Spatiotemporal Compound Wavelet Matrix Framework for Multiscale/Multiphysics Reactor Simulation: Case Study of a Heterogeneous Reaction/Diffusion System

We present a mathematical method for efficiently compounding information from different models of species diffusion from a chemically reactive boundary. The proposed method is intended to serve as a key component of a multiscale/ multiphysics framework for heterogeneous chemically reacting processes. An essential feature of the method is the merging of wavelet representations of the different models and their corresponding time and length scales. Up-and-downscaling of the information between the scales is accomplished by application of a compounding wavelet operator, which is assembled by establishing limited overlap in scales between the models. We show that the computational efficiency gain and potential error associated with the method depend on the extent of scale overlap and wavelet filtering used. We demonstrate the method for an example problem involving a two-dimensional chemically reactive boundary and first order reactions involving two species

COMPRESSED-AIR ENERGY STORAGE SYSTEMS FOR STAND-ALONE OFF-GRID PHOTOVOLTAIC MODULES

ABSTRACT In this work, a low-cost, low-volume, low-maintenance, small-scale compressed-air energy storage system (SS-CAES) is proposed, which can be used in conjunction with off-grid stand-alone photo-voltaic panels, for powering appliances and residential units in order to minimize the dependency on centralized power system grids. As a first step towards achieving this objective, we have designed and examined the compression efficiency of a singlestage, isothermal compression system that utilizes a fluid piston. Preliminary results clearly establish that the prototype holds enormous promise as energy storage systems that are compatible with renewable energy sources such as solar

PROGRESSIVE DAMAGE AND CONSTITUTIVE BEHAVIOR OF GEOMATERIALS INCLUDING ANALYSIS AND IMPLEMENTATION.

In this dissertation, first the experimental and theoretical observations on the deformational characteristics of brittle geomaterials are reviewed and discussed. A basic conclusion is that special features such as strain softening can not be considered as true material (continuum) properties. These conclusions created a renewed emphasis on the constitutive modelling of such materials. A model that accounts for structural changes is developed. Such changes are incorporated in the theory through a tensor form of a damage variable. It is shown subsequently that formation of damage is responsible for the degradation in strength (softening) observed in experiments, for the degradation of the elastic shear modulus and for mechanical, damage induced anisotropy. A generalized plasticity model is incorporated for the so-called topical or continuum part of the behavior, whereas the damage part is represented by the so-called stress-relieved behavior. The question of uniqueness in the strain-softening regime is examined. It is shown that the constitutive equations lead to a unique solution for the case of rate dependent as well as rate independent formulation. Its implementation in finite element analysis shows mesh size insensitivity in the hardening and softening regimes. The general order of bifurcation of differential equations is employed in order to study the effect of damage accumulation on formation of narrow, so-called shear bands. It is shown that as the damage accumulates, the material approaches localization of deformation. The theory of mixtures is employed for further theoretical establishment of the proposed model. Energy considerations show the equivalence of the two-component damage body to an elastoplastic body containing cracks; the equivalence is considered in the Griffith sense. The mechanisms of failure are considered and discussed with respect to multiaxial stress pads. An explanation of failure, at the micro level, is given. The material constants involved in the theory are identified and determined from available experimental data. The model is then verified by back-predicting the observed behavior

Length scale effects and multiscale modeling of thermally induced phase transformation kinetics in NiTi SMA

Thermally induced phase transformation in NiTi shape memory alloys (SMA) shows strong size and shape, collectively termed length scale effects, at the nano to micrometer scales, and that has important implications for the design and use of devices and structures at such scales. This paper, based on a recently developed multiscale model that utilizes molecular dynamics (MD) simulations at small scales and MD-verified phase field (PhF) simulations at larger scales, reports results on specific length scale effects, i.e. length scale effects in martensite phase fraction evolution, transformation temperatures (martensite and austenite start and finish) and in the thermally cyclic transformation between austenitic and martensitic phase. The multiscale study identifies saturation points for length scale effects and studies, for the first time, the length scale effect on the kinetics (i.e. developed internal strains) in the B19 phase during phase transformation. The major part of the work addresses small scale single crystals in specific orientations. However, the multiscale method is used in a unique and novel way to indirectly study length scale and grain size effects on evolution kinetics in polycrystalline NiTi, and to compare the simulation results to experiments. The interplay of the grain size and the length scale effect on the thermally induced martensite phase fraction (MPF) evolution is also shown in this present study. Finally, the multiscale coupling results are employed to improve phenomenological material models for NiTi SMA.12 month embargo; first online 13 March 2017This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

On the stochastic interpretation of gradient-dependent constitutive equations

The paper elaborates on the statistical interpretation of a class of gradient models by resorting to both microscopic and macroscopic considerations. The microscopic stochastic representation of stress and strain fields reflects the heterogeneity inherently present in engineering materials at small scales. A physical argument is advanced to conjecture that stress shows small fluctuations and strong spatial correlations when compared to those of strain; then, a series expansion in the respective constitutive equations renders unimportant stress gradient terms, in contrast to strain gradient terms, which should be retained. Each higher-order strain gradient term is given a physically clear interpretation. The formulation also allows for the underlying microstrain field to be statistically non-stationary, e.g., of fractal character. The paper concludes with a comparison between surface effects predicted by gradient and stochastic formulations. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved