RESEARCH ON INVERSION METHOD OF HYPERELASTIC CONSTITUTIVE PARAMETERS OF SKELETAL MUSCLES BASED ON SIMULATION AND INTELLIGENT ALGORITHM
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摘要: 从事高强度的体力工作者经常会发生肌肉软组织的损伤, 因此对骨骼肌的变形特性和应力分布的研究受到了越来越多的重视. 获取正确的本构参数对于生物软组织的力学行为的研究至关重要, 而本构参数的确定本质上是一个逆过程, 具有很大的挑战性. 本文分别采用K近邻(K-nearest neighbor, KNN)模型和支持向量机回归(support vector machine regression, SVR)模型并结合非线性有限元仿真, 提出了两种确定骨骼肌本构参数的反演方法. 首先建立了骨骼肌压缩的有限元模型, 对其压缩条件下的变形特性进行了有限元仿真, 得到了相应的变形特性及应力分布规律, 同时也建立了骨骼肌组织的名义应力和主伸长之间非线性关系的数据集. 其次, 分别利用KNN模型和SVR模型搭建了针对骨骼肌组织进行本构参数反演的机器学习智能算法, 对相应的数据集进行训练, 结合单轴压缩实验的实验数据预测了材料的本构参数. 最后, 对分别基于KNN模型和SVR模型对骨骼肌超弹性本构参数的误差结果进行了分析, 通过引入相关系数$R$和决定系数$R^{2}$对采用两种反演方法的有效性进行数值上的验证. 结果表明, 利用KNN模型和SVR模型结合有限元仿真是确定骨骼肌超弹性本构参数的有效、准确的方法, 该方法也可进一步推广到其他类型的非线性软组织的本构参数反演.Abstract: Muscle injury and other diseases often occurs in high-intensity physical workers, so the research on the deformation characteristics and the stress distribution of skeletal muscles are of increasing importance. It is important to obtain the correct constitutive parameters for the study of mechanical behavior of biological soft tissues, and the determination of the constitutive parameters is essentially an inverse process, which possesses challenges. In this paper, two inverse methods based on machine learning are proposed to determine the constitutive parameters, which are k-nearest neighbor (KNN) model and support vector machine regression (SVR) model combined with nonlinear finite element simulation. Firstly, based on the principle of nonlinear mechanics, a finite element model is established to simulate the nonlinear deformation of skeletal muscles under compression, and the corresponding deformation characteristics and stress distribution. At the same time, the dataset of nonlinear relationship between nominal stress and principal stretch of skeletal muscles is established by using the finite element model. Then KNN model and SVR model are used to build the machine learning intelligent algorithms for the inversion of constitutive parameters of skeletal muscle tissues, and the corresponding datasets are trained. Combined with the experimental data of uniaxial compression experiment, the constitutive parameters of skeletal muscles are predicted. Finally, intensive studies also have been carried out to compare the performance of KNN model with SVR model to identify the hyperelastic material parameters of skeletal muscles. And the validity of two inversion methods were verified numerically by introducing the correlation coefficient $(R)$ and the decision coefficient ($R^{2})$. The results show that KNN model and SVR model combined with finite element method are effective and accurate method to identify the hyperelastic material parameters of skeletal muscles. This method can also be further extended for the predictions of constitutive parameters of other types of nonlinear soft materials.
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