Influence of Initial Residual Stress on Growth and Pattern Creation for a Layered Aorta

Abstract

Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growth-induced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters.This modelling provides promising avenues for designing and directing some appropriate morphology of a given tissue or organ and achieve some targeted biomedical function. In this paper, we rely on a modified, augmented theory to reveal how we can obtain growth-induced residual stress and pattern evolution of a layered artery by starting from an existing, non-zero initial residual stress state. We use experimentally determined residual stress arXiv:2009.06098v1 [cond-mat.soft] 13 Sep 2020 distributions of aged bi-layered human aortas and quantify their influence by a magnitude factor. Our results show that initial residual stress has a more significant impact on residual stress accumulation and the subsequent evolution of patterns than geometry and material parameters.Additionally, we provide an essential explanation for growth-induced patterns driven by differential growth coupled to an initial residual stress. Finally, we show that initial residual stress is a readily available way to control growth-induced pattern creation for tissues and thus may provide a promising inspiration for biomedical engineering.

Electro-mechanically guided growth and patterns

“…Our numerical results suggest that growth instability and pattern formation can be guided or controlled by an electric field, instead of by purely mechanical means (such as changing elasticity, thickness, and initial residual stress, see Ciarletta et al (2014), Balbi et al (2015), Du, Lu, Liu, Han, Li, Chen, Qu & Destrade (2019), Du, Lü, Destrade & Chen (2019)). In principle, the coupling can be also used to design a pattern prescription strategy, growth self-assembly, drug delivery devices, or 4D bio-mimetic printing in engineering.…”

“…With volume growth theory (Rodriguez et al 1994, Amar & Goriely 2005, residual stress accumulation and pattern evolution are well explained as a result of re-balancing the incompatible volume swelling/absorption and excessive residual stress (Li et al 2011, Ciarletta et al 2014, Balbi et al 2015. Moreover, as residual stress is created and conserved throughout the whole growth process, stress-or strain-dependent growth models have been proposed theoretically and verified experimentally (Fung 1991, Du et al 2018, Du, Lu, Liu, Han, Li, Chen, Qu & Destrade 2019, Du, Lü, Destrade & Chen 2019.…”

Prescribing patterns in growing tubular soft matter by initial residual stress

“…The onset of instability is analyzed by relying on linear incremental theory 30 and on our previous papers 9,26 .…”

“…see 9,26 for details. Finally, by iterating over the wrinkle numbers m and n for the numerical solution of Eq.…”

“…In real-ity, long-term growth and remodelling processes and other biointeractions are impossible to track and reconstruct for living matter. Hence, the stress-free assumption for the initial state is too strong, and neglecting initial residual stress may affect the analysis of growth-induced residual stress and the resulting pattern selection, as we have proofed in our previous paper 26 on the growth human aorta with different initial residual stress.…”