论文标题
通过符号回归自动生成可解释的超弹性材料模型
Automatic generation of interpretable hyperelastic material models by symbolic regression
论文作者
论文摘要
在本文中，我们提出了一种新的程序，可以自动生成可解释的超弹性材料模型。这种方法基于符号回归，该回归代表了一种进化算法，该算法以代数表达的形式搜索数学模型。这导致一个相对简单的模型与实验数据一致。通过以其不变性或其他参数来表达应变能函数，可以在物理环境中解释产生的代数配方。另外，可以直接实施获得的代数方程。为了验证所提出的方法，介绍了基于广义的Mooney-Rivlin模型的基准测试。在所有这些测试中，所选的ANSATZ都可以找到预定义的模型。此外，该方法用于硫化橡胶的多轴加载数据集。最后，评估了针对温度依赖性热塑性聚酯弹性体的数据集。在后一种情况下，获得了与实验数据的良好一致。
In this paper, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in the form of an algebraic expression. This results in a relatively simple model with good agreement to experimental data. By expressing the strain energy function in terms of its invariants or other parameters, it is possible to interpret the resulting algebraic formulation in a physical context. In addition, a direct implementation of the obtained algebraic equation is possible. For the validation of the proposed approach, benchmark tests on the basis of the generalized Mooney-Rivlin model are presented. In all these tests, the chosen ansatz can find the predefined models. Additionally, this method is applied for the multi-axial loading data set of vulcanized rubber. Finally, a data set for a temperature-dependent thermoplastic polyester elastomer is evaluated. In latter cases, good agreement with the experimental data is obtained.
