A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing

Abstract

a b s t r a c tThis paper presents a hybrid procedure for mechanical characterization of hyper-elastic materials based on moiré, finite element analysis and global optimization. The characterization process is absolutely general because does not require any assumption on specimen geometry, loading or/and boundary conditions. The novel experimental approach followed in this research relies on a proper combination of intrinsic moiré and projection moiré which allows 3D displacement components to be measured simultaneously and independently using always the same experimental setup and just one single camera. In order to properly compare experimental data and finite element predictions, 3D displacement information encoded in moiré patterns which are relative to the deformed configuration taken by the specimen are expressed in the reference system of the unloaded state.A global optimization algorithm based on multi-level and multi-point simulated annealing which keeps memory of all best records generated in the optimization is used in order to find the unknown material properties through the minimization of the X functional built by summing over the differences between displacements measured experimentally and those predicted numerically.Feasibility, efficiency and robustness of the proposed methodology are demonstrated for both isotropic and anisotropic specimens subject to increasing pressure loads: a natural rubber membrane and a glutaraldehyde treated bovine pericardium patch, respectively. Remarkably, the results of the characterization process are in very good agreement with target data independently determined. For the isotropic specimen, the maximum error on hyper-elastic constants is less than 1% and the residual error on displacements is less than 3.5%. For the anisotropic specimen, the maximum error on material properties is about 3.5% while the residual error on displacements is less than 3%. The identification process fails or becomes less reliable if ''local" displacement values are considered.

On the mechanics of growing thin biological membranes

“…Computational modeling holds tremendous potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical treatment. Because of their thin structure, biological membranes lend themselves ideally for spatial discretizations using shell elements [11]. However, to the best of our knowledge, the current work is the first to account for a biological growth model that is compatible with discrete shell kinematics.…”

A hybrid characterization framework to determine the visco-hyperelastic properties of a porcine zona pellucida

“…(0) other mechanical characterization studies of nonlinear materials at the micro-and nanoscale [26][27][28]16]. The identification algorithm, coded in the Matlab (The Mathworks Inc., Austin, TX, USA) software environment, minimizes the difference between nanoindentation data and FE analyses via nonlinear optimization.…”

Nanoscale characterization of the biomechanical hardening of bovine zona pellucida

“…actual material properties) must be input into the FE model to obtain the force-indentation curve matching the Fd curve determined experimentally. The suitability of the optimization-based hybrid process for mechanical characterization problems of highly nonlinear materials and heterogeneous biological structures is well-documented in literature [65][66][67]. The inverse problem (2.6) was solved with the powerful sequential quadratic programming (SQP) [68] interfaced with the SQP optimization routine of MATLAB, which processed the results of the FE analysis, compared the computed F-d curves with experimental data, computed the error function V and perturbed material parameters for the subsequent design cycles.…”