Influence of initial residual stress on growth and pattern creation for a layered aorta

Du, Yangkun, Lü, Chaofeng, Destrade, Michel, & Chen, Weiqiu. (2019). Influence of Initial Residual Stress on Growth and Pattern Creation for a Layered Aorta. Scientific Reports, 9(1), 8232. doi: 10.1038/s41598-019-44694-2

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 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.

Publisher

Nature Research

Rights

Attribution-NonCommercial-NoDerivs 3.0 Ireland

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Mathematics (Scholarly Articles)