Bounds on elastic moduli of composites

Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media

“…Partitioning an RVE into smaller elements and introducing the notions of kinematical and static apparent stiffness and compliance tensors relative to the uniform strain and traction boundary conditions, Huet (1990) applied the classical minimum potential and complementary energy principles of linear elasticity to establish hierarchical bounds for the effective stiffness and compliance tensors. Huet's approach has been further developed by his co-workers and others in relation to linear materials (see, e.g., Sab, 1992;Hazanov and Huet, 1994;Hazanov and Amieur, 1995;Balendrana and Nemat-Nasser, 1995;Ostoja-Starzewski, 1996Zohdi et al, 1996;Nemat-Nasser and Hori, 1999), and has been also extended to some nonlinear materials (Hazanov, 1999a,b;Nemat-Nasser and Hori, 1999;He, 2001;Jiang et al, 2001). The notions of kinematical and static apparent stiffness and compliance tensors are particularly relevant to the problem of determination of the minimum RVE size.…”

Minimum Compliance Optimization of a Thermoelastic Lattice Structure with Size-Coupled Effects

“…The research mentioned above mostly used the homogenization method [8,9] or the RVE method [11,12] based on strain energy equivalence to study the relationship between the macro mechanical properties and the microstructure, considering the lattice units or porous materials as a continuum. However, most of the studies mentioned above are limited to the relatively simple microstructure, and it is difficult to guarantee the optimality of application for the actual engineering structure with complex structural configurations and boundary conditions.…”

“…For an equivalent property study, homogenization [8,9] and representative volume element (RVE) [10][11][12] have been widely used. With the equivalent strain energy, Zhou and Deng [13] represented the relevant macro equivalent elastic constants of the sandwich plates with periodic lattice structures and compared the structural response of actual sandwich plates with the equivalent sandwich plates.…”

“…Extensive research [8][9][10][11][12][13][14][15][16] has already been performed on the analysis and optimization of the performance of lattice materials, including their thermal performances. For an equivalent property study, homogenization [8,9] and representative volume element (RVE) [10][11][12] have been widely used.…”

Adaptive modeling of wave propagation in heterogeneous elastic solids

“…Some of the most revered work in mechanics over several decades has been devoted to this subject. As well known examples, the works of Hill [14], Hashin and Shtrikman [13], Balendran and Nemat-Nasser [1], and Nemat-Nasser and Hori [15] are noted. The averaging methods also spawned new mathematical research into what is called homogenization of partial differential equations.…”