upon compression
By including grain shape descriptors other than the grain size into Continuum Breakage Mechanics (CBM), this paper offers a platform to inspect the implications of one of the most common, yet seldom tested, simplifications of granular mechanics models: the representation of particles as spherical bodies
Summary
The significance of particle shape in geosciences, geotechnology and mineral processing is widely recognized [1,2]. Their analysis showed that as grains are less spherical, the rate of increase of their normalized small strain shear stiffness with pressure is intensified Such seemingly conflicting findings are rooted in the experimental difficulty of isolating the influence of the particle shape, which without proper data treatment may be overshadowed by concurrent effects due to different initial packing, fabric and size polydispersity. We argue that the most significant obstacle hindering the interpretation of measurements involving different particle shapes is the lack of a rigorous framework explaining why a departure from perfect particle sphericity influences the storage of elastic strain energy and its subsequent release upon grain crushing To fill this gap, we propose a new constitutive theory for crushable granular materials that captures the effect of initial non-spherical particle shapes on both elastic deformation and yielding, as well as the evolution of the shape of the particles upon compression. We will further consider the effects and evolution of this class of irregularities upon successive grain fracture events
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