A homogenisation method for the multiscale modelling of transversely isotropic skeletal muscle tissue

A homogenisation method for the multiscale modelling of transversely isotropic skeletal muscle... Skeletal muscle tissue shows a wide variation in its mechanical response for different persons or different muscle types of one single person. These distinct mechanical properties are due to variations in the microstructure of the material. For skeletal muscles, especially the arrangement and the stiffness of collagen fibres in the connective tissue define the macroscopic passive stiffness, while the sarcomeres (contractile units) enable an active contractility of the muscles. Phenomenological models lack the ability to take into account such microstructural variations in a natural way and need to be fitted to experimental data, which is, however, not available for every desired muscle type. Thus, this work presents a homogenisation‐based multiscale model for skeletal muscle tissue which enables to include microstructural properties in a continuum‐mechanical framework. The underlying homogenisation is done by means of the tangent‐second‐order (TSO) method, which is appropriately extended in order to account for the transversely isotropic behaviour of the muscle material. Moreover, an angular‐integration model is embedded for a comprehensive description of the connective tissue. Concluding, the presented model allows to directly include microstructural‐based material properties on the continuum‐mechanical macroscale and yet avoids the expensiveness of computational homogenisation methods, like FE2, by using well‐founded analytical homogenisation techniques. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

A homogenisation method for the multiscale modelling of transversely isotropic skeletal muscle tissue

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710061
Publisher site
See Article on Publisher Site

Abstract

Skeletal muscle tissue shows a wide variation in its mechanical response for different persons or different muscle types of one single person. These distinct mechanical properties are due to variations in the microstructure of the material. For skeletal muscles, especially the arrangement and the stiffness of collagen fibres in the connective tissue define the macroscopic passive stiffness, while the sarcomeres (contractile units) enable an active contractility of the muscles. Phenomenological models lack the ability to take into account such microstructural variations in a natural way and need to be fitted to experimental data, which is, however, not available for every desired muscle type. Thus, this work presents a homogenisation‐based multiscale model for skeletal muscle tissue which enables to include microstructural properties in a continuum‐mechanical framework. The underlying homogenisation is done by means of the tangent‐second‐order (TSO) method, which is appropriately extended in order to account for the transversely isotropic behaviour of the muscle material. Moreover, an angular‐integration model is embedded for a comprehensive description of the connective tissue. Concluding, the presented model allows to directly include microstructural‐based material properties on the continuum‐mechanical macroscale and yet avoids the expensiveness of computational homogenisation methods, like FE2, by using well‐founded analytical homogenisation techniques. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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