### Abstract

This work examines the mechanics of the circumferentially prestressed N-layer artery, subject to axial tethering force and the internal pressure of blood, focusing on the uniform stretch state, the uniform circumferential stress states and the transitional states between them. Under increasing pressure the i^{th} layer is shown to experience five distinct stages, two of which are the uniform stretch state and the uniform circumferential stress state. For arbitrary strain energy density, simple analytical expressions are presented for the stress distributions and the internal pressure at these specialized states. For the 1-layer, uniform tubular model of an artery without axial tethering force, the results coincide with those of Destrade et al. (2012). For the 2-layer composite tube, which models the mechanically significant medial and adventitial layers of large elastic arteries, numerical solutions are obtained employing two microstructurally based constitutive models for medial and adventitial arterial tissues, respectively. These results indicate that the uniform stretch state, the uniform circumferential stress state of the medial layer, and the uniform circumferential stress state of the adventitial layer occur at the diastolic blood pressure, the mean blood pressure, and the systolic blood pressure, respectively.

Original language | English (US) |
---|---|

Article number | 110100 |

Journal | Journal of Theoretical Biology |

Volume | 486 |

DOIs | |

State | Published - Feb 7 2020 |

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### Keywords

- Composite tube
- Finite elasticity
- Mechanical homeostasis
- Uniform stretch/stress states
- Vascular mechanics

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

**On the uniform stress/uniform stretch states of prestressed arteries.** / Zhang, Xinyu; Levy, Alan J.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 486, 110100. https://doi.org/10.1016/j.jtbi.2019.110100

}

TY - JOUR

T1 - On the uniform stress/uniform stretch states of prestressed arteries

AU - Zhang, Xinyu

AU - Levy, Alan J.

PY - 2020/2/7

Y1 - 2020/2/7

N2 - This work examines the mechanics of the circumferentially prestressed N-layer artery, subject to axial tethering force and the internal pressure of blood, focusing on the uniform stretch state, the uniform circumferential stress states and the transitional states between them. Under increasing pressure the ith layer is shown to experience five distinct stages, two of which are the uniform stretch state and the uniform circumferential stress state. For arbitrary strain energy density, simple analytical expressions are presented for the stress distributions and the internal pressure at these specialized states. For the 1-layer, uniform tubular model of an artery without axial tethering force, the results coincide with those of Destrade et al. (2012). For the 2-layer composite tube, which models the mechanically significant medial and adventitial layers of large elastic arteries, numerical solutions are obtained employing two microstructurally based constitutive models for medial and adventitial arterial tissues, respectively. These results indicate that the uniform stretch state, the uniform circumferential stress state of the medial layer, and the uniform circumferential stress state of the adventitial layer occur at the diastolic blood pressure, the mean blood pressure, and the systolic blood pressure, respectively.

AB - This work examines the mechanics of the circumferentially prestressed N-layer artery, subject to axial tethering force and the internal pressure of blood, focusing on the uniform stretch state, the uniform circumferential stress states and the transitional states between them. Under increasing pressure the ith layer is shown to experience five distinct stages, two of which are the uniform stretch state and the uniform circumferential stress state. For arbitrary strain energy density, simple analytical expressions are presented for the stress distributions and the internal pressure at these specialized states. For the 1-layer, uniform tubular model of an artery without axial tethering force, the results coincide with those of Destrade et al. (2012). For the 2-layer composite tube, which models the mechanically significant medial and adventitial layers of large elastic arteries, numerical solutions are obtained employing two microstructurally based constitutive models for medial and adventitial arterial tissues, respectively. These results indicate that the uniform stretch state, the uniform circumferential stress state of the medial layer, and the uniform circumferential stress state of the adventitial layer occur at the diastolic blood pressure, the mean blood pressure, and the systolic blood pressure, respectively.

KW - Composite tube

KW - Finite elasticity

KW - Mechanical homeostasis

KW - Uniform stretch/stress states

KW - Vascular mechanics

UR - http://www.scopus.com/inward/record.url?scp=85076757837&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076757837&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2019.110100

DO - 10.1016/j.jtbi.2019.110100

M3 - Article

C2 - 31794705

AN - SCOPUS:85076757837

VL - 486

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

M1 - 110100

ER -