G. Frantziskonis

Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media

Transmission of acoustic waves in two-dimensional binary solid/solid composite media composed of arrays of Duralumin cylindrical inclusions embedded in an epoxy resin matrix is studied. The experimental transmission spectrum and theoretical band structure of two periodic arrays of cylinders organized on a square lattice and on a centred rectangular network are reported. Absolute gaps extending throughout the first two-dimensional Brillouin zone are predicted. The measured transmission is observed to drop to noise level throughout frequency intervals in reasonable agreement with the calculated forbidden frequency bands.

Constitutive model with strain softening

Abstract The aim or this paper is to propose a simple yet realistic model for the mechanical behavior of geologic materials such as concrete and rock. The effect of structural changes in such materials is addressed and incorporated in the theory through a tensor form of a damage variable. It is shown that formation of damage is responsible for the softening in strength observed in experiments, for the degradation of the elastic shear modulus, and for 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 parameters required to define the model are identified and determined from multiaxial testing of a concrete. The predictions are compared with observed behavior for a number of stress paths. The model shows very good agreement with the observed response.

Elastoplastic model with damage for strain softening geomaterials

SummaryThe paper examines certain important aspects of a rate independent model that accounts for distributed damage due to microcrack growth. Material behavior is considered as a mixture of two elastic-plastic interacting components, one termed topical (undamaged), and the other termed damaged. Energy considerations show the equivalence of the two-component body to an elastic-plastic body containing cracks; the equivalence is considered in the Griffith sense. The mechanisms of failure are considered and discussed with respect to multiaxial stress paths. An explanation of failure, at the microlevel, is given. A series of laboratory tests on a concrete are used to illustrate the development of failure.

Wavelet methods for analysing and bridging simulations at complementary scales - the compound wavelet matrix and application to microstructure evolution

We introduce a novel wavelet-based compound matrix to bridge models (Lennard-Jones model simulated with molecular dynamics and a lattice Q-states Potts model with a Monte Carlo simulation) that describe grain growth over different ranges of spatial and time scales. The compound wavelet matrix provides full statistical information on the microstructure at the range of scales that is the union of those handled by the two models.

Stochastic modeling of heterogeneous materials - A process for the analysis and evaluation of alternative formulations

Abstract The paper addresses the problem of understanding and modeling the constitutive behavior of complex, heterogeneous solid materials. Several issues in the area of stochastic material modeling remain open, thus a process for the analysis of different formulations is proposed and examined in detail. Using the proposed process, it is shown that a number of basic models are stochastically similar to each other. Furthermore, often, small apparently unimportant changes in a formulation may result in significant changes in the predicted response. For some formulations, inequalities are established that when satisfied it is guaranteed that the entropy of a structure/system cannot decrease. Attention is given to stochastic formulations within the context of non-local theories because such formulations provide new information to the subject of localization of deformation and fracture toughness.

Wavelet-based analysis of multiscale phenomena: application to material porosity and identification of dominant scales

The paper presents a general process that utilizes wavelet analysis in order to link information on material properties at several scales. In the particular application addressed analytically and numerically, multiscale porosity is the source of material structure or heterogeneity, and the wavelet-based analysis of multiscale information shows clearly its role on properties such as resistance to mechanical failure. Furthermore, through the statistical properties of the heterogeneity at a hierarchy of scales, the process clearly identifies a dominant scale or range of scales. Special attention is paid to porosity appearing at two distinct scales far apart from each other since this demonstrates the process in a lucid fashion. Finally, the paper suggests ways to extend the process to general multiscale phenomena, including time scaling.

WAVELET-BASED MULTISCALING IN SELF-AFFINE RANDOM MEDIA

Wavelet analysis is used to determine particular properties of self-affine random media, i.e. ones with homogeneous increments. When such media are filtered through introducing upper and lower cutoffs — corresponding to the domain and sample support scales — interesting properties result from wavelet analysis. In particular, we show that the filtered media can be used for transferring information along scales. Furthermore, we show that a wavelet-based approach for determining the underlying Hurst exponent is highly efficient. Examples relating to size and surface effects in materials demonstrate applications of the relevant multiscaling. Finally, we show that the wavelet-based approach and a method based on mode superposition complement each other nicely.

Modeling the coupling of reaction kinetics and hydrodynamics in a collapsing cavity

We introduce a model of cavitation based on the multiphase Lattice Boltzmann method (LBM) that allows for coupling between the hydrodynamics of a collapsing cavity and supported solute chemical species. We demonstrate that this model can also be coupled to deterministic or stochastic chemical reactions. In a two-species model of chemical reactions (with a major and a minor species), the major difference observed between the deterministic and stochastic reactions takes the form of random fluctuations in concentration of the minor species. We demonstrate that advection associated with the hydrodynamics of a collapsing cavity leads to highly inhomogeneous concentration of solutes. In turn these inhomogeneities in concentration may lead to significant increase in concentration-dependent reaction rates and can result in a local enhancement in the production of minor species.

Influence of soil variability on differential settlements of structures

The paper addresses the interaction of a structure with spatially varying soil properties. In particular, the problem of a two-span continuous beam founded on a heterogeneous soil is solved analytically. The geometrical and stiffness characteristics of the structure interact strongly with the spatial properties of the heterogeneous soil. For a certain value of the correlation distance, a feature of the heterogeneous soil formation, the uncertainty and the risk of high values, not predicted with deterministic models, in estimating differential settlements and forces (bending moments, shear forces, etc.) on the structure becomes maximum. The analytical solution uses a series expansion of the soil properties relative to those of the structure. The error in the solution, due to the truncation of the series expansion, is estimated by relevant numerical results. The paper shows clearly that the forces on the structure founded on a heterogeneous soil can differ widely from those usually predicted by a deterministic model. Furthermore, a usual deterministic approach can underestimate the safety level of the structure significantly. # 2003 Elsevier Science Ltd. All rights reserved.

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.