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dc.contributor.authorDu, Yangkun
dc.contributor.authorLü, Chaofeng
dc.contributor.authorChen, Weiqiu
dc.contributor.authorDestrade, Michel
dc.identifier.citationDu, Yangkun, Lü, Chaofeng, Chen, Weiqiu, & Destrade, Michel. (2018). Modified multiplicative decomposition model for tissue growth: Beyond the initial stress-free state. Journal of the Mechanics and Physics of Solids, 118, 133-151. doi:
dc.description.abstractThe multiplicative decomposition model is widely employed for predicting residual stresses and morphologies of biological tissues due to growth. However, it relies on the assumption that the tissue is initially in a stress-free state, which conflicts with the observations that any growth state of a biological tissue is under a significant level of residual stresses that helps to maintain its ideal mechanical conditions. Here, we propose a modified multiplicative decomposition model in which the initial state (or reference configuration) of a biological tissue is endowed with a residual stress instead of being stress-free.Releasing theoretically the initial residual stress, the initially stressed state is first transmitted into a virtual stress-free state, thus resulting in an initial elastic deformation. The initial virtual stress-free state subsequently grows to another counterpart with a growth deformation, and the latter is further integrated into its natural configuration of a real tissue with an excessive elastic deformation that ensures tissue compatibility. With this decomposition, the total deformation arising during growth may be expressed as the product of elastic deformation, growth deformation and initial elastic deformation, while the corresponding free energy density should depend on the initial residual stress and the total deformation. Three key issues including the explicit expression of the free energy density, the predetermination of the initial elastic deformation, and the initial residual stress are addressed.Finally, we consider a tubular organ as a representative example to demonstrate the effects of the proposed initial residual stress on stress distribution and on shape formation through an incremental stability analysis. Our results suggest that the initial residual stress exerts a major influence on the growth stress and the morphology of biological tissues. The model bridges the gap between any two growth states of a biological tissue that is endowed with a certain level of residual stresses. (C) 2018 Elsevier Ltd. All rights reserved.en_IE
dc.description.sponsorshipThis work was supported by the National Natural Science Foundation of China through grant Nos. 11621062 and 11772295, and was also partly supported by the Fundamental Research Funds for the Central Universities 2016XZZX001-05.en_IE
dc.relation.ispartofJournal Of The Mechanics And Physics Of Solidsen
dc.subjectModified multiplicative decomposition modelen_IE
dc.subjectTissue growthen_IE
dc.subjectInitial residual stressen_IE
dc.subjectVirtual stress-free stateen_IE
dc.titleModified multiplicative decomposition model for tissue growth: Beyond the initial stress-free stateen_IE
dc.contributor.funderNational Natural Science Foundation of Chinaen_IE
dc.contributor.funderFundamental Research Funds for the Central Universitiesen_IE
dc.local.contactMichel Destrade, Room Adb-1002, Áras De Brun, School Of Mathematics, Nui Galway. 2344 Email:

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