The emergence of large regions of nonbulk polymer might lower the energy barrier for some toughening mechanisms ( Zappalorto et al., 2012a). Furthermore, a large particle density reduces the load transfer from the matrix to the nanofillers by strain shielding ( Chen et al., 2008), affecting the overall mechanical response.Īnother issue to be carefully accounted for is the interfacial region surrounding the nanofiller, a zone of altered chemistry, chain mobility, degree of cure, and crystallinity, whose properties are not just a synergistic combination of those of each bulk constituent ( Zax et al., 2000 VanderHart et al., 2001 Ng et al., 2001 Odegard et al., 2005 Yu et al., 2009). A proper nanofiller distribution and dispersion is, indeed, essential to obtain high SSA, which would be compromised by the emergence of clusters that are potentially accountable for brittle response ( Becker et al., 2003). This task is made even more difficult by the reduced filler size that is, on one hand, the source of the extraordinary properties of nanocomposites, but is, on the other hand, responsible for their very complex behavior in terms of damaging and the main cause of tangling phenomena such as agglomeration, limiting their performances ( Fiedler et al., 2006 Wichmann et al., 2006a,b).
To this end, a different way of thinking is necessary with respect to that adopted for conventional composites, where micromechanics is used to address problems concerning two different characteristic lengths (microscale and macroscale) both described, within reason, by continuum mechanics. The successful application of nanocomposites requires the availability of predictive models able to include their hierarchical structure. Zappalorto, in Toughening Mechanisms in Composite Materials, 2015 4.5.1 Preliminary remarks However, their strength and potential will be referred to in an assessment of future developments for DEMs. As lattice models typically do not consider activation of new contacts following link fracture, they will not be discussed in the present context in more detail. Such a jointed particulate medium resembles developments in lattice models ( Schlangen and van Mier, 1992 Jirasek and Bazant, 1995 D’Addetta et al., 1999 Morizumi and Hirai, 1999 Schlangen and van Mier, 1991) very closely for heterogenous fracturing media.
Steady-state solutions are obtained through the dynamic relaxation (local or global damping, viscous, or kinetic). The solution algorithm remains usually an explicit time stepping scheme, i.e., the overall stiffness matrix is never assembled ( Lazarevic and Dvornik, 2001). Despite often very simple bond failure rules, bonded particulate assemblies have been shown to reproduce macroscopic manifestations of softening, dilation, and progressive fracturing. Bond failure is typically considered on the basis of limited strength, but some softening lattice models for quasi-brittle material have also considered a gradual reduction of strength, i.e., softening, before a complete breakage of the bond takes place ( Arslan et al., 2002). Typically two types of interparticle bonds are considered-a simple normal bond (or truss) and a parallel bond (or beam)-which can be seen as a microscopic representation of the Cosserat continuum.
Furthermore, bonded particle assemblies were also used to represent a solid material and the spring stiffness terms were derived on the basis of equivalent continuum strain energy and solid fracturing is realized through breakage of particle bonds.
Later DEM implementations considered particles bonded into clusters (to form more complex particle shapes). The particles were considered rigid with a “soft” contact, with normal and shear stiffness springs. 3.08.2.1 Particle Clusters and Assemblies, Fracturing of Assemblies of ParticlesĮarly discrete element modeling frameworks analyzed granular media-the movement and interaction of assemblies of circular two-dimensional (2D) or spherical (3D) particles.
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