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Article Dans Une Revue Mathematics Année : 2022

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

Résumé

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.
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hal-03887798 , version 1 (29-06-2023)

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Louis Belgrand, Isabelle Ramière, Rodrigue Largenton, Frédéric Lebon. Proximity Effects in Matrix-Inclusion Composites: Elastic Effective Behavior, Phase Moments, and Full-Field Computational Analysis. Mathematics , 2022, 10 (23), pp.4437. ⟨10.3390/math10234437⟩. ⟨hal-03887798⟩
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