Muscle soreness can occur after working beyond the habitual load, especially for people engaged in high-intensity work load. Prediction of hyperelastic material parameters is essentially an inverse process, which possesses challenges. This work presents a novel procedure that combines nonlinear finite element method (FEM), two-way neural networks (NNs) together with experiments, to predict the hyperelastic material parameters of skeletal muscles. FEM models are first established to simulate nonlinear deformation of skeletal muscles subject to compressions. A dataset of nonlinear relationship between nominal stress and principal stretch of skeletal muscles is created using our FEM models. The dataset is then used to establish two-way NNs, in which a forward NN is trained and it is in turn used to train the inverse NN. The inverse NN is used to predict the hyperelastic material parameters of skeletal muscles. Finally, experiments are carried out using fresh skeletal muscles to validate the predictions in great detail. In order to examine the accuracy of the two-way NNs predicted values against the experimental ones, a decision coefficient RADJ2 with penalty factor is introduced to evaluate the performance. Studies have also been conducted to compare the present two-way NNs approach with the other existing methods, including the directly (one-way) inverse problem NN, and improved niche genetic algorithm (INGA). The comparison results show that two-way NNs model is an accurate approach to identify the hyperelastic parameters of skeletal muscles. The present two-way NNs method can be further expanded to the predictions of constitutive parameters of other type of nonlinear materials.

中文翻译：

---

一种使用双向神经网络的超弹性骨骼肌本构参数识别程序

超过习惯性负荷后，会出现肌肉酸痛，尤其是从事高强度工作的人。超弹性材料参数的预测本质上是一个逆过程，具有挑战性。这项工作提出了一种将非线性有限元方法 (FEM)、双向神经网络 (NN) 与实验相结合的新程序，以预测骨骼肌的超弹性材料参数。最初建立 FEM 模型是为了模拟受压缩的骨骼肌的非线性变形。使用我们的 FEM 模型创建了标称应力和骨骼肌主要拉伸之间的非线性关系数据集。然后使用该数据集建立双向 NN，其中训练正向 NN，然后用于训练逆向 NN。逆神经网络用于预测骨骼肌的超弹性材料参数。最后，使用新鲜骨骼肌进行实验，以非常详细地验证预测。为了检查双向神经网络预测值与实验值的准确性，决策系数R调整2引入惩罚因子来评估性能。还进行了研究以将目前的双向神经网络方法与其他现有方法进行比较，包括直接（单向）逆问题神经网络和改进的利基遗传算法（INGA）。比较结果表明，双向神经网络模型是识别骨骼肌超弹性参数的准确方法。目前的双向神经网络方法可以进一步扩展到其他类型非线性材料的本构参数的预测。