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.
翻译:在本文中,我们提出了一个自动生成可解释的超弹性材料模型的新程序。 这种方法基于象征性回归, 代表一种渐进式算法, 以代数表达式的形式寻找数学模型。 这导致一个相对简单的模型, 与实验数据相当一致。 通过用其变异性或其他参数来表达压力能量功能, 可以在物理背景下解释由此产生的代谢配方。 此外, 直接实施所获得的代数方程是可能的。 为了验证拟议方法, 提供了基于普遍月球- 利弗林模型的基准测试。 在所有这些测试中, 所选的 ansatz 可以找到预设的模型 。 此外, 这种方法适用于硫化橡胶的多轴载数据集 。 最后, 将评估一个温度依赖热塑胶聚酯弹性体的数据集 。 在后一种情况下, 将获得与实验数据的良好一致 。