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.
|Title of host publication
|New Trends in the Physics and Mechanics of Biological Systems
|Oxford University Press (OUP)
|Number of pages
|Published - Oct 11 2011
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.