数据驱动的各向异性可调Spinodoid材料拓扑优化
Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy
摘要：
我们提出了一个两尺度的拓扑优化框架的宏观机构的设计与优化的弹性响应，这是通过在微观尺度上的空间变化的细胞架构。所选择的spinodoid拓扑结构的细胞网络的微观尺度上（这是由自然的微结构形成的spinodal分解过程中的灵感）承认一个无缝的空间分级以及可调的弹性各向异性，它是参数化的一个小的设计参数与底层的高斯随机场。宏尺度边值问题采用有限元离散，有限元除了位移场外，还连续插值微尺度设计参数。通过假设尺度分离，在宏观尺度上的局部本构行为被识别为基于局部设计参数的微结构的均匀化弹性响应。作为从经典的FE $^2$型方法出发，我们取代了昂贵的微尺度均匀化的数据驱动的代理模型，使用深神经网络，它准确，高效地映射到有效的弹性张量的设计参数。该模型是训练均匀化的刚度数据从有限元数值均匀化。作为一个额外的好处，机器学习设置允许自动微分，因此可以精确计算灵敏度（优化问题所需的），而不需要数值导数-这一策略的前景远远超出了弹性刚度。因此，该框架为基于数据驱动的代理模型的多尺度拓扑优化提供了新的机会。
英文摘要：
We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid topology for the cellular network on the microscale (which is inspired by natural microstructures forming during spinodal decomposition) admits a seamless spatial grading as well as tunable elastic anisotropy, and it is parametrized by a small set of design parameters associated with the underlying Gaussian random field. The macroscale boundary value problem is discretized by finite elements, which in addition to the displacement field continuously interpolate the microscale design parameters. By assuming a separation of scales, the local constitutive behavior on the macroscale is identified as the homogenized elastic response of the microstructure based on the local design parameters. As a departure from classical FE$^2$-type approaches, we replace the costly microscale homogenization by a data-driven surrogate model, using deep neural networks, which accurately and efficiently maps design parameters onto the effective elasticity tensor. The model is trained on homogenized stiffness data obtained from numerical homogenization by finite elements. As an added benefit, the machine learning setup admits automatic differentiation, so that sensitivities (required for the optimization problem) can be computed exactly and without the need for numerical derivatives - a strategy that holds promise far beyond the elastic stiffness. Therefore, this framework presents a new opportunity for multiscale topology optimization based on data-driven surrogate models.
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