Nonlinear Morphoelastic Plates I: Genesis of Residual Stress

Abstract

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed and the existence of residually stressed states is established.