Mathematical modelling of residual-stress based volumetric growth in soft matter

Ruoyu Huang, Raymond W. Ogden, Raimondo Penta

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
23 Downloads (Pure)


Growth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the "opening-angle" in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.
Original languageEnglish
Pages (from-to)223-241
Number of pages19
JournalJournal of Elasticity
Issue number1-2
Publication statusPublished - 20 May 2021


  • residual stress
  • volumetric growth
  • nonlinear elasticity


Dive into the research topics of 'Mathematical modelling of residual-stress based volumetric growth in soft matter'. Together they form a unique fingerprint.

Cite this