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Mechano-Chemical Fluid-structure Interactions and Active Materials

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Fluid-structure Interactions

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 118))

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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.

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References

  1. F. Brinkmann, Mathematical models and numerical simulation of mechanochemical pattern formation in biological tissues, Ph.D. thesis, University of Heidelberg, 2017

    Google Scholar 

  2. M.A.K. Bulelzai, J.L.A. Dubbeldam, Long time evolution of atherosclerotic plaques. J. Theor. Biol. 297, 1–10 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. 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)

    Article  MathSciNet  MATH  Google Scholar 

  4. 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)

    Article  MathSciNet  MATH  Google Scholar 

  5. 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

  6. L. Formaggia, A. Quarteroni, A. Veneziani, Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System (Springer, Milan, 2009)

    Book  MATH  Google Scholar 

  7. 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)

    Article  MathSciNet  MATH  Google Scholar 

  8. 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

    Google Scholar 

  9. 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)

    Article  MathSciNet  MATH  Google Scholar 

  10. G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering (Wiley-Blackwell, Chichester, 2000)

    MATH  Google Scholar 

  11. G.W. Jones, S.J. Chapman, Modeling growth in biological materials. SIAM Rev. 54(1), 52–118 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. E.K. Rodriguez, A. Hoger, A.D. McCulloch, Stress-dependent finite growth in soft elastic tissues. J. Biomech. 4, 455–467 (1994)

    Article  Google Scholar 

  13. F. Sonner, Analysis of temporal multiscales with partial differential equations, Ph.D. thesis, University of Erlangen-Nuremberg, 2018 (in preparation)

    Google Scholar 

  14. 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

    Google Scholar 

  15. 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)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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)

    Article  MathSciNet  Google Scholar 

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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

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