数据驱动多尺度力学中深层物质网络的三维结构探索
Exploring the 3D architectures of deep material network in data-driven multiscale mechanics
摘要：
本文扩展了Liu等人（2019）提出的深度材料网络（DMN），以解决具有任意材料和几何非线性的一般三维（3D）问题。它发现了一种新的方法来描述多尺度非均匀材料的多层网络结构和机械积木。详细讨论了DMN的数据驱动框架，包括离线训练和在线外推两个阶段。基于界面平衡条件和运动学约束，推导了小应变和有限应变两种形式的双层结构三维积木的解析解。通过在代表性体积单元（RVE）上直接数值模拟产生的线弹性数据，网络可以在离线阶段使用随机梯度下降和先进的模型压缩算法来有效地训练。通过数值实验验证了DMN在解决具有复杂形貌和材料规律的三维RVE挑战方面的效率和准确性，包括1）具有Mullins效应的超弹性颗粒增强橡胶复合材料; 2）具有率相关晶体塑性的多晶材料; 3）具有纤维各向异性弹性和基体塑性的碳纤维增强聚合物（CFRP）复合材料。特别是，我们展示了一个三尺度的均匀化过程的CFRP系统连接的微观和介观尺度的材料网络。DMN的完整学习和外推程序为多尺度材料建模和设计建立了可靠的数据驱动框架。
英文摘要：
This paper extends the deep material network (DMN) proposed by Liu et al. (2019) to tackle general 3-dimensional (3D) problems with arbitrary material and geometric nonlinearities. It discovers a new way of describing multiscale heterogeneous materials by a multi-layer network structure and mechanistic building blocks. The data-driven framework of DMN is discussed in detail about the offline training and online extrapolation stages. Analytical solutions of the 3D building block with a two-layer structure in both small- and finite-strain formulations are derived based on interfacial equilibrium conditions and kinematic constraints. With linear elastic data generated by direct numerical simulations on a representative volume element (RVE), the network can be effectively trained in the offline stage using stochastic gradient descent and advanced model compression algorithms. Efficiency and accuracy of DMN on addressing the long-standing 3D RVE challenges with complex morphologies and material laws are validated through numerical experiments, including 1) hyperelastic particle-reinforced rubber composite with Mullins effect; 2) polycrystalline materials with rate-dependent crystal plasticity; 3) carbon fiber reinforced polymer (CFRP) composites with fiber anisotropic elasticity and matrix plasticity. In particular, we demonstrate a three-scale homogenization procedure of CFRP system by concatenating the microscale and mesoscale material networks. The complete learning and extrapolation procedures of DMN establish a reliable data-driven framework for multiscale material modeling and design.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
