Valentin Gallican (Univ. La Plata, Argentine) Variational estimates for the elastic properties of dilute solid suspensions with imperfect interfacial bonding

While relatively scarce in terms of volume fraction, the binding phase strongly impacts the overall thermomechanical behavior of bonded granular solids. Because of irreversible phenomena such as viscous deformations, the damage evolution mostly occurs within that phase as a result of the granular morphology and local thermomechanical contrast. When the intergrain spacing is much smaller than the grain size, the binding phase can be regarded as an interphase of vanishing thickness while aggregates can be seen as microstructured solids with imperfect intergranular bonding exhibiting hereditary behavior. A  rst step towards the description of such material systems can be the prediction of the macroscopic response of dilute solid suspensions with imperfect interfacial bonding exhibiting linearly elastic behavior. Various models have been proposed in the literature to generate such results with varying degrees of generality and rigor. The purpose of the present work is the derivation of two estimates from variational theorems allowing us to reproduce exact results for weakly anisotropic but otherwise arbitrarily large interface compliances, that will easily accommodate interfacial dissipative processes for more challenging constitutive laws. Although similar, the variational estimates di er through the way the elastic properties of the interface are averaged. They both allow arbitrary elastic anisotropy of the constitutive phases but are restricted to spherical geometry of the suspensions. Comparisons are made to evaluate the accuracy of these estimates with exact results available for sliding inclusions and FFT full- eld computations in the case of arbitrarily anisotropic interfaces.

Keywords: Elasticity, Imperfect interface, Composite materials, FFT.