A corotational membrane finite element for biological tissues analysis

In the field of cardiovascular disease, reliable, predictive, patient-specific biomechanical analyses would be extremely useful for diagnosis and optimisation of therapy, but their achievement is a difficult challenge. Several biological organs or constructs, e.g. aortic valve leaflets or aortic root, are shell-like structures undergoing large displacements and small-to-moderate strains in their physiological or pathological functioning. This makes corotational shell finite-element formulations particularly attractive for the biomechanical analysis of those structures. However, most of available corotational formulations deal with linear elastic material, whereas biological tissues are characterised by a complex nonlinear constitutive behaviour, often modeled by means of anisotropic hyperelastic constitutive relationships. The aim of this work is to investigate the feasibility of extending corotational shell finite-element formulations to the realm of biological hyperelastic materials. For the sake of simplicity, this study is restricted to membranal behaviour. A Matlab-based corotational code has been developed, implementing classical membrane elements with drilling degrees of freedom, such as OPT and ITW elements. Different modifications of their weak formulations, implying hyperelastic anisotropic constitutive behaviour in the framework of either small or moderate strains, are proposed, implemented and compared. The performance of the obtained elements and their range of applicability are evaluated by comparison with available analytical or numerical solutions of benchmark problems.