Behavior of a net of fibers linked by viscous interactions: theory and mechanical properties

Abstract

International audienceThis paper presents an investigation of the macroscopic mechanical behavior of highly concentrated fiber suspensions for which the mechanical behavior is governed by local fiber-fiber interactions. The problem is approached by considering the case of a net of rigid fibers of uniform length, linked by viscous point interactions of power-law type. Those interactions may result in local forces and moments located at the contacting point between two fibers, and respectively power-law functions of the local linear and angular velocity at this point. Assuming the existence of an elementary representative volume which size is small compared to the size of the whole structure, the fiber net is regarded as a periodic assembly of identical cells. Macroscopic equilibrium and constitutive equations of the equivalent continuum are then obtained by the discrete and periodic media homogenization method, based on the use of asymptotic expansions. Depending on the order of magnitude of local translational viscosities and rotational viscosities, three types of the equivalent continua are proved to be possible. One of them leads to an effective Cosserat medium, the other ones being usual Cauchy media. Lastly, formulations that enable an effective computation of constitutive equations are detailed. They show that the equivalent continuum behaves like an anisotropic power-law fluid

Dynamics of discrete framed structures: a unified homogenized description

“…Asymptotic homogenization methods [Sánchez-Palencia 1980] have been developed for homogeneous and periodic beams [Trabucho and Viaño 1996;Buannic and Cartraud 2001a;2001b], for periodic discrete structures [Bakhvalov and Panasenko 1989;Caillerie et al 1989], and in parallel with the homogenization of periodic media with multiple parameters and scale changes [Cioranescu and Saint Jean Paulin 1999]. Amongst the applications of homogenization of periodic discrete media (HPDM) we mention the papers [Tollenaere 1994;Moreau and Caillerie 1998;Boutin and Hans 2003], dealing respectively with the statics, buckling and dynamics of trusses; [Pradel and Sab 1998], on the constitutive laws of foams; and [Le Corre et al 2004], involving fluid mechanics.…”

Towards the simulation of mould filling with polymer composites reinforced with mineral fillers and short fibres

“…However, it is not able to relate finely the BMC's rheology with their microstructures. Based on an experimental analysis of flow-induced microstructures, such a model could be in future replaced by more sophisticated rheological models dedicated to these types of fibre suspensions [4,24,32,33,38,51,52,56,58]. -This phenomenological model was implemented into a FE code dedicated to the compression of compounds [19].…”

“…These studies were the basis to establish or validate rheological models that can be used to simulate the forming processes of these composites (e.g. [4,16,32,33,37,49,52,56,58]). …”

Kinetic Theory Microstructure Modeling in Concentrated Suspensions

“…The contact law is assumed viscous, and its intensity is modified for ranging from deformable to rigid clusters. For additional details on the direct simulation at the microscopic scale (at the scale of the rods), the interested readers can refer to [8,26,27] and the references therein. Figure 3 depicts the initial isotropic configuration, where the yellow points represent the contact points at which different rods interact.…”

“…At the macroscopic scale, one could try to fit some power-law constitutive equation; however, this description does not allow one to describe the microstructure. At the microscopic scale, direct numerical simulations describing complex fiber-fiber interactions can be carried out in small enough representative volumes [26,27]. A natural candidate to be a reasonable compromise between (fine) micro and (fast) macro descriptions consists of considering, again, a kinetic theory description.…”