基于张量基神经网络的超弹性各向异性学习
Learning hyperelastic anisotropy from data via a tensor basis neural network
摘要：
具有微观结构的材料的力学响应的各向异性是常见的，但难以评估和建模。为了构建仅给出应力-应变数据的精确响应模型，我们采用经典表示理论，新颖的神经网络层和L1正则化。建议的张量基神经网络可以发现的类型和方向的各向异性，并提供一个精确的模型的应力响应。该方法证明了从超弹性材料与离轴横向各向同性和正交各向异性，以及材料与纤维或球形夹杂物引起的不太明确的对称性的数据。平原前馈神经网络和输入凸神经网络配方的开发和测试。利用后者，可以建立一个多凸势，它通过满足增长条件可以保证边值问题解的存在性。
英文摘要：
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.
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