Morphoelasticity: A theory of elastic growth

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.