On the micromechanics of deep material networks
On the micromechanics of deep material networks
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DOI：
10.1016/j.jmps.2020.103984
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发表时间：
2020-09-01
影响因子：
5.3
通讯作者：
Boehlke, Thomas
中科院分区：
文献类型：
--
作者：
Gajek, Sebastian;Schneider, Matti;Boehlke, Thomas
我们研究了 Liu 等人最近提出的深度材料网络（DMN）。 [计算。方法应用M.，卷。 345，第 1138-1168 页，2019]，从小应变下的经典微观力学的角度。我们的目标是建立深层材料网络的基本微观力学原理，阐明构建块的特性，并为非弹性深层材料网络引入一种简单、稳健和快速的求解技术。在最初的表述中，DMN 仅由线性弹性数据进行训练，但以惊人的精度应用于非线性和非弹性问题。我们通过证明在应变率的一阶中，复合材料的有效非弹性行为是由线弹性局部化决定的，从理论上阐明了这一现象。我们的论证适用于由小应变下的非线性广义标准材料组成的任意微观结构。主要技术工具是广义标准材料应力的 Volterra 级数近似，它是根据非线性动力系统理论改编的。接下来，我们建立深层材料网络从其相位继承热力学一致性和应力应变单调性。这些属性植根于 DMN 作为分层层压树的定义，并与神经网络在材料定律近似方面的其他应用形成对比，在远离训练集的情况下，通常无法保证一致性和单调性。最后但并非最不重要的一点是，我们引入了具有任意层压方向的无旋转 DMN，并开发了一种新颖的公式，将任意树拓扑和多相层压板的 DMN 的实现结合起来，并将我们的见解应用于工业复杂性的微观结构。 (C) 2020 Elsevier Ltd. 保留所有权利。
We investigate deep material networks (DMNs), recently introduced by Liu et al. [Comput. Method Appl. M., vol. 345, pp. 1138-1168, 2019], from the viewpoint of classical micromechanics at small strains. We aim to establish the basic micromechanical principles of deep material networks, shed light on the characteristics of the building blocks and introduce a simple, robust and fast solution technique for inelastic deep material networks.In their original formulation, DMNs are solely trained by linear elastic data, but applied to nonlinear and inelastic problems with astonishing accuracy. We clarify this phenomenon theoretically by showing that, to first order in the strain rate, the effective inelastic behavior of composite materials is determined by linear elastic localization. Our argumentation applies to arbitrary microstructures comprising nonlinear generalized standard materials at small strains. The main technical tool is a Volterra series approximation of the stress of a generalized standard material, which we adapt from nonlinear dynamical systems theory.Next, we establish that deep material networks inherit thermodynamic consistency and stress-strain monotonicity from their phases. These properties root in the definition of the DMN as a tree of hierarchical laminates and contrast with other applications of neural networks to the approximation of material laws, where consistency and monotonicity typically cannot be guaranteed far away from the training set.Last but not least, we introduce rotation-free DMNs with arbitrary directions of lamination and exploit a novel formulation, uniting the implementation of DMNs of arbitrary tree topology and multi-phase laminates, and apply our insights to microstructures of industrial complexity. (C) 2020 Elsevier Ltd. All rights reserved.