对具有裂缝的分子动力学数据进行粗粒化的统一的非局部、周向学框架
Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures
摘要：
分子动力学（MD）已成为设计材料的有力工具，减少了对实验室测试的依赖。然而，直接使用MD来处理材料在细观尺度上的变形和破坏仍然是遥不可及的。在这里，我们提出了一个学习框架，从MD模拟的材料断裂数据集提取一个周波模型作为中尺度连续介质替代。首先，我们提出了一种新的粗粒化方法，自动处理材料断裂及其相应的不连续性的MD位移数据集。受加权基本非振荡格式的启发，该方法的核心思想在于自适应地自动选择局部最光滑的模板，然后将粗粒度的材料位移场重建为包含不连续性的分段光滑解。然后，基于粗粒度的MD数据，提出了一种基于两阶段优化的学习方法，以推断最优的周波模型与损伤准则。在第一阶段，我们从没有材料损伤的数据集中识别出最优的非局部核函数，以捕获材料的刚度特性。然后，在第二阶段，材料损伤准则是从裂缝的数据学习作为一个平滑的阶梯函数。结果，获得了一个周波替代。我们的周波代理模型可以用于进一步的预测任务与不同的网格分辨率从训练，因此允许大幅降低计算成本相比，MD。我们说明了所提出的方法的有效性与单层石墨烯的几个数值测试。我们的测试表明，所提出的数据驱动模型是鲁棒的和可推广的：它能够在离散化和加载设置下对裂缝的初始化和生长进行建模，这些设置与训练期间使用的设置不同。
英文摘要：
Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. Herein, we propose a learning framework to extract a peridynamic model as a mesoscale continuum surrogate from MD simulated material fracture datasets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in MD displacement dataset. Inspired by the Weighted Essentially Non-Oscillatory scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from datasets without material damage, to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. Our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our tests show that the proposed data-driven model is robust and generalizable: it is capable in modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.
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