School of Mechanical Engineering, Hebei University of Technology, Tianjin, P.R. China.
Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, Ohio, USA.
Comput Methods Biomech Biomed Engin. 2021 Nov;24(15):1647-1659. doi: 10.1080/10255842.2021.1906235. Epub 2021 Mar 31.
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.
研究受力骨骼肌的变形特征和应力分布变得越来越重要。可靠地预测超弹性材料参数需要一个反演过程，这具有一定的挑战性。本工作提出了两种反演程序来识别骨骼肌的超弹性材料参数。第一种方法将非线性有限元法（FEM）、随机森林（RF）模型和贝叶斯优化（BO）算法集成在一起。另一种方法将 FEM、RF 和混合网格搜索（GS）和随机搜索（RS）算法集成在一起。首先根据非线性力学原理，建立 FEM 模型来模拟骨骼肌在压缩下的非线性变形。使用我们的 FEM 模型创建了一个骨骼肌名义应力和主伸长之间的非线性关系数据集，并通过 RF 模型学习了这种非线性关系。BO、混合 GS 和 RS 算法用于调整 RF 中的主要模型参数。然后，利用单轴压缩实验，优化后的 RF 用于预测骨骼肌的超弹性材料参数。还进行了深入的研究，比较了 RF-BO 方法和 RF-Search 方法，比较结果表明，RF-BO 方法是一种识别骨骼肌超弹性材料参数的有效且准确的方法。目前的 RF-BO 模型可以进一步扩展，用于预测其他类型非线性软材料的本构参数。
