Mechanical Characterization of Biological Membranes with Moiré Techniques and Multi-Point Simulated Annealing

Abstract

This paper describes an hybrid procedure for mechanical characterization of biological membranes. The in-plane displacement field of a glutaraldehyde treated bovine pericardium patch obtained with an equi-biaxial tension test is measured with intrinsic moire and then compared with finite element predictions. Preliminary analysis of moire patterns observed in the experiments justifies the assumption of the constitutive model based on transversely isotropic hyperelasticity. In order to determine the 16 hyperelastic constants included in the constitutive model and the fiber orientation, the difference Ω between displacement values measured with moire and their counterpart determined numerically is minimized by means of multi-level and multi-point simulated annealing. Results clearly demonstrate the efficiency of the identification procedure presented in this research: in fact, residual difference between experimental data and numerical values of in-plane displacements is less than 2%. In order to validate the entire identification process, another experimental test is conducted by inflating the same specimen. Out-of-plane displacements, now measured with projection moire, are compared with predictions of a new finite element model reproducing the experimental test. The 16 hyper-elastic constants previously determined are given in input to the inflation test FE model. Remarkably, experimental and numerical results are again in excellent agreement: maximum percent error on w-displacement is less than 3%.