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

Huang, Ruoyu and Ogden, Raymond W. and Penta, Raimondo (2021) Mathematical modelling of residual-stress based volumetric growth in soft matter. Journal of Elasticity, 145 (1-2). pp. 223-241. ISSN 0374-3535 (

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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.