Inverse identification of hyperelastic constitutive parameters of skeletal muscles via optimization of AI techniques

Abstract

Studies on the deformation characteristics and stress distribution in loaded skeletal muscles are of increasing importance. Reliable prediction of hyperelastic material parameters requires an inverse process, which possesses challenges. This work proposes two inverse procedures to identify the hyperelastic material parameters of skeletal muscles. The first one integrates nonlinear finite element method (FEM), random forest (RF) model, and Bayesian optimization (BO) algorithm. The other one integrates FEM, RF and hybrid Grid Search (GS), and Random Search (RS) algorithm. FEM models are first established to simulate nonlinear deformation of skeletal muscles subject to compression based on nonlinear mechanics principals. A dataset of nonlinear relationship between the nominal stress and principal stretch of skeletal muscles is created using our FEM models and the nonlinear relationship is learned through RF model. The BO, hybrid GS and RS algorithms are used to adjust the major model parameters in RF. Then the optimized RF is utilized to predict hyperelastic material parameters of skeletal muscles, with the help of uniaxial compression experiments. Intensive studies also have been carried out to compare the RF-BO approach with RF-Search approach, and the comparison results show that RF-BO approach is an effective and accurate approach to identify the hyperelastic material parameters of skeletal muscles. The present RF-BO model can be further extended for the predictions of constitutive parameters of other types of nonlinear soft materials.

Keywords:

• Random forest
• finite element method
• skeletal muscles
• parameter identification
• Bayesian optimization

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Natural Science Foundation of China (Grant No. 11832011) Tianjin Excellent Special correspondent Project (Grant No. 16JCTPJC53100) and Hebei Natural Science Foundation (Grand No. A2020202015).