Overall Mechanical Response of Soft Composite Materials with Particulate Microstructure at Finite Strains
Many soft, composite materials manufactured or found in nature consist of a homogeneous matrix phase and a random distribution of micron-sized particles in the matrix. Examples among engineering materials include reinforced elastomers, microgel suspensions and polymer-matrix composites, whereas biological tissues and fluids, such as intervertebral disc and blood, provide examples of natural materials. In this thesis, we present homogenization-based models for the overall constitutive behavior of such composite materials when subjected to mechanical loadings. These models account for the constitutive nonlinearities associated with the local behavior of the matrix and particle phases, as well as for the nonlinearities associated with possible evolution of the microstructure. In this thesis, we present models for three different classes of particulate composite materials. In the first part of this thesis, we propose a new model for the overall constitutive behavior of particle-reinforced elastomers when subjected to three-dimensional, large deformations. A key advantage of this model is that it incorporates the change in the orientation of rigid particles as the deformation proceeds, and therefore also incorporates the major influence of such changes on the development of material instabilities in the composites. We consider the application of this model to composites consisting of incompressible elastomers reinforced by aligned, spheroidal particles, undergoing non-aligned loadings. In the second part of this work, we present a homogenization-based model for the rheological behavior of suspensions of soft viscoelastic particles in Newtonian fluids as well as in yield stress fluids under uniform, Stokes flow conditions. We investigate the effects of the shape dynamics and constitutive properties of the fluid and particle phases on the macroscopic rheological behavior of the suspensions. In the last part of this work, we present a model to estimate the effective behavior of particulate composites consisting of elasto-viscoplastic matrices and elastic, spheroidal particles, subjected to small strains. Here, we explore the effect of the local properties and loading conditions on the effective behavior and field statistics in these composites for the case of elastic-ideally plastic matrices.