Nonlocal Model Based on Crack Interactions: A Localization Study

A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions (Bazˇant, 1992) can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one-dimensional description. Strain localization in an infinite layer under plain stress is studied using both the old and the new nonlocal formulations. The importance of renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out.

Download Full-text

Long waves in a straight channel with non-uniform cross-section

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.147 ◽

2015 ◽

Vol 770 ◽

pp. 156-188 ◽

Cited By ~ 5

Author(s):

Patricio Winckler ◽

Philip L.-F. Liu

Keyword(s):

Boundary Layer ◽

Wave Propagation ◽

Cross Section ◽

Three Dimensional ◽

Channel Cross Section ◽

Cross Sectional ◽

New Model ◽

One Dimensional ◽

Uniform Channel ◽

The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Download Full-text

A Generalized Elasto-Plastic Micro-Polar Constitutive Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.798.505 ◽

2015 ◽

Vol 798 ◽

pp. 505-509 ◽

Cited By ~ 3

Author(s):

Lapo Gori ◽

Roque Luiz da Silva Pitangueira ◽

Samuel Silva Penna ◽

Jamile Salim Fuina

Keyword(s):

Structural Analysis ◽

Constitutive Model ◽

Numerical Method ◽

Strain Localization ◽

Continuum Model ◽

Constitutive Models ◽

Localization Problem ◽

Polar Model ◽

Basic Characteristics ◽

Analysis Environment

This paper summarizes the implementation of an elasto-plastic constitutive model for a micro-polar continuum in the constitutive models framework of the software INSANE (INteractive Structural ANalysis Environment). Such an implementation is based on the tensorial format of a unified constitutive models formulation, that allows to implement different constitutive models independently on the peculiar numerical method adopted for the solution of the problem. The basic characteristics of the micro-polar continuum model and of the unified formulation of constitutive models are briefly recalled. A generalization of the micro-polar model is then introduced in order to include this model in the existent tensor-based formulation. Finally, an enhanced version of the general closest-point algorithm, ables to manage the generalized micro-polar formulation, is derived. A strain localization problem modeling illustrates the implementation.

Download Full-text

One-Dimensional Nonlocal Model for Gyratory Compaction of Hot Asphalt Mixtures

Journal of Engineering Mechanics ◽

10.1061/(asce)em.1943-7889.0002073 ◽

2022 ◽

Vol 148 (2) ◽

Author(s):

Tianhao Yan ◽

Mihai Marasteanu ◽

Jia-Liang Le

Keyword(s):

Asphalt Mixtures ◽

Nonlocal Model ◽

One Dimensional ◽

Gyratory Compaction

Download Full-text

Two-Dimensional Model for Wave-Induced Pore Pressure Accumulation in Marine Sediments

Volume 6: Polar and Arctic Sciences and Technology; Offshore Geotechnics; Petroleum Technology Symposium ◽

10.1115/omae2013-10223 ◽

2013 ◽

Author(s):

Hongyi Zhao ◽

Dong-Sheng Jeng ◽

Huijie Zhang ◽

Jisheng Zhang

Keyword(s):

Pore Pressure ◽

Marine Sediments ◽

Wave Motion ◽

Present Model ◽

Two Dimensional ◽

New Model ◽

One Dimensional ◽

Wave Cycle ◽

Previous Solution ◽

Wave Induced

In this paper, a two-dimensional (2D) porous model is established to investigate the predication of the wave-induced pore pressure accumulations in marine sediments. In the new model, the VARANS equation is used as the governing equation for the wave motion, while the Biot’s consolidation theory is used for porous seabed. The present model is verified with the previous experimental data [1] and provides a better prediction of pore pressure accumulation than the previous solution [2]. With the new model, a 2D liquefied zone is formed at the beginning of the process, and then gradually move down. After a certain wave cycle (for example, 30 wave cycles in the numerical example), the liquefaction zone will become one-dimensional (1D) and continuously move down and eventually approaches to a constant. Numerical results also conclude the maximum liquefaction depth increases as wave height increases and in shallow water.

Download Full-text

Comment on “New Model System for a One-Dimensional Electron Liquid: Self-OrganizedAtomic Gold Chains on Ge(001)”

Physical Review Letters ◽

10.1103/physrevlett.103.209701 ◽

2009 ◽

Vol 103 (20) ◽

Cited By ~ 18

Author(s):

Arie van Houselt ◽

Daan Kockmann ◽

Tijs F. Mocking ◽

Bene Poelsema ◽

Harold J. W. Zandvliet

Keyword(s):

Model System ◽

Dimensional Electron ◽

New Model ◽

One Dimensional

Download Full-text

Localization of gravity waves on a channel with a random bottom

Journal of Fluid Mechanics ◽

10.1017/s0022112088000254 ◽

1988 ◽

Vol 186 ◽

pp. 521-538 ◽

Cited By ~ 69

Author(s):

Pierre Devillard ◽

François Dunlop ◽

Bernard Souillard

Keyword(s):

Gravity Waves ◽

Theoretical Study ◽

Localization Length ◽

Full Potential ◽

Matrix Approach ◽

Localization Problem ◽

One Dimensional ◽

Localization Phenomenon ◽

Localization Theory ◽

Transfer Matrix Approach

We present a theoretical study of the localization phenomenon of gravity waves by a rough bottom in a one-dimensional channel. After recalling localization theory and applying it to the shallow-water case, we give the first study of the localization problem in the framework of the full potential theory; in particular we develop a renormalized-transfer-matrix approach to this problem. Our results also yield numerical estimates of the localization length, which we compare with the viscous dissipation length. This allows the prediction of which cases localization should be observable in and in which cases it could be hidden by dissipative mechanisms.

Download Full-text