The existing topology optimization methods are mostly based on traditional continuum mechanics approaches to deal with cross-scale and multi-material problems considering interfaces. Unfortunately, the inability of traditional continuum mechanics models to capture the size dependence of microscale structural deformation behavior limits their application in the optimization design of advanced micro and nanostructures. Hence, a new cross-scale optimization of multi-material structures considering interface is proposed based on Wei-Hutchinson strain gradient theory, which could describe and explain the size dependence during optimization process. Firstly, a new interpolation scheme is developed to identify interfaces between two arbitrary materials and ensure precise control of the interface width. Then, through geometric adaptive projection techniques, the behavior at the interface and the macro-micro mechanical behaviors are cleverly projected and solved within a nine-node quadrilateral finite element set. After that, the geometric parameters of adaptive geometric components under the framework of the movable deformable component method introduce non-periodic infill microstructures into multi-material topology optimization considering interfaces, achieving minimization of compliance. Results show that the compliance of the non-periodically infilled microstructure multi-material layout can be significantly improved by considering size effects compared with periodically uniform infilled microstructure multi-material layouts in the process of cross-scale optimization. Furthermore, the new optimization algorithm can effectively control the stress levels of the overall structure as well as the stress at the interfaces of heterogeneous materials, thereby reducing the stress concentration effects in critical stress region.

中文翻译：

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考虑界面应变梯度的并行跨尺度和多材料优化


现有的拓扑优化方法大多基于传统的连续介质力学方法，以处理考虑界面的跨尺度和多材料问题。遗憾的是，传统的连续介质力学模型无法捕捉微尺度结构变形行为的尺寸依赖性，这限制了它们在先进微纳米结构优化设计中的应用。因此，基于 Wei-Hutchinson 应变梯度理论，提出了一种新的考虑界面的多材料结构跨尺度优化，可以描述和解释优化过程中的尺寸依赖性。首先，开发了一种新的插值方案来识别两种任意材料之间的界面，并确保对界面宽度的精确控制。然后，通过几何自适应投影技术，在九节点四边形有限元集中巧妙地投影和宏微观力学行为并求解界面处的行为。然后，在可动变形构件法框架下，将自适应几何构件的几何参数引入考虑界面的多材料拓扑优化中，实现柔度最小化。结果表明，在跨尺度优化过程中，与周期性均匀的填充微结构多材料布局相比，考虑尺寸效应可以显著提高非周期性填充微结构多材料布局的柔顺性。 此外，新的优化算法可以有效控制整体结构的应力水平以及非均质材料界面处的应力，从而降低临界应力区域的应力集中效应。