scholarly journals Model order reduction for deformable porous materials in thin domains via asymptotic analysis

2021 ◽  
Author(s):  
Alaa Armiti-Juber ◽  
Tim Ricken
Keyword(s):  
Asymptotic Analysis ◽  
Porous Materials ◽  
Numerical Solutions ◽  
Order Reduction ◽  
Longitudinal Direction ◽  
Reduced Model ◽  
Thin Domains ◽  
Strongly Coupled ◽  
Biphasic Model ◽  
Limit Model

AbstractWe study fluid-saturated porous materials that undergo poro-elastic deformations in thin domains. The mechanics in such materials are described using a biphasic model based on the theory of porous media (TPM) and consisting of a system of differential equations for material’s displacement and fluid’s pressure. These equations are in general strongly coupled and nonlinear, such that exact solutions are hard to obtain and numerical solutions are computationally expensive. This paper reduces the complexity of the biphasic model in thin domains with a scale separation between domain’s width and length. Based on standard asymptotic analysis, we derive a reduced model that combines two sub-models. Firstly, a limit model consists of averaged equations that describe the fluid pore pressure and displacement in the longitudinal direction of the domain. Secondly, a corrector model re-captures the mechanics in the transverse direction. The validity of the reduced model is finally tested using a set of numerical examples. These demonstrate the computational efficiency of the reduced model, while maintaining reliable solutions in comparison with original biphasic TPM model in thin domain.

A Yield Criterion of Porous Materials With Anisotropy Caused by Geometry or Distribution of Pores

1991 ◽  
Vol 113 (4) ◽  
pp. 425-429 ◽  
Author(s):  
T. Hisatsune ◽  
T. Tabata ◽  
S. Masaki
Keyword(s):  
Velocity Field ◽  
Porous Materials ◽  
Upper Bound ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Longitudinal Direction ◽  
Axisymmetric Deformation ◽  
The Other ◽  
The Matrix ◽  
Spherical Cells

Axisymmetric deformation of anisotropic porous materials caused by geometry of pores or by distribution of pores is analyzed. Two models of the materials are proposed: one consists of spherical cells each of which has a concentric ellipsoidal pore; and the other consists of ellipsoidal cells each of which has a concentric spherical pore. The velocity field in the matrix is assumed and the upper bound approach is attempted. Yield criteria are expressed as ellipses on the σm σ3 plane which are longer in longitudinal direction with increasing anisotropy and smaller with increasing volume fraction of the pore. Furthermore, the axes rotate about the origin at an angle α from the σm-axis, while the axis for isotropic porous materials is on the σm-axis.

New model for acoustic waves propagating through a vortical flow

2017 ◽  
Vol 823 ◽  
pp. 658-674 ◽  
Author(s):  
Jim Thomas
Keyword(s):  
Asymptotic Analysis ◽  
Wave Field ◽  
Time Scale ◽  
Acoustic Waves ◽  
High Frequency ◽  
Spatial Scales ◽  
Amplitude Equation ◽  
Vortical Flow ◽  
Reduced Model ◽  
Scale Separation

A new amplitude equation is derived for high-frequency acoustic waves propagating through an incompressible vortical flow using multi-time-scale asymptotic analysis. The reduced model is derived without an explicit spatial-scale separation ansatz between the wave and vortical fields. As a consequence, the model is seen to capture very well the features of the wave field in the regime where the spatial scales of the wave and vortical fields are comparable, a regime for which an optimal reduced model does not seem to be available.

Simplification by pruning as a model order reduction approach for RF-MEMS switches

2019 ◽  
Vol 39 (2) ◽  
pp. 511-523
Author(s):  
Gabriela Ciuprina ◽  
Daniel Ioan ◽  
Aurel-Sorin Lup ◽  
Luis Miguel Silveira ◽  
Anton Duca ◽  
...  
Keyword(s):  
Rf Mems ◽  
Approximation Error ◽  
Order Reduction ◽  
Projection Methods ◽  
Reduced Model ◽  
Minimal Order ◽  
Content Type ◽  
Mems Switches ◽  
Rf Mems Switches ◽  
Physical Phenomena

Purpose This paper proposes an algorithm for the extraction of reduced order models of MEMS switches, based on using a physics aware simplification technique. Design/methodology/approach The reduced model is built progressively by increasing the complexity of the physical model. The approach starts with static analyses and continues with dynamic ones. Physical phenomena are introduced sequentially in the reduced model whose order is increased until accuracy, computed by assessing forces that are kept in the reduced model, is acceptable. Findings The technique is exemplified for RF-MEMS switches, but it can be extended for any device where physical phenomena can be included one by one, in a hierarchy of models. The extraction technique is based on analogies that are carried out for both the multiphysics and the full-wave electromagnetic phenomena and their couplings. In the final model, the multiphysics electromechanical phenomena is reduced to a system with lumped components with nonlinear elastic and damping forces, coupled with a system with distributed and lumped components which represents the reduced model of the RF electromagnetic phenomena. Originality/value Contrary to the order reduction by projection methods, this approach has the advantage that the simplified model can be easily understood, the equations and variables have significance for the user and the algorithm starts with a model of minimal order, which is increased until the approximation error is acceptable. The novelty of the proposed method is that, being tailored to a specific application, it is able to keep physical interpretation inside the reduced model. This is the reason why, the obtained model has an extremely low order, much lower than the one achievable with general state-of-the-art procedures.

Boundary layer over spinning blunt body of revolution at incidence including Magnus forces

1978 ◽  
Vol 363 (1714) ◽  
pp. 357-380 ◽  
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Blunt Body ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Meridional Flow ◽  
Meridional Plane ◽  
Magnus Force ◽  
Displacement Thickness

An incompressible laminar flow over a spinning blunt-body at incidence is investigated. The approach follows strictly the three-dimensional boundary layer theory, and the lack of initial profiles is readily resolved. The rule of the dependence zone is satisfied with the Krause scheme, and complete numerical solutions are obtained for an ellipsoid of revolution at 6° incidence and two spin rates. Spinning causes asymmetry which, in turn, introduces the Magnus force. The asymmetry is most pronounced in crossflow, but is also noticeable in the skin friction and displacement thickness of the meridional flow. A variety of crossflow profiles are determined as are the streamline patterns in the cross- and meridional-plane which are especially useful in visualizing the flow structure. Detailed distribution of skin friction, displacement thickness, and centrifugal pressure are presented. A negative crossflow displacement thickness is found to be physically meaningful. The Magnus forces due to the crossflow skin friction and the centrifugal pressure are determined; these two forces partly compensate for each other. At lower spin rate, the frictional force is larger, resulting in a positive Magnus force. At high spin rate, the opposite is obtained. At high incidence (30°) the present boundary layer calculations could be carried out in the longitudinal direction, only up to the beginning of an open separation.

scholarly journals Analysis of electro-permeation of hydrogen in metallic alloys

2017 ◽  
Vol 375 (2098) ◽  
pp. 20160409 ◽  
Author(s):  
A. Raina ◽  
V. S. Deshpande ◽  
N. A. Fleck
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Solutions ◽  
Local Equilibrium ◽  
Reaction Diffusion ◽  
Metallic Alloys ◽  
Diffusion Type ◽  
Thermal Desorption Spectrometry ◽  
Modelling Framework ◽  
Numerical Predictions ◽  
Study Support

A reaction–diffusion type modelling framework is presented to analyse both electro-permeation (EP) and thermal desorption spectrometry (TDS) measurements of hydrogen in metallic alloys. It is assumed that the kinetics of hydrogen motion is governed by diffusion through the lattice, along with trapping/detrapping at specific sites such as dislocations, grain boundaries, etc. It is shown that the trapping and detrapping rates are typically much faster than the diffusion rate, and consequently a simplification of the governing equations suffices such that local equilibrium exists between lattice and trapped hydrogen. Using this local equilibrium assumption, we then present an asymptotic analysis of the governing kinetic equation for the EP test. This asymptotic analysis reveals that four regimes of behaviour exist, ranging from negligible trapping to the complete filling of deep traps. The analysis suggests that EP tests should be so-arranged that three regimes of behaviour are spanned, in order to extract the relevant material properties associated with hydrogen transport. The numerical solutions presented in this study support the asymptotic analysis. The hydrogen kinetics framework is also deployed to analyse both EP and TDS tests on the same martensitic steel. The EP measurements all lie in regime I and are thus insufficient to uniquely determine both the trap density and binding energy. Reasonable agreement is obtained between measurements and numerical predictions of TDS tests using parameters estimated from the EP tests. Further improvements in measurements are required to confirm the fidelity of this modelling approach. This article is part of the themed issue ‘The challenges of hydrogen and metals’.

scholarly journals Model-Order-Reduction Approach for Structural Health Monitoring of Large Deployed Structures With Localized Operational Excitations

2021 ◽  
Author(s):  
Mohamed Aziz Bhouri
Keyword(s):  
Correlation Function ◽  
Time Domain ◽  
Numerical Solutions ◽  
Moving Load ◽  
Order Reduction ◽  
Training Dataset ◽  
Support Vector ◽  
Reduced Basis ◽  
Moving Vehicle ◽  
Classification Errors

Abstract We present a simulation-based classification approach for large deployed structures with localized operational excitations. The method extends the two-level Port-Reduced Reduced-Basis Component (PR-RBC) technique to provide faster solution estimation to the hyperbolic partial differential equation of time-domain elastodynamics with a moving load. Time-domain correlation function-based features are built in order to train classifiers such as Artificial Neural Networks and Support-Vector Machines and perform damage detection. The method is tested on a bridge-shaped structure with a moving vehicle (playing the role of a digital twin) in order to detect cracks’ existence. Such problem has 45 parameters and shows the merits of the two-level PR-RBC approach and of the correlation function-based features in the context of operational excitations, other nuisance parameters and added noise. The quality of the classification task is enhanced by the sufficiently large synthetic training dataset and the accuracy of the numerical solutions, reaching test classification errors below 0.1% for disjoint training set of size 7 × 103 and test set of size 3 × 103. Effects of the numerical solutions accuracy and of the sensors locations on the classification errors are also studied, showing the robustness of the proposed approach and the importance of constructing a rich and accurate representation of possible healthy and unhealthy states of interest.

An obstacle problem for Koiter’s shells

2019 ◽  
Vol 24 (10) ◽  
pp. 3061-3079 ◽  
Author(s):  
Philippe G Ciarlet ◽  
Paolo Piersanti
Keyword(s):  
Asymptotic Analysis ◽  
A Priori ◽  
Elastic Shell ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Model ◽  
Limit Model ◽  
Membrane Shells ◽  
Point Of Departure ◽  
Confinement Condition

In this paper, we define, a priori, a natural two-dimensional Koiter’s model of a ‘general’ linearly elastic shell subject to a confinement condition. As expected, this model takes the form of variational inequalities posed over a non-empty closed convex subset of the function space used for the ‘unconstrained’ Koiter’s model. We then perform a rigorous asymptotic analysis as the thickness of the shell, considered a ‘small’ parameter, approaches zero, when the shell belongs to one of the three main classes of linearly elastic shells, namely elliptic membrane shells, generalized membrane shells and flexural shells. To illustrate the soundness of this model, we consider elliptic membrane shells to fix ideas. We then show that, in this case, the ‘limit’ model obtained in this fashion coincides with the two-dimensional ‘limit’ model obtained by means of another rigorous asymptotic analysis, but this time with the three-dimensional model of a ‘general’ linearly elastic shell subject to a confinement condition as a point of departure. In this fashion, our proposed Koiter’s model of a linearly elastic shell subject to a confinement condition is fully justified in this case, even though it is not itself a ‘limit’ model.

scholarly journals Solute dispersion along unsteady groundwater flow in a semi-infinite aquifer

1998 ◽  
Vol 2 (1) ◽  
pp. 93-100 ◽  
Author(s):  
N. Kumar ◽  
M. Kumar
Keyword(s):  
Groundwater Flow ◽  
Numerical Solutions ◽  
Seasonal Pattern ◽  
Longitudinal Direction ◽  
Time Dependent ◽  
Input Concentration ◽  
Sources Of Pollution ◽  
Time Period ◽  
Spatially Distributed ◽  
Human Use

Abstract. Analytical and numerical solutions are obtained for dispersion of pollutants along unsteady groundwater flow in a longitudinal direction through semi-infinite aquifers the permeability of which is either uniform or varies with position. Sources of pollution are both a concentrated point input at the origin and a spatially distributed background source. One expression chosen to represent the seasonal pattern of the time dependent velocity is sinusoidal behaviour over a year. The solutions obtained predict the time and distance from the location at which an input concentration is introduced at which the pollution concentration becomes harmless. Also, the time period for rehabilitating a polluted aquifer for human use can also be assessed.

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