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Evolution Law (evolution + law)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

Homogenization-based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2009
Q. Z. Zhu
Abstract This paper is devoted to micromechanical modeling of induced anisotropic damage in brittle geomaterials. The formulation of the model is based on a proper homogenization procedure by taking into account unilateral effects and interactions between microcracks. The homogenization procedure is developed in the framework of Eshelby's inclusion solution and Ponte-Castaneda and Willis (J. Mech. Phys. Solids 1995; 43:1919,1951) estimate. The homogenization technique is combined with the thermodynamics framework at microscopic level for the determination of damage evolution law. A rigorous crack opening,closure transition condition is established and an energy-release-rate-based damage criterion is proposed. Computational aspects on the implementation of micromechanical model are also discussed. The proposed model is evaluated by comparing numerical predictions with experimental data for various laboratory tests on concrete. Parametric studies on unilateral effects and influences of microcracks interactions are finally performed and analyzed. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Model error and sequential data assimilation: A deterministic formulation

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008
A. Carrassi
Abstract Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modelled on the basis of simple assumptions such as bias, white noise, and first-order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behaviour of model errors in marked contrast with previous approaches. This new scheme is applied in the context of a spatially distributed system proposed by Lorenz. First, it is found that, for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short-time dynamics of the estimation error covariance. Second, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained compared with the classical white-noise assumption. The universal short-time quadratic law for the evolution of the model error covariance matrix seems very promising for modelling estimation error dynamics in sequential data assimilation. Copyright © 2008 Royal Meteorological Society [source]

Micromechanical analysis of failure propagation in frictional granular materials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2009
Antoinette Tordesillas
Abstract The extent to which the evolution of instabilities and failure across multiple length scales can be reproduced with the aid of a bifurcation analysis is examined. We adopt an elastoplastic micropolar constitutive model, recently developed for dense cohesionless granular materials within the framework of thermomicromechanics. The internal variables and their evolution laws are conceived from a direct consideration of the dissipative mechanism of force chain buckling. The resulting constitutive law is cast entirely in terms of the particle scale properties. It thus presents a unique opportunity to test the potential of micromechanical continuum formulations to reproduce key stages in the deformation history: the development of material instabilities and failure following an initially homogeneous deformation. Progression of failure, initiating from frictional sliding and rolling at contacts, followed by the buckling of force chains, through to macroscopic strain softening and shear banding, is reproduced. Bifurcation point, marking the onset of shear banding, occurred shortly after the peak stress ratio. A wide range of material parameters was examined to show the effect of particle scale properties on the progression of failure. Model predictions on the thickness and angle of inclination of the shear band and the structural evolution inside the band, namely the latitudinal distribution of particle rotations and the angular distributions of contacts and the normal contact forces, are consistent with observations from numerical simulations and experiments. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A minimization principle for finite strain plasticity: incremental objectivity and immediate implementation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2002
Eric Lorentz
Abstract A finite strain plasticity formulation is proposed which meets several requirements that often appear contradictory. On a physical ground, it is based on a multiplicative split of the deformation, hyperelasticity for the reversible part of the behaviour and the maximal dissipation principle to define the evolution laws. On a numerical ground, it is incrementally objective and the integration over a time increment can be expressed as a minimization problem, a proper framework to examine the questions of existence and uniqueness of the solutions. Last but not least, the implementation is immediate since it relies on the same equations for finite and infinitesimal transformations. Finally, the formulationis applied to von Mises plasticity with isotropic linear hardening and introduced in the finite element software Code_Aster®. The numerical computation of a cantilever beam shows that it leads to results in good agreement with those obtain with common approaches. Copyright © 2002 John Wiley & Sons, Ltd. [source]