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High Order Whitney Forms on Simplices and the Question of Potentials Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Some Mathematical Properties of Morphoelasticity

Authors : Ginger Egberts, Daan Smits, Fred Vermolen, Paul van Zuijlen

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

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Abstract

We consider a morphoelastic framework that models permanent deformations. The text treats a stability assessment in one dimension and a preservation of symmetry in multiple dimensions. Next, we treat the influence of uncertainty in some of the field variables onto the predicted behaviour of tissue.

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previous chapter Equilibrium Path Analysis Including Bifurcations with an Arc-Length Method Avoiding A Priori Perturbations
next chapter Approximating Eigenvectors with Fixed-Point Arithmetic: A Step Towards Secure Spectral Clustering
Literature
1.
Hall, C.L.: Modelling of some biological materials using continuum mechanics. PhD-thesis at the Queensland University of Technology (2008)
2.
Rodriguez E., Hoger A., McCulloch A.: Stress-dependent finite growth in soft elastic tissues. J Biomech 27, 455–467 (1994)CrossRef
3.
Prokharau, P., Vermolen, F.J.: Stability analysis for a peri-implant osseointegration model. J. Math. Biol, 66, 351–382 (2013)MathSciNetCrossRef
4.
Koppenol, D.C., Vermolen, F.J.: Biomedical implications from a morphoelastic continuum model for the simulation of contracture formation in skin-grafts that cover excised burns. Biomech Model Mechanobiol, 16 (4), 1187–1206 (2017)CrossRef
Metadata
Title
Some Mathematical Properties of Morphoelasticity
Authors
Ginger Egberts
Daan Smits
Fred Vermolen
Paul van Zuijlen
Copyright Year
2021
Book
Numerical Mathematics and Advanced Applications ENUMATH 2019

Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-55874-1_111

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