Orientation-based Continuum Damage Models for Rocks

A general formulation of the Helmholtz free energy used in thermodynamics of damage process of rocks is derived within a multi-scale framework. Such a physically-based thermodynamic state potential has a hybrid, discrete/continuum, nature in the sense tha

Infrared Magnitude-Redshift Relations for Luminous Radio Galaxies

Infrared magnitude-redshift relations for the 3CR and 6C samples of radio galaxies are presented for a wide range of plausible cosmological models, including those with non-zero cosmological constant OmegaLambda. Variations in the galaxy formation redshift, metallicity and star formation history are also considered. The results of the modelling are displayed in terms of magnitude differences between the models and no-evolution tracks, illustrating the amount of K-band evolution necessary to account for the observational data. Given a number of plausible assumptions, the results of these analyses suggest that: (i) cosmologies which predict T_0xH_0>1 (where T_0 denotes the current age of the universe) can be excluded; (ii) the star formation redshift should lie in the redshift interval 5radio galaxies are more luminous (ie. more massive) than those nearby in models with finite OmegaLambda, including the favoured model with Omega=0.3, OmegaLambda=0.7. For cosmological models with larger values of T_0xH_0, the conclusions are the same regardless of whether any adjustments are made or not. The implications of these results for cosmology and models of galaxy formation are discussed.

Stochastic Structural Model of Rock and Soil Aggregates by Continuum-Based Discrete Element Method

This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.

A Constrained Particle Dynamics for Continuum-Particle Hybrid Method in Micro- and Nano-Fluidics

A hybrid method of continuum and particle dynamics is developed for micro- and nano-fluidics, where fluids are described by a molecular dynamics (MD) in one domain and by the Navier-Stokes (NS) equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip boundary conditions.

Trans-Scale Mechanics: Looking For The Missing Links Between Continuum And Micro/Nanoscopic Reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frameworks of either particle or continuum mechanics. In this paper, four cases studies (shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics) are provided to illustrate the three levels of trans-scale problems (problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/molecules and a finite size body at micro/nano-level) and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.