We present experimental results on the mechanical behavior of static granular assemblies confined in a vertical column. Our measurements confirm the universal Janssen scaling for the stress saturation curve. We show consequently, in the context of isotropic elasticity, a relation between the Poisson ratio and the granular packing fraction. Moreover, using a systematic study of the overshoot effect created by a top mass equal to the saturation mass, we show behaviors that are reproduced qualitatively by isotropic elastic materials but of a spectacular amplitude in the case of a granular assembly. These experimental results are strong tests for any theory of granular matter.

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T(g) and for the elastic properties of the glassy state are presented. We find that T(g) increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T(g) is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T(g) via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T(g) from below, the shear modulus μ displays a much stronger decrease near T(g). From the present simulation data it is not possible to decide whether μ takes a finite value at T(g), as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.

The principal criteria used to predict cavitation in rubber materials are reviewed, and experimental evidence is recalled for three different configurations: in the bulk, in the vicinity of a rigid particle, and in small rubber particles embedded in a rigid polymer matrix. Two major classes of cavitation criteria are defined, those based on an elastic instability (i.e., related to a stress state and finite strains) and those based on the energy balance (i.e., involving surface energies). The different criteria, in which various hyperelastic behavior laws are considered, are compared in numerical applications, and the tendencies are derived. The particular case of accounting for the surface tension of the rubber, a parameter common to the stress state and the energy balance, is treated in detail. It appears that the understanding of the genesis of a microcavity in a rubber material, when no pre-existing flaw is assumed, still constitutes a difficulty for the analysis of mechanical damage in polymers containing a rubber phase.