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    Morphoelasticity: A theory of elastic growth

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    Type
    Book Chapter
    Authors
    Goriely, Alain cc
    Moulton, Derek
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2011-10-11
    Online Publication Date
    2011-10-11
    Print Publication Date
    2011-05-26
    Permanent link to this record
    http://hdl.handle.net/10754/624960
    
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    Abstract
    This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.
    Citation
    Goriely A, Moulton D (2011) Morphoelasticity: A theory of elastic growth. New Trends in the Physics and Mechanics of Biological Systems: 153–176. Available: http://dx.doi.org/10.1093/acprof:oso/9780199605835.003.0006.
    Sponsors
    This work was supported by the National Science Foundation under grant DMS- 0907773 (AG). This publication is also based on work supported by Award No. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST).
    Publisher
    Oxford University Press (OUP)
    Journal
    New Trends in the Physics and Mechanics of Biological Systems
    DOI
    10.1093/acprof:oso/9780199605835.003.0006
    ae974a485f413a2113503eed53cd6c53
    10.1093/acprof:oso/9780199605835.003.0006
    Scopus Count
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