The effective shear modulus for an n‐layered composite sphere

• Published in: Proceedings in applied mathematics and mechanics Vol. 17; no. 1; pp. 609 - 610
• Main Authors: Lenz, Peter, Dammann, Christian, Mahnken, Rolf
• Format: Journal Article
• Language: English
• Published: Berlin WILEY‐VCH Verlag 01.12.2017
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.201710274

This work presents the derivation of the effective shear modulus for a heterogeneous material composed of multi‐layered composite spheres embedded in a linear elastic matrix. It is based on the composite spheres model known from the literature. In contrast to previous publications the effective shear modulus is obtained by equating the results of two models: In the first model, a heterogeneous sphere is embedded in an equivalent homogeneous material, whereas in the second model, the heterogeneous sphere is replaced by an equivalent homogeneous sphere. In the context of both, a shear stress approach and a shear deformation approach, this results into an overdetermined system of equations which is solved with the least squares method. In a numerical study our results are compared to effective moduli and bounds from the literature. Furthermore, a convincing agreement with experimental data for glass microspheres embedded in a polyester matrix is demonstrated. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)