Two-stage data-driven homogenization for nonlinear solids using a reduced order model
Two-stage data-driven homogenization for nonlinear solids using a reduced order model
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DOI：
10.1016/j.euromechsol.2017.11.007
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发表时间：
2018-05-01
影响因子：
4.1
通讯作者：
Kunc, Oliver
中科院分区：
文献类型：
--
作者：
Fritzen, Felix;Kunc, Oliver
使用数据驱动的方法研究具有三维微观结构的材料的非线性行为。关键的创新是将两个预计算层次与明智选择的采样点和自适应插值函数相结合：首先，在微观结构层面上进行有限元（FE）模拟。开发了一种复杂的采样策略，以保持较低的昂贵的有限元计算数量。其次，生成的仿真数据用作降阶模型（ROM）的输入。 ROM 可以实现 10-100 倍的显着加速。尽管如此，其性能仍低于实际双尺度模拟的要求。为了获得所需的加速，在第三步中，建议使用径向数值显式势（RNEXP）。后者将单向三次插值函数与对测地距离进行操作的径向基函数相结合。 RNEXP 近似的评估几乎是实时实现的。它受益于 ROM 的计算效率，因为与使用直接 FE 模拟相比，可以实现更多数量的采样点。凭借专用采样策略，与文献中的竞争技术相比，需要更少的样本，因此需要预计算（FE 和 ROM）。这些措施使得 RNEXP 的离线成本可以在工作站计算机上进行管理。此外，所选的采样方向显示有利于所采用的核插值。研究了具有各向同性和各向异性微观结构的高度非线性超弹性（伪塑性）复合材料的数值例子。使用 RNEXP 解决了结构层面上超过 106 个自由度的双尺度模拟，并量化了微观结构对结构行为的影响。
The nonlinear behavior of materials with three-dimensional microstructure is investigated using a data-driven approach. The key innovation is the combination of two hierarchies of precomputations with sensibly chosen sampling sites and adapted interpolation functions: First, finite element (FE) simulations are performed on the microstructural level. A sophisticated sampling strategy is developed in order to keep the number of costly FE computations low. Second, the generated simulation data serves as input for a reduced order model (ROM). The ROM allows for considerable speed-ups on the order of 10-100. Still, its performance is below the demands for actual twoscale simulations. In order to attain the needed speed-ups, in a third step, the use of radial numerically explicit potentials (RNEXP) is proposed. The latter combine uni-directional cubic interpolation functions with radial basis functions operating on geodesic distances. The evaluation of the RNEXP approximation is realized almost in real-time. It benefits from the computational efficiency of the ROM since a higher number of sampling points can be realized than if direct FE simulations were used. By virtue of the dedicated sampling strategy less samples and, thus, precomputations (both FE and ROM) are needed than in competing techniques from literature. These measures render the offline cost of the RNEXP manageable on workstation computers. Additionally, the chosen sampling directions show favorable for the employed kernel interpolation. Numerical examples for highly nonlinear hyperelastic (pseudo-plastic) composite materials with isotropic and anisotropic microstructure are investigated. Twoscale simulations involving more than 106 DOF on the structural level are solved using the RNEXP and the influence of the microstructure on the structural behavior is quantified.