The Mathematical Institute, University of Oxford, Eprints Archive

The Physics and Mechanics of Biological Systems

Goriely, A. and Moulton, D. E. (2011) The Physics and Mechanics of Biological Systems. In: New Trends in the Physics and Mechanics or Biological Systems: Lecture Notes of the Les Houches Summer Schools, Vol 92. Oxford University Press.

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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.

Item Type:Book Section
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:987
Deposited By:Peter Hudston
Deposited On:08 Nov 2011 09:48
Last Modified:08 Nov 2011 09:48

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