When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressure is applied to these aggregates, they densify by particle rearrangement. Here we introduce experimental and computational results suggesting that densification by particle rearrangement occurs in the form of a phase transition between two configurational phases of the aggregate. Then we show that the energy landscape associated with particle rearrangement is nonconvex and therefore consistent with our interpretation of the experimental and computational results. Our conclusions are relevant to many technological processes and natural phenomena. DOI: 10.1103/PhysRevLett.88.204302 PACS numbers: 45.70.Cc Cohesive granular materials have been the focus of only a small fraction of recent research into the granular state [1]. Yet cohesive granular materials will surely draw increasing attention from scientists and engineers, if only because they are used in numerous applications. One conspicuous application is the forming of ceramic parts, powder metallurgy components, and pharmaceutical tablets by compaction of fine powders [2]. The cohesiveness of powders stems from the large surface-to-volume ratio of their particles, which enhances the effect of attractive van der Waals forces among the particles. In other applications (e.g., the stabilization of soils), the cohesiveness is due to the presence of liquid menisci among the particles. Our interest in the densification of cohesive granular materials was prompted by the recent compaction study of Kong and Lannutti [3]. These authors used x-ray tomography to document the evolution of density during the static compaction of alumina powders (of particle diameter ϳ60 mm). By "static compaction" we mean that the densification was effected by slowly applying pressure, without shaking. (There exists an important body of work on compaction by shaking, for the most part on noncohesive granular materials [4][5][6].) Kong and Lannutti reached the tantalizing conclusion that densification "seems to proceed as a wave initiated at the advancing ram" [3]. Our aim here is to elucidate the nature of this 'wave,' and to relate its behavior to the micromechanics of densification in cohesive granular aggregates.When, preceding compaction, a cohesive granular material is poured into a container, the mobility of the particles reaching the bottom of the container is hindered by the cohesive forces (Fig. 1a). As a result, a low-density, open aggregate of particles is established inside the container (Fig. 1b). Open aggregates densify by particle rearrangement at relatively low pressure [7]. It has been proposed [8] that particle rearrangement occurs when the rings of particles of the open aggregate collapse by snap-through buckling (Figs. 1c-1e). To investigate this phenomenon we prepared a quasi-two-dimensional open aggregate [9] by filling a narrow Plexiglas container (of thickness ϳ1.9 mm) with monosized glass beads (of diameter ϳ1.7 mm). Before pouring the beads into the c...
In this article we present a formulation to account for the effect of cell size distribution on the mechanical behavior of foams. The present approach averages the response of unit cells with different sizes via a Taylor averaging approach. This technique can be applied to different unit cell models where the cell size is explicitly given. In order to keep the averaging formulation analytically traceable, we select a unit cell model, bubble model (Ortiz, M., Gioia, G. and Cuitino,A.M. Manuscript in preparation), that considers the behavior of an homogeneous array of thin-walled spherical cells undergoing uniform finite deformation. This model relays on the computation of the strain energy density for the deformed configuration due to membrane stretching and bending. For this unit cell model, the effect of the cell size distribution is described only by the first three moments of the distribution, or the mean radius, variance and skeweness. The effect of these parameters on the foam behavior subjected to uniaxial compression is analyzed for two different values of the relative density of the foam. The model is compared against a unixial compression test of a ductile foam system with nearly spherical cells of different sizes. The cell size distribution is measured independenly and introduced to the model as a input. The prediction of load displacement response is in general good agreement with the experimental test.
In order to quantitatively evaluate the effect of partial debonding on the reduction of overall elastic moduli and overall elastoplastic strength of a fiber-reinforced composite, a combined homogenization and finite-element study is carried out to examine how the debonding angle affects these mechanical properties. In the development of the elastichomogenization theory, the relative strain concentration tensors of the interfacial cracks and fibers with respect to that of the matrix are first determined from Toya’s complex-variable solution [Toya, M. (1974). A Crack Along the Interface of a Circular Inclusion Embedded in an Infinite Solid, J. Mech. Phys. Solids., 22: 325–348.], and then the fibers, cracks, and matrix are assembled together to form the composite. Extension of the elastic formulation to the nonlinear elastoplastic behavior is accomplished through a secant-moduli approach in conjunction with a field-fluctuation method. The developed theory is intended primarily for conditions with low fiber concentration. The finite-element method makes use of the ANSYS program with a carefully constructed mesh near the crack tips. Both the homogenization and the finite-element calculations disclose significant effect of the debonding angle on the overall transverse Young’s modulus along the debonding direction, and on the plane-strain tensile bulk modulus of the composite. In the plastic range the transverse tensile stress–strain curves of the debonded composite are found to be significantly lowered due to the presence of the interfacial cracks.
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