In the present work, neural networks are applied to formulate parametrised hyperelastic constitutive models. The models fulfill all common mechanical conditions of hyperelasticity by construction. In particular, partially input-convex neural network (pICNN) architectures are applied based on feed-forward neural networks. Receiving two different sets of input arguments, pICNNs are convex in one of them, while for the other, they represent arbitrary relationships which are not necessarily convex. In this way, the model can fulfill convexity conditions stemming from mechanical considerations without being too restrictive on the functional relationship in additional parameters, which may not necessarily be convex. Two different models are introduced, where one can represent arbitrary functional relationships in the additional parameters, while the other is monotonic in the additional parameters. As a first proof of concept, the model is calibrated to data generated with two differently parametrised analytical potentials, whereby three different pICNN architectures are investigated. In all cases, the proposed model shows excellent performance.

翻译：本研究采用神经网络构建参数化超弹性本构模型。该模型通过构造方法满足超弹性理论中所有常见力学条件。具体而言，基于前馈神经网络架构实现了部分输入凸神经网络（pICNN）。pICNN接收两组不同输入参数，在其中一组参数上保持凸性，而对另一组参数则表征任意（不必然为凸）的函数关系。通过这种方式，模型既能满足力学推导中的凸性约束，又不会对额外参数（可能不具凸性）的函数关系施加过度限制。本文提出了两种模型：一种可表征额外参数下的任意函数关系，另一种则在额外参数上具有单调性。为验证概念可行性，采用两种不同参数形式的解析势函数生成数据进行模型校准，并研究了三种不同的pICNN架构。所有测试案例中，所提模型均表现出优异性能。