考虑断裂性能的仿生周期性多层级复合材料拓扑优化

The topology optimization of material microstructural unit cell that considers fracture performance is one of the most challenging problems in topology optimization-based material design. Based on the heavy demand of composite materials in the industrial field, this project is to study the basic mechanism of topology optimization concerning biomimetic and periodic hierarchical composite materials, explore the reasonable expressions of the optimization indicators for fracture toughness, fracture strength and fracture tolerance, and develop the topology optimization model of hierarchical composite materials with consideration of fracture performance. For scientific problems about the mechanism to tune the fracture toughness and fracture strength of the periodic hierarchical composite materials, the key aspects that affect the material’s fracture tolerance, and the topology optimization model of hierarchical composite materials that are suitable for preparation with consideration of fracture performance, new achievements are expected in the researches of reasonable expressions of optimization objective functions that represent the fracture toughness and fracture strength of the composite materials, the topology optimization constraint concerning the composite material’s fracture tolerance, and the topology optimization model for periodic hierarchical composite considering fracture performance. These works will provide meaningful guidance to the in-depth understanding of the design of periodic hierarchical composite considering fracture performance and the improvement in the composite materials design.

考虑断裂性能的材料设计问题是材料单胞微结构拓扑优化中极具挑战性的问题之一。本项目以工业领域中大量的复合材料应用需求为背景，深入研究仿生周期性多层级复合材料拓扑优化基础机理，探究合理表征多层级复合材料断裂韧性、断裂强度以及断裂容忍性的优化性能指标，并发展考虑断裂性能的多层级复合材料拓扑优化模型。针对多层级复合材料多失效模式下断裂韧性及断裂强度的调控机理、影响多层级复合材料断裂容忍性的结构机制、适于制备的多层级复合材料断裂性能拓扑优化模型等关键科学问题，预期在建立准确表征多层级复合材料断裂韧性及断裂强度的优化双目标函数、提出有效限定其断裂容忍性的拓扑优化约束条件、建立考虑断裂性能的多层级复合材料单胞拓扑优化列式及求解方法方面开展系统的创新性研究。项目对深入理解多层级复合材料设计机理，完善考虑断裂性能的复合材料优化方法，提高拓扑优化引导的复合材料设计水平具有指导意义。

面向刚度、强韧性等力学性能的材料微结构拓扑优化是超材料设计的研究热点之一。本项目以工业领域中大量的轻质、高刚度/强韧性材料应用需求为背景，基于生物材料微结构构型启发，深入研究周期性复合材料拓扑优化基础机理，探究高效表征周期性复合材料微结构的拓扑降维参数化方法，发展针对强韧性等力学性能的复合材料微结构非梯度拓扑优化模型及材料与结构一体化拓扑优化方法。针对复合材料微结构构型的拓扑降维表征模型、周期性复合材料多种力学性能指标的调控机理、材料微结构/材料与结构一体化优化列式及求解方法等关键科学问题，提出了基于周期性材料场级数展开的材料微结构拓扑表征方法，建立了确保多类单胞微结构优化过程中任意空间排布可连接性的可制造性优化约束，发展了面向刚度强度等力学性能指标的周期性复合材料单胞及材料与结构一体化拓扑优化列式及求解方法，获得了创新的复合材料微结构设计，显著增强多尺度优化设计的增材制造可制造性。项目对深入理解周期性复合材料设计机理，完善复合材料优化方法，提高拓扑优化引导的复合材料设计水平具有指导意义。