论文标题
通过张量基础神经网络从数据中学习超弹性各向异性
Learning hyperelastic anisotropy from data via a tensor basis neural network
论文作者
论文摘要
具有微观结构的材料机械响应中的各向异性很常见，但很难评估和模型。为了构建仅给出应力 - 应变数据的准确响应模型，我们采用经典表示理论，新型神经网络层和L1正则化。提出的张量基-Basis神经网络可以发现各向异性的类型和方向，并提供了应力反应的准确模型。该方法用来自具有离轴横向各向同性和正交型的高弹性材料的数据以及纤维或球形夹杂物引起的较不明确对称性的材料。开发和测试了两个普通的前馈神经网络和输入 - 传感器神经网络公式。使用后者，可以建立多凸电势，通过满足生长条件可以保证存在边界价值问题解决方案。
Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel neural network layers, and L1 regularization. The proposed tensor-basis neural network can discover both the type and orientation of the anisotropy and provide an accurate model of the stress response. The method is demonstrated with data from hyperelastic materials with off-axis transverse isotropy and orthotropy, as well as materials with less well-defined symmetries induced by fibers or spherical inclusions. Both plain feed-forward neural networks and input-convex neural network formulations are developed and tested. Using the latter, a polyconvex potential can be established, which, by satisfying the growth condition can guarantee the existence of boundary value problem solutions.
