A peridynamics model for strain localization analysis of geomaterials

Geomaterials such as sand and clay are highly heterogeneous multiphase materials. Nonlocality (or a characteristic length scale) in modeling geomaterials based on the continuum theory can be associated with several factors, for instance, the physical interactions of material points within finite distance, the homogenization or smoothing process of material heterogeneity, and the particle or problem size-dependent mechanical behavior (eg, the thickness of shear bands) of geomaterials. In this article, we formulate a nonlocal elastoplastic constitutive model for geomaterials by adapting a local elastoplastic model for geomaterials at a constant suction through the constitutive correspondence principle of the state-based peridynamics theory. We numerically implement this nonlocal constitutive model via the classical return-mapping algorithm of computational plasticity. We first conduct a one-dimensional compression test of a soil sample at a constant suction through the numerical model with three different values of the nonlocal variable (horizon) δ. We then present a strain localization analysis of a soil sample under the constant suction and plane strain conditions with different nonlocal variables. The numerical results show that the proposed nonlocal model can be used to simulate the inception and propagation of shear banding as well as to capture the thickness of shear bands in geomaterials at a constant suction.     

Lithium isotope composition of ordinary and carbonaceous chondrites, and differentiated planetary bodies: Bulk solar system and solar reservoirs

In order to better constrain the Li isotope composition of the bulk solar system and Li isotope fractionation during accretion and parent body processes, Li isotope compositions and concentrations were determined on a number of meteorite falls and finds. This is the first comprehensive study that systematically investigates a representative set of samples from carbonaceous chondrites (CI, CM2, CO3, CV3, CK4 and one ungrouped member), enstatite chondrites (EH, EL), ordinary chondrites (H, L, LL), and achondrites (one eucrite, diogenites, one pallasite, and a silicate inclusion from a IAB iron).

Carbonaceous chondrites have an average isotope composition of δ⁷Li = + 3.2‰ ± 1.9 (2σ) which agrees with the average composition of relatively pristine olivines (representative for the bulk composition) from the Earth primitive upper mantle (PUM). This is lighter than the average δ⁷Li of the basaltic differentiates of the Earth, Moon and Mars and the achondrites. It is an important observation, however, that the lighter end of the isotopic range of the differentiates always coincides with the averages of the mantle olivines and the carbonaceous chondrites. From this we conclude that the bulk of the inner solar system consists mostly of material from carbonaceous chondrites and that the variation seen in the differentiates is due to planetary body processes. Ordinary chondrites are significantly lighter than carbonaceous chondrites. No significant differences in δ⁷Li exist between enstatite chondrites (n = 3) and carbonaceous or ordinary chondrites. The difference between carbonaceous and ordinary chondrites and the variability within the chondrites could indicate the existence of distinct Li isotope reservoirs in the early solar nebula.