A new formulation of slight compressibility for arterial tissue and its Finite Element implementation

Abstract

In order to avoid the numerical difficulties in locally enforcing the incompressibility constraint using the displacement formulation of the Finite Element Method, slight compressibility is typically assumed when simulating the mechanical response of arterial tissue. The current standard method of accounting for slight compressibility of hyperelastic soft tissue assumes an additive decomposition of the strain-energy function into a volumetric and a deviatoric part. This has been shown, however, to be inconsistent with the linear theory and results in cubes retaining their cuboid shape under hydrostatic tension and compression, which seems at variance with the reinforcement of arterial tissue with two families of collagen fibres. A remedy for these defects is proposed here, a solution which generalises the current standard model of slight compressibility to include two additional terms, one of which is quadratic in the invariants and the other quadratic in . Experimental data are used to motivate typical values for the associated material constants of these additional terms. Some simulations are performed to allow contrasts and comparisons to be made between the current standard model of slight compressibility and its generalisation proposed here.

Keywords:

• Anisotropic materials
• arterial tissue
• slight compressibility
• finite element method
• two families of fibres

Acknowledgements

This paper has been improved by the incorporation of the suggestions and comments of the anonymous reviewers, to whom we are grateful for their constructive criticism.

Notes

No potential conflict of interest was reported by the authors.

Supplemental data for this article can be accessed here http://dx.doi.org/10.1080/10255842.2016.1236371

Additional information

Funding

The work of DMacM and BP was supported by Science Foundation Ireland [project number 12/IP/1732].