通过非侵入性减少基法从微观结构模拟中采用非侵入性减少基法进行微观结构模拟的学习构成模型:扩展至几何参数化 (Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method: Extension to geometrical parameterizations)

Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties. However, they are typically computationally expensive and infeasible in multi-query contexts such as optimization and material design. To make such analyses amenable, the microscopic simulations can be replaced by surrogate models that must be able to handle a wide range of microstructural parameters. This work focuses on extending the methodology of a previous work, where an accurate surrogate model was constructed for microstructures under varying loading and material parameters using proper orthogonal decomposition and Gaussian process regression, to treat geometrical parameters. To this end, a method that transforms different geometries onto a parent domain is presented. We propose to solve an auxiliary problem based on linear elasticity to obtain the geometrical transformations. Using these transformations, combined with the nonlinear microscopic problem, we derive a fast-to-evaluate surrogate model with the following key features: (1) the predictions of the effective quantities are independent of the auxiliary problem, (2) the predicted stress fields fulfill the microscopic balance laws and are periodic, (3) the method is non-intrusive, (4) the stress field for all geometries can be recovered, and (5) the sensitivities are available and can be readily used for optimization and material design. The proposed methodology is tested on several composite microstructures, where rotations and large variations in the shape of inclusions are considered. Finally, a two-scale example is shown, where the surrogate model achieves a high accuracy and significant speed up, demonstrating its potential in two-scale shape optimization and material design problems.

翻译：理解结构- 财产关系是最佳设计特定应用材料的关键。通常使用两个尺度的模拟来分析微结构对某个部件的宏皮特性的影响。但是, 在诸如优化和材料设计等多细背景中,它们通常计算成本昂贵且不可行。为了便于进行这种分析, 微型模拟可以被代用模型所取代, 这些模型必须能够处理广泛的微结构参数。这项工作的重点是扩大先前工作的方法, 即使用正确的正向分流分流和材料参数为不同的装货和材料参数的微结构结构构建准确的代金模型, 以分析某个部件的宏形结构对某个部件的宏大结构的影响。但是, 要达到这个目的, 将不同的地貌形状转换为母体域。我们提议用线性弹性模型来解决一个辅助问题, 以便处理广泛的微结构变异。利用这些转换, 结合非线性微缩微变变变的变变, 我们用两个快速到评价的基底部模型, 以下列关键特性为精度的精度的精度 : (1), 将精确变变法的精度是精确变法度, 的精度是精确的精度的精度的精度的精度的精度, 的精度的精度是精确度的精度的精度的精度的精度的精度。最后的精度。

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