Bounds and estimates for linear composites with strain gradient effects

• Published in: Journal of the mechanics and physics of solids Vol. 42; no. 12; pp. 1851 - 1882
• Main Authors: Smyshlyaev, V.P., Fleck, N.A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.12.1994; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Lower bound; Upper bound; Elastic constants; Composite materials; Size effect; Self consistency; Dispersion reinforced material; Numerical method; Effective medium model
• ISSN: 0022-5096
• DOI: 10.1016/0022-5096(94)90016-7

Overall mechanical properties are studied for linear composites demonstrating a size effect. Variational principles of Hashin-Shtrikman type are formulated for incompressible composites involving the gradient of strain in their constitutive description. These variational principles are applied to linear, statistically homogeneous and isotropic two-phase composites. Upper and lower bounds of Hashin-Shtrikman type for the effective shear modulus and related self-consistent estimates are derived in terms of volume fraction and a two-point correlation function accounting for the scale of microstructure. An alternative selfconsistent scheme for matrix-inclusion strain-gradient composites is also proposed by a development of the approach laid down by Budiansky and Hill. Some numerical results are given to demonstrate the size effect.