Proximity Effects in Matrix-Inclusion Composites: Elastic Effective Behavior, Phase Moments, and Full-Field Computational Analysis

Louis Belgrand, Isabelle Ramière (), Rodrigue Largenton and Frédéric Lebon
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Louis Belgrand: CEA, DES, IRESNE, DEC, SESC, LSC, Cadarache, F-13108 Saint-Paul-Lez Durance, France
Isabelle Ramière: CEA, DES, IRESNE, DEC, SESC, LSC, Cadarache, F-13108 Saint-Paul-Lez Durance, France
Rodrigue Largenton: EDF R&D, Département Matériaux et Mécanique des Composants, Cadarache, F-13108 Saint-Paul-Lez Durance, France
Frédéric Lebon: Aix-Marseille Université, CNRS, Centrale Marseille, LMA, CEDEX 13, F-13453 Marseille, France

Mathematics, 2022, vol. 10, issue 23, 1-31

Abstract: This work focuses on the effects of inclusion proximity on the elastic behavior of dilute matrix-inclusion composites. Rigid or soft monodisperse spherical inclusions are considered with moderate volume fractions. To conduct this study, Representative Volume Elements (RVE) with an effective local minimum distance between inclusions varying between the sphere’s radius and one-tenth of the radius are built. Numerical finite element calculations on the RVE are performed. The obtained homogenized elastic properties, as well as the phase stress moments (first and second), are compared to Mori–Tanaka estimates, which are well established for this kind of composite. The behavior of local fields (stresses) in the microstructure with respect to inclusion proximity is also analyzed. It follows that the effective properties and phase stress moments converge asymptotically to the Mori–Tanaka estimates when the minimal distance between spheres increases. The asymptote seems to be reached around a distance equal to the sphere’s radius. Effective and phase behaviors show a deviation that can achieve and even exceed (for the second moments) ten percent when the inclusions are close. The impact of the inclusions’ proximities is even more important on local stress fields. The maximum stress values (hydrostatic or equivalent) can be more than twice as high locally.

Keywords: heterogeneous materials; dilute matrix inclusion; proximity effect; homogenization; first and second moments; local behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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