Abstract
Many aspects in solid dynamics cannot be explained by an elastic response of the material. In some applications, the material undergoes active changes, e.g. by growth, swelling or generation of material, by chemically induced contractions or bending. In other situations, the reference state is not stress-free. If a log of wood is cut in two pieces, these will afterwards deform and spread.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
F. Brinkmann, Mathematical models and numerical simulation of mechanochemical pattern formation in biological tissues, Ph.D. thesis, University of Heidelberg, 2017
M.A.K. Bulelzai, J.L.A. Dubbeldam, Long time evolution of atherosclerotic plaques. J. Theor. Biol. 297, 1–10 (2012)
S. Čanić, E.H. Kim, Mathematical analysis of the quasilinear effects in a hyperbolic model of blood flow through compliant axisymmetric vessels. Math. Methods Appl. Sci. 26(14), 1161–1186 (2003)
C.X. Chen, Y. Ding, J.A. Gear, Numerical simulation of atherosclerotic plaque growth using two-way fluid-structural interaction. ANZIAM J. 53, 278–291 (2012)
M. Cilla, E. Peña, M.A. Martínez, Mathematical modelling of atheroma plaque formation and development in coronary arteries. J. R. Soc. Interface 11(90) (2013). http://dx.doi.org/10.1098/rsif.2013.0866
L. Formaggia, A. Quarteroni, A. Veneziani, Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System (Springer, Milan, 2009)
D. Forti, A. Quaini, M. Bukač, S. Čanić, S. Deparis, A monolithic approach to fluid-composite structure interaction. J. Sci. Comput. 71(1), 396–421 (2017)
S. Frei, Eulerian finite element methods for interface problems and fluid-structure interactions, Ph.D. thesis, Universität Heidelberg, Aug 2016. doi:10.11588/heidok.00021590
S. Frei, T. Richter, T. Wick, Long-term simulation of large deformation, mechano-chemical fluid-structure interactions in ALE and fully Eulerian coordinates. J. Comput. Phys. 321, 874–891 (2015)
G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering (Wiley-Blackwell, Chichester, 2000)
G.W. Jones, S.J. Chapman, Modeling growth in biological materials. SIAM Rev. 54(1), 52–118 (2012)
E.K. Rodriguez, A. Hoger, A.D. McCulloch, Stress-dependent finite growth in soft elastic tissues. J. Biomech. 4, 455–467 (1994)
F. Sonner, Analysis of temporal multiscales with partial differential equations, Ph.D. thesis, University of Erlangen-Nuremberg, 2018 (in preparation)
Y. Yang, Mathematical modeling and simulation of the evolution of plaques in blood vessels, Ph.D. thesis, Universität Heidelberg, 2014. doi:10.11588/heidok.00016425
Y. Yang, W. Jäger, M. Neuss-Radu, T. Richter, Mathematical modeling and simulation of the evolution of plaques in blood vessels. J. Math. Biol. 72(4), 973–996 (2016)
Y. Yang, T. Richter, W. Jaeger, M. Neuss-Radu, An ALE approach to mechano-chemical processes in fluid-structure interactions. Int. J. Numer. Math. Fluids 84(4), 199–220 (2017)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Richter, T. (2017). Mechano-Chemical Fluid-structure Interactions and Active Materials. In: Fluid-structure Interactions. Lecture Notes in Computational Science and Engineering, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-63970-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-63970-3_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63969-7
Online ISBN: 978-3-319-63970-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)