Inverse nonlinear elastostatic analysis of heterogeneous pre-stressed arterial cross-sections with elastic bed supports: an unfitted approach

• Novel formulation for inverse finite elastostatics in problems with elastic bed support. • Immerse boundary finite elements framework using hierarchic level-sets to describe the geometry. • The methodology effectively identifies the unloaded configuration of arterial sections. This manuscript presents a novel formulation for inverse finite elastostatics in problems with elastic bed support on the external boundary (elastic bed boundary condition), replacing the classical Dirichlet boundary condition. An unfitted strategy to compute the solution of the mechanical problem is devised, inspired in the Immersed Boundary (IB) framework, and using level sets to describe the geometry. The method is applied to study realistic atherosclerotic arterial sections, which are known to exhibit a pre-stressed configuration. Furthermore, we demonstrate that our method effectively identifies the unloaded configuration. Taking as reference a classical finite elements solver in a commercial code, the method presented results in error lower than 3 % in displacements, for sufficiently fine meshes.