Energetically stable curve fitting to hyperelastic models based on uniaxial and biaxial tensile tests.

Hyperelastic constitutive laws in biomechanics are used to model soft tissues, and material model parameters are often determined by performing curve fitting on data from uniaxial or biaxial tensile tests. The strain energy function of the applied constitutive law must to be energetically stable; however, this condition is not inherently provided by most currently available models. This study provides a procedure to determine stable strain energy functions in a biaxial strain space based on either uniaxial or biaxial tensile tests. Instead of conservative, strain-independent conditions, a stability region is defined in the strain space based on the sample's tensile tests, thus allowing optimisation within a wider parameter space, resulting in better approximations. An extension of the Levenberg-Marquardt algorithm incorporating user-defined stability constraints is proposed, and the constrained optimisation algorithm is applied to isotropic and anisotropic models. The uniqueness of solutions of the Fung model is also discussed. The material model parameters of stable solutions for soft tissue measurements from various literature sources are determined to demonstrate the proposed procedure. Applying appropriate constraints in the optimisation algorithm resulted in stable and physically permissible constrained solutions for the strain energy function, in contrast to the results of most unconstrained optimisation cases.

Novel curve fitting method based on constrained optimization for the modelling of human brain aneurysms using Mooney-Rivlin hyperelastic materials in the entire range of deformations til rupture.

PURPOSE: Brain aneurysms often prove fatal if ruptured, therefore, understanding their mechanical behaviour in the coupled system of vessels and blood flow can significantly help preventive surgical treatment. The purpose of this work was to analyse measurement data and to determine material parameters for the hyperelastic Mooney-Rivlin model for model building and numerical simulations of aneurysms. METHODS: A total of 88 human brain aneurysm specimens of 41 patients obtained from surgery were processed in this work based on the tests performed by the authors in a previous project. A novel algorithm was proposed and applied in this work to fit stress-stretch ratio curves for multiple measurement data using constrained optimization with hard conditions to comply with known mechanical behaviour. RESULTS: The method produced parameters of stretch ratio-stress curves for a number of groups of the specimens representing the average as well as the extreme stresses, separately for male and female subsamples. Stretch range both in compression and in tension up to rupture was covered and material stability for the entire range was also verified. CONCLUSIONS: The fitted curves with recommended range of validity are directly applicable to numerical finite element or coupled simulations of aneurysms supporting preventive medical treatment or decision making.