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The deal.II Library, Version 8.5

by jppelteret

Authors:
D. Arndt, W. Bangerth, D. Davydov, T. Heister, L. Heltai, M. Kronbichler, M. Maier, J-P. Pelteret, B. Turcksin, D. Wells

This paper provides an overview of the new features of the finite element library deal.II version 8.5. [1]

[1] [doi] D. Arndt, W. Bangerth, D. Davydov, T. Heister, L. Heltai, M. Kronbichler, M. Maier, J-P. Pelteret, B. Turcksin, and D. Wells, “The \textttdeal.II Library, Version 8.5,” Journal of Numerical Mathematics, 2017.
[Bibtex]
@Article{arndt2017a,
author = {Arndt, D. and Bangerth, W. and Davydov, D. and Heister, T. and Heltai, L. and Kronbichler, M. and Maier, M. and Pelteret, J-P. and Turcksin, B. and Wells, D.},
title = {The \texttt{deal.II} Library, Version 8.5},
journal = {Journal of Numerical Mathematics},
year = {2017},
abstract = {This paper provides an overview of the new features of the finite element library deal.II version 8.5.},
comment = {Accepted},
doi = {10.1515/jnma-2017-0058},
owner = {Jean-Paul Pelteret},
timestamp = {2017.03.23},
}

Preparation of magnetorheological elastomers and their slip-free characterization by means of parallel-plate rotational rheometry

by jppelteret

Authors: B. L. Walter, J-P. Pelteret, J. Kaschta, D. W. Schubert and P. Steinmann

A systematic study is presented to highlight a methodology of sample preparation and subsequent slip-free characterization of magnetorheological (MR) elastomers in parallel-plate rotational rheometry. Focusing on the magnetic field-dependent nonlinear viscoelastic behavior an array of oscillatory strain sweep measurements is conducted with samples cured within the rheometer.
The examined nonlinear material response (i.e. the amplitude dependence of the storage and loss moduli) as a function of the applied magnetic field is found to be qualitatively similar to the amplitude dependence of particle reinforced elastomers (i.e. the Payne effect). Therefore, the experimental data (both moduli) is decomposed similar to that for reinforced elastomers and a phenomenological model is formulated for both the storage and loss modulus to account for the physical mechanisms governing the nonlinear material characteristics.
Parameter identification suggests that the material response at low magnetic fields is dominated by the polymeric network whereas the strong magneto-reinforced microstructure governs the linear and nonlinear viscoelastic behavior at high magnetic fields. The overall experimental outcome further suggests that the underlying concept of the phenomenological model for particle reinforced elastomers (i.e. destruction and reformation of the filler network) can be transfered to magnetorheological materials. Consequently, the proposed phenomenological model can be applied to quantify and further analyze the nonlinear response characteristics of MR elastomers (i.e. the amplitude dependence of the storage and loss modulus as a function of the applied magnetic field) that is closely linked to microstructural changes of the magnetizable particle network. [1]

[1] [doi] B. L. Walter, J-P. Pelteret, J. Kaschta, D. W. Schubert, and P. Steinmann, “Preparation of magnetorheological elastomers and their slip-free characterization by means of parallel-plate rotational rheometry,” Smart Materials and Structures, 2017.
[Bibtex]
@Article{walter2017c-preprint,
author = {Walter, B. L. and Pelteret, J-P. and Kaschta, J. and Schubert, D. W. and Steinmann, P.},
title = {Preparation of magnetorheological elastomers and their slip-free characterization by means of parallel-plate rotational rheometry},
journal = {Smart Materials and Structures},
year = {2017},
note = {Accepted},
abstract = {A systematic study is presented to highlight a methodology of sample preparation and subsequent slip-free characterization of magnetorheological (MR) elastomers in parallel-plate rotational rheometry. Focusing on the magnetic field-dependent nonlinear viscoelastic behavior an array of oscillatory strain sweep measurements is conducted with samples cured within the rheometer.
The examined nonlinear material response (i.e. the amplitude dependence of the storage and loss moduli) as a function of the applied magnetic field is found to be qualitatively similar to the amplitude dependence of particle reinforced elastomers (i.e. the Payne effect). Therefore, the experimental data (both moduli) is decomposed similar to that for reinforced elastomers and a phenomenological model is formulated for both the storage and loss modulus to account for the physical mechanisms governing the nonlinear material characteristics.
Parameter identification suggests that the material response at low magnetic fields is dominated by the polymeric network whereas the strong magneto-reinforced microstructure governs the linear and nonlinear viscoelastic behavior at high magnetic fields. The overall experimental outcome further suggests that the underlying concept of the phenomenological model for particle reinforced elastomers (i.e. destruction and reformation of the filler network) can be transfered to magnetorheological materials. Consequently, the proposed phenomenological model can be applied to quantify and further analyze the nonlinear response characteristics of MR elastomers (i.e. the amplitude dependence of the storage and loss modulus as a function of the applied magnetic field) that is closely linked to microstructural changes of the magnetizable particle network.},
doi = {10.1088/1361-665X/aa6b63},
file = {walter2017c-preprint.pdf:PDF/walter2017c-preprint.pdf:PDF},
keywords = {magnetorheological elastomers (MREs), field-responsive materials, large amplitude oscillatory shear (LAOS), magnetorheometry, magneto-induced Payne effect},
owner = {Jean-Paul Pelteret},
timestamp = {2017.03.07},
}

On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry – II. Influence of experimental conditions

by jppelteret

Authors: B. L. Walter, J-P. Pelteret, J. Kaschta, D. W. Schubert and P. Steinmann

The use of parallel-plate rotational rheometery to characterize ex situ pre-prepared samples of rubber-like polymers is motivated by, for example, the investigation of magneto-rheological elastomers. When exceeding a critical excitation amplitude in oscillatory shear experiments, these elastomeric samples are prone to slip at the sample-plate contact interface. This phenomenon, known as wall slip, starts to occur at the sample’s outer rim and leads to an imperfect force transfer onto the sample. This results in a systematic error of measured rheological material quantities.
A thorough investigation is presented to reveal how this phenomenon is affected by selected experimental conditions, namely the static axial preload and measuring frequency. For this purpose disc-shaped samples composed of an unfilled silicone rubber are prepared by casting and examined by means of a controlled stress rotational rheometer equipped with a serrated rotor configuration.
The oscillatory strain sweep experiments suggest that wall slip, exclusively present at the serrated rotor surface, is significantly influenced by the static preload. In contrast, only a slight frequency dependence is observed within the examined experimental conditions.
Further insights into the wall slip mechanism were attained by two novel methodologies. It is shown that it is possible to produce a master curve for the various applied preloads. This demonstrates that the physical mechanism behind wall slip is independent of the axial force. Furthermore, we derive an empirical model for the criterion governing the onset of wall slip. This links the critical stress at which wall slip is initiated to the static friction condition and geometrical aspects of the rotor configuration. From this it is anticipated that the conditions for reliable experiments involving ex situ pre-prepared samples composed of low damping elastomers can, in the future, be estimated a priori. [1]

[1] [doi] B. L. Walter, J-P. Pelteret, J. Kaschta, D. W. Schubert, and P. Steinmann, “On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry — II. Influence of experimental conditions,” Polymer Testing, 2017.
[Bibtex]
@Article{walter2017b-preprint,
author = {Walter, B. L. and Pelteret, J-P. and Kaschta, J. and Schubert, D. W. and Steinmann, P.},
title = {On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry -- II. Influence of experimental conditions},
journal = {Polymer Testing},
year = {2017},
note = {Accepted},
abstract = {The use of parallel-plate rotational rheometery to characterize ex situ pre-prepared samples of rubber-like polymers is motivated by, for example, the investigation of magneto-rheological elastomers. When exceeding a critical excitation amplitude in oscillatory shear experiments, these elastomeric samples are prone to slip at the sample-plate contact interface. This phenomenon, known as wall slip, starts to occur at the sample's outer rim and leads to an imperfect force transfer onto the sample. This results in a systematic error of measured rheological material quantities.
A thorough investigation is presented to reveal how this phenomenon is affected by selected experimental conditions, namely the static axial preload and measuring frequency. For this purpose disc-shaped samples composed of an unfilled silicone rubber are prepared by casting and examined by means of a controlled stress rotational rheometer equipped with a serrated rotor configuration.
The oscillatory strain sweep experiments suggest that wall slip, exclusively present at the serrated rotor surface, is significantly influenced by the static preload. In contrast, only a slight frequency dependence is observed within the examined experimental conditions.
Further insights into the wall slip mechanism were attained by two novel methodologies. It is shown that it is possible to produce a master curve for the various applied preloads. This demonstrates that the physical mechanism behind wall slip is independent of the axial force. Furthermore, we derive an empirical model for the criterion governing the onset of wall slip. This links the critical stress at which wall slip is initiated to the static friction condition and geometrical aspects of the rotor configuration. From this it is anticipated that the conditions for reliable experiments involving ex situ pre-prepared samples composed of low damping elastomers can, in the future, be estimated a priori.},
doi = {10.1016/j.polymertesting.2017.05.036},
file = {walter2017b-preprint.pdf:PDF/walter2017b-preprint.pdf:PDF},
keywords = {wall slip, adhesive failure, measuring artifact, large amplitude oscillatory shear, parallel-plate rotational rheometry},
owner = {Jean-Paul Pelteret},
timestamp = {2017.03.07},
}

On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry – I. Detecting wall slip

by jppelteret

Authors: B. L. Walter, J-P. Pelteret, J. Kaschta, D. W. Schubert and P. Steinmann

A systematic study is presented in order to reveal the occurrence of wall slip of pre-prepared elastomeric samples characterized with the use of rotational rheometry. To exclude effects that could be attributed to additional functional fillers, both an unfilled (primarily used) and lightly silica reinforced (complementary system) silicone rubber are evaluated. Cylindrical samples are prepared by casting using a standardized methodology and examined by means of a stress-controlled parallel-plate rotational rheometer. As a control test, samples are also cured within the rheometer (in situ), thereby fixing them to the measuring plates and firmly establishing their response in “no-slip” conditions. The experiments suggest that wall slip, postulated to be caused by an adhesive failure at the sample-plate interface, may occur if the deformation is sufficiently large and no cohesive failure is present. It is detected by an increase in the loss modulus that is related to the adhesive failure associated with local dynamic friction, resulting in increased dissipated energy. Direct (via raw waveform data and normalized Lissajous figures) and indirect (via fast-Fourier-transformation) analysis of the overall system response for a single steady state deformation cycle provided further insights into the mechanism of wall slip. [1]

[1] [doi] B. L. Walter, J-P. Pelteret, J. Kaschta, D. W. Schubert, and P. Steinmann, “On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry — I. Detecting wall slip,” Polymer Testing, 2017.
[Bibtex]
@Article{walter2017a-preprint,
author = {Walter, B. L. and Pelteret, J-P. and Kaschta, J. and Schubert, D. W. and Steinmann, P.},
title = {On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry -- I. Detecting wall slip},
journal = {Polymer Testing},
year = {2017},
note = {Accepted},
abstract = {A systematic study is presented in order to reveal the occurrence of wall slip of pre-prepared elastomeric samples characterized with the use of rotational rheometry. To exclude effects that could be attributed to additional functional fillers, both an unfilled (primarily used) and lightly silica reinforced (complementary system) silicone rubber are evaluated. Cylindrical samples are prepared by casting using a standardized methodology and examined by means of a stress-controlled parallel-plate rotational rheometer. As a control test, samples are also cured within the rheometer (in situ), thereby fixing them to the measuring plates and firmly establishing their response in "no-slip" conditions. The experiments suggest that wall slip, postulated to be caused by an adhesive failure at the sample-plate interface, may occur if the deformation is sufficiently large and no cohesive failure is present. It is detected by an increase in the loss modulus that is related to the adhesive failure associated with local dynamic friction, resulting in increased dissipated energy. Direct (via raw waveform data and normalized Lissajous figures) and indirect (via fast-Fourier-transformation) analysis of the overall system response for a single steady state deformation cycle provided further insights into the mechanism of wall slip.},
doi = {10.1016/j.polymertesting.2017.05.035},
file = {walter2017a-preprint.pdf:PDF/walter2017a-preprint.pdf:PDF},
keywords = {wall slip, adhesive failure, measuring artifact, large amplitude oscillatory shear, silicone rubber, parallel-plate rotational rheometry},
owner = {Jean-Paul Pelteret},
timestamp = {2017.03.07},
}

On the h-adaptive PUM and the hp-adaptive FEM approaches applied to PDEs in quantum mechanics

by jppelteret

Authors: D. Davydov, T. Gerasimov, J-P. V. Pelteret, and P. Steinmann

In this paper the h-adaptive partition-of-unity method and the h- and hp-adaptive finite element method are applied to partial differential equations arising in quantum mechanics, namely, the Schrodinger equation with Coulomb and harmonic potentials, and the Poisson problem. Implementational details of the partition-of-unity method related to enforcing continuity with hanging nodes and the degeneracy of the basis are discussed. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling implementation of error-controlled adaptive mesh refinement strategies. To that end, local interpolation error estimates are derived for the partition-of-unity method enriched with a class of exponential functions. The results are the same as for the finite element method and thereby admit the usage of standard residual error indicators. The efficiency of the h -adaptive partition-of- unity method is compared to the h – and h p -adaptive finite element method. The latter is implemented by adopting the analyticity estimate from Legendre coefficients. An extension of this approach to multiple solution vectors is proposed. Numerical results confirm the remarkable accuracy of the h -adaptive partition-of-unity approach. In case of the Hydrogen atom, the h -adaptive linear partition-of-unity method was found to be comparable to the hp -adaptive finite element method for the target eigenvalue accuracy of 10-3. [1]

[1] D. Davydov, T. Gerasimov, J-P. Pelteret, and P. Steinmann, “On the h-adaptive PUM and the hp-adaptive FEM approaches applied to PDEs in quantum mechanics,” Journal of Scientific Computing, 2017.
[Bibtex]
@Article{davydov2016a-preprint,
author = {Davydov, D. and Gerasimov, T. and Pelteret, J-P. and Steinmann, P.},
title = {On the h-adaptive PUM and the hp-adaptive FEM approaches applied to PDEs in quantum mechanics},
journal = {Journal of Scientific Computing},
year = {2017},
note = {Submitted},
abstract = {In this paper the h-adaptive partition-of-unity method and the h- and hp-adaptive finite element method are applied to partial differential equations arising in quantum mechanics, namely, the Schrodinger equation with Coulomb and harmonic potentials, and the Poisson problem. Implementational details of the partition-of-unity method related to enforcing continuity with hanging nodes and the degeneracy of the basis are discussed. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling implementation of error-controlled adaptive mesh refinement strategies. To that end, local interpolation error estimates are derived for the partition-of-unity method enriched with a class of exponential functions. The results are the same as for the finite element method and thereby admit the usage of standard residual error indicators. The efficiency of the h -adaptive partition-of- unity method is compared to the h - and h p -adaptive finite element method. The latter is implemented by adopting the analyticity estimate from Legendre coefficients. An extension of this approach to multiple solution vectors is proposed. Numerical results confirm the remarkable accuracy of the h -adaptive partition-of-unity approach. In case of the Hydrogen atom, the h -adaptive linear partition-of-unity method was found to be comparable to the hp -adaptive finite element method for the target eigenvalue accuracy of 10-3.},
comment = {Submitted},
file = {davydov2016a-preprint.pdf:Users/jp/Documents/Academic/My_articles/Website/davydov2016a-preprint.pdf:PDF},
keywords = {Adaptive finite element method, partition-of-unity method, error estimators, hp-adaptive finite element method, Schrodinger equation, local interpolation error estimates},
owner = {Jean-Paul Pelteret},
timestamp = {2016.05.19},
url = {https://arxiv.org/abs/1612.02305},
}

Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space

by jppelteret

Authors: J-P. V. Pelteret, D. Davydov, A. McBride, D. K. Vu, and P. Steinmann

In this work a mixed variational formulation to simulate quasi-incompressible electro- or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media. [1]

[1] [doi] J-P. V. Pelteret, D. Davydov, A. McBride, D. K. Vu, and P. Steinmann, “Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space,” International Journal for Numerical Methods in Engineering, vol. 108, iss. 11, pp. 1307-1342, 2016.
[Bibtex]
@Article{pelteret2016a-preprint,
author = {Pelteret, J-P. V. and Davydov, D. and McBride, A. and Vu, D. K. and Steinmann, P.},
title = {Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space},
journal = {International Journal for Numerical Methods in Engineering},
year = {2016},
volume = {108},
number = {11},
pages = {1307--1342},
abstract = {In this work a mixed variational formulation to simulate quasi-incompressible electro- or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem. Exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media.},
comment = {PREPRINT},
doi = {10.1002/nme.5254},
file = {pelteret2016a-preprint.pdf:PDF/pelteret2016a-preprint.pdf:PDF},
keywords = {Nonlinear electro-/magneto-elasticity; quasi-incompressible media; free space; finite strain},
owner = {Jean-Paul Pelteret},
timestamp = {2016.03.21},
}

Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure

by jppelteret

Authors: P. Saxena, J-P. V. Pelteret, and P. Steinmann

Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a ‘chain deformation gradient’ and a ‘chain magnetic field’. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading. [1]

[1] [pdf] [doi] P. Saxena, J-P. V. Pelteret, and P. Steinmann, “Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure,” European Journal of Mechanics A/Solids, vol. 50, pp. 132-151, 2015.
[Bibtex]
@Article{saxena2015a-preprint,
author = {Saxena, P. and Pelteret, J-P. V. and Steinmann, P.},
title = {Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure},
journal = {European Journal of Mechanics A/Solids},
year = {2015},
volume = {50},
pages = {132--151},
month = {March--April},
abstract = {Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a 'chain deformation gradient' and a 'chain magnetic field'. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading.},
doi = {10.1016/j.euromechsol.2014.10.005},
file = {saxena2015a-preprint.pdf:PDF/saxena2015a-preprint.pdf:PDF},
keywords = {Nonlinear magnetoelasticity; Anisotropy; Chain dispersion},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

Magnetic force and torque on particles subject to a magnetic field

by jppelteret

Authors: F. Vogel, J-P. V. Pelteret, S. Kaessmair, and P. Steinmann

Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier. [1]

[1] [pdf] [doi] F. Vogel, J-P. V. Pelteret, S. Kaessmair, and P. Steinmann, “Magnetic force and torque on particles subject to a magnetic field,” European Journal of Mechanics A/Solids, vol. 48, pp. 23-31, 2014.
[Bibtex]
@Article{vogel2014a-preprint,
author = {Vogel, F. and Pelteret, J-P. V. and Kaessmair, S. and Steinmann, P.},
title = {Magnetic force and torque on particles subject to a magnetic field},
journal = {European Journal of Mechanics A/Solids},
year = {2014},
volume = {48},
pages = {23--31},
month = {November--December},
abstract = {Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier.},
doi = {10.1016/j.euromechsol.2014.03.007},
file = {vogel2014a-preprint.pdf:PDF/vogel2014a-preprint.pdf:PDF},
keywords = {Magnetoactive materials; Magnetoelasticity; Finite-element method},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

Comparison of several staggered atomistic-to-continuum concurrent coupling strategies

by jppelteret

Authors: D. Davydov, J-P. V. Pelteret, and P. Steinmann

In this contribution several staggered schemes used to couple continuum mechanics (CM) and molecular mechanics (MM) are proposed. The described approaches are based on the atomistic-to-continuum correspondence, obtained by spatial averaging in the spirit of Irving and Kirkwood, and Noll. Similarities between this and other concurrent coupling schemes are indicated, thus providing a broad overview of different approaches in the field. The schemes considered here are decomposed into the surface-type (displacement or traction boundary conditions) and the volume-type. The latter restricts the continuum displacement field (and possibly its gradient) in some sense to the atomistic (discrete) displacements using Lagrange multipliers. A large-strain CM formulation incorporating Lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented. Finally, the described coupling methods are numerically examined using two examples: uniaxial deformation and a plate with a hole relaxed under surface tension. Accuracy and convergence rates of each method are reported. It was found that the displacement (surface) coupling scheme and the Lagrangian (volume) scheme based on either discrete displacements or the H1 norm derived from continuous displacement fields provide the best performance. [1]

[1] [pdf] [doi] D. Davydov, J-P. Pelteret, and P. Steinmann, “Comparison of several staggered atomistic-to-continuum concurrent coupling strategies,” Computer Methods in Applied Mechanics and Engineering, vol. 277, pp. 260-280, 2014.
[Bibtex]
@Article{davydov2014a-preprint,
author = {Davydov, D. and Pelteret, J-P. and Steinmann, P.},
title = {Comparison of several staggered atomistic-to-continuum concurrent coupling strategies},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2014},
volume = {277},
pages = {260--280},
month = {August},
abstract = {In this contribution several staggered schemes used to couple continuum mechanics (CM) and molecular mechanics (MM) are proposed. The described approaches are based on the atomistic-to-continuum correspondence, obtained by spatial averaging in the spirit of Irving and Kirkwood, and Noll. Similarities between this and other concurrent coupling schemes are indicated, thus providing a broad overview of different approaches in the field. The schemes considered here are decomposed into the surface-type (displacement or traction boundary conditions) and the volume-type. The latter restricts the continuum displacement field (and possibly its gradient) in some sense to the atomistic (discrete) displacements using Lagrange multipliers. A large-strain CM formulation incorporating Lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented.
Finally, the described coupling methods are numerically examined using two examples: uniaxial deformation and a plate with a hole relaxed under surface tension. Accuracy and convergence rates of each method are reported. It was found that the displacement (surface) coupling scheme and the Lagrangian (volume) scheme based on either discrete displacements or the H1 norm derived from continuous displacement fields provide the best performance.},
doi = {10.1016/j.cma.2014.04.013},
file = {davydov2014a-preprint.pdf:PDF/davydov2014a-preprint.pdf:PDF},
keywords = {Concurrent multiscale methods; Atomic-to-continuum coupling methods; Molecular mechanics; Irving-Kirkwood-Noll procedure; Finite elements; Large strain},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
}

A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea

by jppelteret

Author: J-P. V. Pelteret

Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnoea. The anatomy of the tongue and other upper airway tissues, and the ability to model their behaviour, is central to such investigations.

In this thesis, details of the construction and development of a three-dimensional finite element model of soft tissues of the human upper airway, as well as a simplified fluid model of the airway, are provided. The anatomical data was obtained from the Visible Human Project, and its underlying micro-histological data describing tongue musculature were also extracted from the same source and incorporated into the model. An overview of the mathematical models used to describe tissue behaviour, both at a macro- and microscopic level, is given. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group to a priori unknown external forces was determined through the use of a genetic algorithm-based neural control model.

The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. The response of the various muscles of the tongue to the complex loading developed during breathing is determined, with a particular focus being placed to that of the genioglossus. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. A comparison is then made to the response determined under quasi-static conditions using the pressure distribution extracted from computational fluid-dynamics results. An analytical model describing the time-dependent response of the components of the tongue musculature most active during oral breathing is developed and validated. It is then modified to simulate the activity of the tongue during sleep and under conditions relating to various possible neural and physiological pathologies. The retroglossal movement of the tongue resulting from the pathologies is quantified and their role in the potential to induce airway collapse is discussed. [1]

[1] [pdf] J-P. V. Pelteret, “A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea,” Engineering PhD Thesis, Rondebosch, Western Cape, South Africa, 2013.
[Bibtex]
@PhdThesis{pelteret2013b-phd_thesis,
author = {Pelteret, J-P. V.},
title = {A computational neuromuscular model of the human upper airway with application to the study of obstructive sleep apnoea},
school = {University of Cape Town},
year = {2013},
type = {Engineering},
address = {Rondebosch, Western Cape, South Africa},
month = {November},
abstract = {Numerous challenges are faced in investigations aimed at developing a better understanding of the pathophysiology of obstructive sleep apnoea. The anatomy of the tongue and other upper airway tissues, and the ability to model their behaviour, is central to such investigations.
In this thesis, details of the construction and development of a three-dimensional finite element model of soft tissues of the human upper airway, as well as a simplified fluid model of the airway, are provided. The anatomical data was obtained from the Visible Human Project, and its underlying micro-histological data describing tongue musculature were also extracted from the same source and incorporated into the model. An overview of the mathematical models used to describe tissue behaviour, both at a macro- and microscopic level, is given. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group to a priori unknown external forces was determined through the use of a genetic algorithm-based neural control model.
The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. The response of the various muscles of the tongue to the complex loading developed during breathing is determined, with a particular focus being placed to that of the genioglossus. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. A comparison is then made to the response determined under quasi-static conditions using the pressure distribution extracted from computational fluid-dynamics results. An analytical model describing the time-dependent response of the components of the tongue musculature most active during oral breathing is developed and validated. It is then modified to simulate the activity of the tongue during sleep and under conditions relating to various possible neural and physiological pathologies. The retroglossal movement of the tongue resulting from the pathologies is quantified and their role in the potential to induce airway collapse is discussed.},
file = {pelteret2013b-phd_thesis.pdf:PDF/pelteret2013b-phd_thesis.pdf:PDF},
keywords = {sleep-disordered breathing; obstructive sleep apnoea; tongue; human upper airway; computational model; skeletal muscle model; Hill three-element model; neural control model; genetic algorithm; finite element method},
owner = {Jean-Paul Pelteret},
timestamp = {2015.10.11},
url = {http://hdl.handle.net/11427/9519},
}