scholarly journals Apprehending the effects of mechanical deformations in cardiac electrophysiology: A homogenization approach

2019 ◽  
Vol 29 (13) ◽  
pp. 2377-2417
Author(s):  
Annabelle Collin ◽  
Sébastien Imperiale ◽  
Philippe Moireau ◽  
Jean-Frédéric Gerbeau ◽  
Dominique Chapelle
Keyword(s):  
Cardiac Electrophysiology ◽  
Microscopic Level ◽  
Numerical Results ◽  
Specific Cell ◽  
Periodic Media ◽  
Cell Problem ◽  
Mechanical Deformations ◽  
Ionic Motion ◽  
Homogenization Approach ◽  
Homogenized Model

We follow a formal homogenization approach to investigate the effects of mechanical deformations in electrophysiology models relying on a bidomain description of ionic motion at the microscopic level. To that purpose, we extend these microscopic equations to take into account the mechanical deformations, and proceed by recasting the problem in the framework of classical two-scale homogenization in periodic media, and identifying the equations satisfied by the first coefficients in the formal expansions. The homogenized equations reveal some interesting effects related to the microstructure — and associated with a specific cell problem to be solved to obtain the macroscopic conductivity tensors — in which mechanical deformations play a nontrivial role, i.e. they do not simply lead to a standard bidomain problem posed in the deformed configuration. We then present detailed numerical illustrations of the homogenized model with coupled cardiac electrical–mechanical simulations — all the way to ECG simulations — albeit without taking into account the abundantly-investigated effect of mechanical deformations in ionic models, in order to focus here on other effects. And in fact our numerical results indicate that these other effects are numerically of a comparable order, and therefore cannot be disregarded.

Simulation-based verification of homogenization approach in predicting effective thermal conductivities of wavy orthotropic fiber composite

2019 ◽  
Vol 08 (04) ◽  
pp. 1950015
Author(s):  
C. Mahesh ◽  
K. Govindarajulu ◽  
V. Balakrishna Murthy
Keyword(s):  
Volume Fraction ◽  
Fiber Composite ◽  
Micromechanical Model ◽  
Two Stage ◽  
Micromechanics Models ◽  
Simulation Based ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Good Agreement ◽  
Thermal Conductivities

In this work, applicability of homogenization approach is verified with the micromechanics approach by considering wavy orthotropic fiber composite. Thermal conductivities of [Formula: see text]-300 orthotropic wavy fiber composite are determined for micromechanical model and compared with the results obtained by two stage homogenized model over volume fraction ranging from 0.1 to 0.6. Also, a methodology is suggested for reducing percentage deviation between homogenization and micromechanical approaches. Effect of debond on the thermal conductivities of wavy orthotrophic fiber composite is studied and compared with perfectly aligned fiber composite for different volume fraction. It is observed that results obtained by the homogenization approach are in good agreement with the results obtained through micromechanics approach. Maximum percentage deviation between homogenized and micromechanics models is 2.13%.

EFFECTIVE SLIP LENGTH: SOME ANALYTICAL AND NUMERICAL RESULTS

2015 ◽  
Vol 57 (1) ◽  
pp. 79-88
Author(s):  
XINGYOU (PHILIP) ZHANG ◽  
NAT J. LUND ◽  
SHAUN C. HENDY
Keyword(s):  
Stokes Flow ◽  
Traditional Method ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Numerical Results ◽  
Micro Scale ◽  
Slip Boundary ◽  
Effective Slip Length ◽  
Homogenization Approach ◽  
Effective Slip

More and more experimental evidence demonstrates that the slip boundary condition plays an important role in the study of nano- or micro-scale fluid. We propose a homogenization approach to study the effective slippage problem. We show that the effective slip length obtained by homogenization agrees with the results obtained by the traditional method in the literature for the simplest Stokes flow; then we use our approach to deal with two examples which seem quite hard by other analytical methods. We also include some numerical results to validate our analytical results.

scholarly journals A Rigorous Homogenization for a Two-Scale Convergence Approach to Piping Flow Erosion with Deposition in a Spatially Heterogeneous Soil

2020 ◽  
pp. 9-25
Author(s):  
Adu Sakyi ◽  
Peter Amoako-Yirenkyi ◽  
Isaac Kwame Dontwi
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Behaviour ◽  
Particle Deposition ◽  
Particle Concentration ◽  
Soil Particle ◽  
Length Scale ◽  
Soil Mixture ◽  
Heterogeneous Soil ◽  
Homogenization Approach ◽  
Homogenized Model

We present a rigorous homogenization approach to modelling piping ow erosion in a spatially heterogeneous soil. The aim is to provide a justication to a formal homogenization approach to piping ow erosion with deposition in a spatially heterogeneous soil. Under the assumption that the soil domain is perforated periodically with cylindrical repeating microstructure, we begin by proving that a solution to the proposed set of microscopic equations exist. Two-scale convergence is then used to study the asymptotic behaviour of solutions to the microscopic problem as the microscopic length scale approaches zero(0). We thus derive rigorously a homogenized model or macro problem as well as explicit formula for the eective coecients. A strong observation from the numerical simulation was that, soil particle concentration in the water/soil mixture decreases but at a decreasing rate whereas soil particle deposition increases at regions with increasing amount of particle concentration in the ow causing a reduction in bare pore spaces across the soil domain.

scholarly journals HOMOGENIZATION OF TRANSPORT PROCESSES AND HYDRATION PHENOMENA IN FRESH CONCRETE

2020 ◽  
Vol 60 (1) ◽  
pp. 12-24
Author(s):  
Michal Beneš ◽  
Radek Štefan
Keyword(s):  
Closed Form ◽  
Fresh Concrete ◽  
Mesoscale Model ◽  
Computational Cost ◽  
Cost Savings ◽  
Transport Processes ◽  
Cell Problem ◽  
Periodic Cell ◽  
Homogenized Model ◽  
Effective Models

The problem of hydration and transport processes in fresh concrete is strongly coupled and non- inear, and therefore, very difficult for a numerical modelling. Physically accurate results can be obtained using fine-scale simulations, which are, however, extremely time consuming. Therefore, there is an interest in developing new physically accurate and computationally effective models. In this paper, a new fully coupled two-scale (meso-macro) homogenization framework for modelling of simultaneous heat transfer, moisture flows, and hydration phenomena in fresh concrete is proposed. A modified mesoscalemodelisfirstintroduced. Inthismodel, concreteisassumedasacompositematerialwithtwo periodically distributed mesoscale components, cement paste and aggregates. A homogenized model is then derived by an upscaling method from the mesoscale model. The coefficients for the homogenized model are obtained from the solution of a periodic cell problem. For solving the periodic cell problem, two approaches are used – a standard finite element method and a simplified closed-form approximation taken from literature. The homogenization framework is then implemented in MATLAB environment and finally employed for illustrative numerical experiments, which verify that the homogenized model provides physically accurate results comparable with the results obtained by the mesoscale model. Moreover, it is verified that, using the homogenization framework with a closed-form approach to the periodic cell problem, significant computational cost savings can be achieved.

RESONANT DRIFT OF SPIRAL WAVES INDUCED BY MECHANICAL DEFORMATION

2010 ◽  
Vol 24 (29) ◽  
pp. 5733-5741 ◽  
Author(s):  
JIANG-XING CHEN ◽  
JIANG-RONG XU ◽  
HE-PING YING
Keyword(s):  
Explicit Formula ◽  
Drift Velocity ◽  
Mechanical Deformation ◽  
Spiral Waves ◽  
Numerical Results ◽  
Excitable Medium ◽  
Mechanical Deformations

The drift of rigidly rotating spiral waves in an excitable medium induced by synchronous and asynchronous mechanical deformation is investigated numerically and analytically. The resonant drift of spiral waves induced by a mechanical deformation with ω = ω0 and ω = 3ω0 is observed. At ω = ω0, synchronous and greatest degree of asynchronous mechanical deformations are specially investigated. For the case ω = 3ω0, synchronous mechanism deformation locks the spiral while decreasing of degree of synchronization increases the drift velocity. We derive an approximate but explicit formula of the spiral drift velocity and direction which is consistent with the numerical results.

scholarly journals On Some Thermoelastic Problem of a Nonhomogeneous Long Pipe

2021 ◽  
Vol 39 (5) ◽  
pp. 1430-1442
Author(s):  
Roman Kulchytsky-Zhyhailo ◽  
Stanisław J. Matysiak ◽  
Dariusz M. Perkowski
Keyword(s):  
Axial Stress ◽  
Layered Composite ◽  
Functionally Graded ◽  
Thermoelastic Problem ◽  
Graded Materials ◽  
Varying Thickness ◽  
Representative Cell ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Pipe Materials

The paper deals with the thermoelastic problem of a multilayered pipe subjected to normal loadings on its inner surface and temperature differences on its internal and external surfaces. Two types of nonhomogeneous pipe materials of pipe are considered: (1) a ring-layered composite composed of two repeated thermoelastic solids with varying thickness and (2) a functionally graded ring layer. The ring-layered pipe with periodic structure is investigated by using the homogenized model with microlocal parameters. A homogenization approach is proposed for the modelling of the FGM pipe. The analysis of obtained circumferential, radial and axial stress is presented in the form of figures and discussed in detail. It was shown that the proposed approach to the homogenization allows us to correctly calculate the averaged characteristics in the representative cell (the macro-characteristics) and also the characteristics dependent on the choice of the component in the representative cell (the micro-characteristics) for both microperiodic composites and functionally graded materials.

scholarly journals A Formal Homogenization Approach to Piping Flow Erosion with Deposition in a Spatially Heterogeneous Soil

2020 ◽  
pp. 26-45
Author(s):  
Adu Sakyi ◽  
Peter Amoako-Yirenkyi ◽  
Isaac Kwame Dontwi
Keyword(s):  
Particle Concentration ◽  
Seepage Flow ◽  
Soil Mass ◽  
Cylindrical Structures ◽  
Proposed Model ◽  
Effective Coefficients ◽  
Heterogeneous Soil ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Piping Erosion

We model and simulate piping erosion phenomena with deposition in a spatially heterogeneous soil mass motivated by seepage flow. The soil is considered to be a porous media with periodic positioning of pores spread around cylindrical structures or microstructures making the heterogeneities periodic in space.The period of the heterogeneities defines a microscopic length scale ϵ of the microscopic problem and this allows the use of periodic homogenization methods.We studied the asymptotic behaviour of the solutions to the micro problem as ϵ ! 0 and obtained a homogenized model or macro problem with explicit formula for effective coefficients. Numerical simulations of the proposed model captures the expected behaviour of soil particle concentration and deposition as observed in piping flow erosion phenomena.

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