The elastic properties of dilute solid suspensions with imperfect interfacial bonding: asymptotic expansions, variational approximations, full-field simulations

M. I. IDIART; V. M. GALLICAN; M. ZECEVIC; R. A. LEBENSOHN

Minneapolis

Conferencia; 2023 SES Annual Technical Meeting; 2023

Deformation processes occurring at interfaces and their vicinities can play a prominent role in the mechanical performance of microstructured solids. Illustrative examples include particle-matrix decohesion in reinforced composites, viscoelastic relaxation in plastic-bonded granular materials, and grain boundary sliding in polycrystalline aggregates. When acting as sites for localized deformation these regions are often idealized as imperfectly bonded sharp interfaces requiring continuity of tractions but permitting discontinuity of displacements. Mean-field descriptions for the macroscopic constitutive behavior are then generated by means of homogenization procedures that can be brought to bear on problems with jumps of the microscopic displacement field. Central to the confection of these mean-field descriptions are fundamental results for dilute solid suspensions with elementary microgeometries and compliant interfacial bonding exhibiting linearly elastic behavior. This talk will present simple variational approximations for suspensions of spherical particles. Two approximations are considered which display the exact same format but differ in the way the interfacial compliance is averaged over the interfaces: the first approximation depends on an `arithmetic' mean while the second approximation depends on a `harmonic' mean. The approximations are then confronted to exact asymptotic expansions and full-field numerical simulations for assessment. The expansions are performed for suspensions with weakly and strongly imperfect interfaces. Simulations are performed by means of a Fast Fourier Transform algorithm suitably implemented to handle suspensions with imperfect interfaces. Also included in the comparisons are available results for suspensions with extremely anisotropic bondings. Overall, the `harmonic' approximation is found to be much more precise than the `arithmetic' approximation. The finding is of practical relevance given the widespread use of `arithmetic' approximations in existing descriptions based on modified Eshelby tensors.