Patterns,fabric, anisotropy,and soil elasto-plasticity

This paper proposes a new method in the theory of soil plasticity – an advance on Hill [The Mathematical Theory of Plasticity, Clarendon Press, Oxford]. The method assumes that soil fabric consists of inter-locking, inter-twining, inter-laced, juxtaposed, and superposed elementary units called “patterns”. A mechanics of patterns is developed. As well as elastic and plastic components, a third strain-increment component is deduced which helps explain non-associated flow. The proposed method leads to explanations of critical states, anisotropy, sensitivity, the Bauschinger effect, and swept-out memory. All these appear in the method as near-inescapable features of plastic solids. Results are illustrated in detail for plane strain biaxial processes.     

Diffusion models for innovation: s-curves, networks, power laws, catastrophes, and entropy

This article considers models for the diffusion of innovation would be most relevant to the dynamics of early 21st century technologies. The article presents an overview of diffusion models and examines the adoption S-curve, network theories, difference models, influence models, geographical models, a cusp catastrophe model, and self-organizing dynamics that emanate from principles of network configuration and principles of heat diffusion. The diffusion dynamics that are relevant to information technologies and energy-efficient technologies are compared. Finally, principles of nonlinear dynamics for innovation diffusion that could be used to rehabilitate the global economic situation are discussed.     

Physiology,mechanics, and rheology

Biological systems possess rather specialized mechanical properties, acquired as part and parcel of the evolutionary development of the system as a whole. Their optimization permits the system to function physiologically in the context of a biologically essential, but mechanically often widely varying environment with adequate efficiency. The system's environment is its source of food and shelter; it represents the space in which it forages or preys on other creatures and in which it has to defend itself against still others. Thus, the system has to develop an adequately pliant, rheologically matched, energy-use efficient, mechanical interface between it and its surroundings. This must be an interface that both effectively excludes, but also effectively admits, the external. Internally, as well, it has to adapt the mechanical properties of cell and connective tissue to physiological function and the efficient performance of useful work. This will be illustrated by way of examples. Blood rheology is briefly discussed and put into the context of clinical hemorheology and epithelial protection; and function, by way of a mucus coating or a mucociliary clearance system, is reviewed in some detail. The importance of all aspects of rheological matching is demonstrated.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

One-dimensional,time-dependent,homogeneous, two-phase flow in volcanic conduits

A one-dimensional, time-dependent, isothermal, homogeneous, two-phase flow model was developed to study magma ascent in volcanic conduits. The physical modeling equations were numerically solved by means of a TVD (total variation diminishing) predictor-corrector procedure and by means of a predictor-corrector technique based on the method of characteristics. The results from the transient model were verified with an analytical solution for wave propagation in conduits without friction and gravitational effects. The numerical solutions were also compared with those of a steady-state, homogeneous, two-phase model for basaltic and rhyolitic magma ascents in the fissures and circular conduits of Vesuvius and Mt St. Helens. An application of the model to magma decompression in conduits indicates very short times for gas exsolution, fragmentation, and shock wave propagation, implying that the modelling of gas exsolution should involve non-equilibrium kinetics effects. Future coupling of the transient magma ascent model with magma chamber and pyroclastic dispersion models should allow for more realistic simulations of the time-dependent behavior of real volcanic eruptions.     

Steady,oblique, detonation waves

Normal and oblique, steady planar detonation waves have been theoretically and computationally examined using the Zeldovich, von Neumann, Döring model. Combustion is between a methane/hydrogen mixture and dry air assuming, first, complete combustion, then an equilibrium solution. Prescribed parameters are the upstream values for the pressure, temperature, and Mach number, the fuel/air equivalence ratio, a hydrogen/methane ratio, and the detonation wave angle. For a given upstream state, the angle varies from its normal wave value in increments of 10 ^o to non-integer wave angles that correspond to the Chapman-Jouguet state for complete combustion and for an equilibrium solution. For each solution, detailed results are provided for the upstream state, the state just downstream of the shock, and the two downstream states. Over 340 solutions in a report (Emanuel and Tuckness 2002) are provided, thereby establishing, for the first time, comprehensive tables that can be used to provide quick estimates, establish trends, and check CFD results. This paper describes the basis for the model, briefly outlines the analytical and numerical method, and discusses several insights.     

Cool,Dry, Nano-scale DIC Patterning of Delicate,Heterogeneous, Non-planar Specimens by Micro-mist Nebulization

Experimental Mechanics - Background: Application of patterns to enable high-resolution Digital Image Correlation (DIC) at the small scale (μm/nm) is known to be very challenging as techniques...     

Growth,mass transfer,and remodeling in fiber-reinforced,multi-constituent materials

We represent a biological tissue by a multi-constituent, fiber-reinforced material, in which we consider two phases: fluid, and a fiber-reinforced solid. Among the various processes that may occur in such a system, we study growth, mass transfer, and remodeling. To us, mass transfer is the reciprocal exchange of constituents between the phases, growth is the variation of mass of the system in response to interactions with the surrounding environment, and remodeling is the evolution of its internal structure. We embrace the theory according to which these events, which lead to a structural reorganization of the system and anelastic deformations, require the introduction of balance laws, which complete the physical picture offered by the standard ones. The former are said to be non-standard. Our purposes are to determine the rates of anelastic deformation related to mass transfer and growth, and to study fiber reorientation in the case of a statistical distribution of fibers. In particular, we discuss the use of the non-standard balance laws in modeling transfer of mass, and compare our results with a formulation in which such balance laws are not introduced.