广义连续体框架下面向增材制造的金属材料本构模型研究

Additive manufacturing (AM) is an advanced technology for fabricating complex metallic parts rapidly and integrally. The problems relating to the modelling and calculation of AM are recent issues in academia. To construct a constitutive model, which describes the microstructural properties of additive manufactured metallic materials and enables the finite element analysis of the parts with complex geometries, is important to the structural analysis for additive manufactured parts, as well as an important component of the “process-properties-structure” frame of simulation and calculation for AM. To solve the problem that the constitutive model for AM has to balance the demand of accuracy and that of efficiency, this project will develop a constitutive model for additive manufactured metallic material and apply it to the structural analysis of parts. The theoretical frame of constitutive modelling in generalized continua and the simplification method of machine learning are used. In details, the project 1) will utilize the generalized media to develop a multi-scale constitutive model, meeting the requirement for accuracy; 2) will introduce the space-time four-dimensional formalism to derive covariant model, meeting the requirement for computability; 3) will apply the machine learning methods to optimizing the model, meeting the requirement for efficiency; 4) will implement the finite element analysis of the complex geometry, in order to evaluate the model’s accuracy and cost. The achievements of this project will meet the demand of simulations and calculations for AM in the aspect of technical research; at the same time, it will promote the application of advanced constitutive modeling theories and optimization methods in the development of manufacturing technology in the aspect of theoretical research.

增材制造是快速整体制造复杂金属构件的先进技术，相关模拟计算研究是当今热点。构建能够合理描述增材制造金属材料微观特性并适用于复杂形状构件有限元计算的本构模型，是增材制造构件结构分析的关键，是增材制造“工艺参数-材料性能-产品性能”模拟计算体系重要一环。本项目针对增材制造本构模型需要在精确性和高效性中取得平衡的难题，借助广义连续体本构建模理论框架和机器学习模型简化方法，构建实用化的增材制造金属材料本构模型，并将模型应用于构件结构分析。具体包括：1）为满足精确性要求，使用广义连续体构建多尺度本构模型；2）为满足计算性要求，使用时空四维方程构建协变的本构模型；3）为满足经济性要求，使用机器学习方法优化本构模型；4）为评价模型准确性和经济性，进行复杂形状有限元结构计算。本项目的成果在技术研究上将满足增材制造模拟计算的需求，同时在理论研究上将推动先进本构理论和模型优化方法在制造技术中的应用。

增材制造材料具有复杂的微观结构而增材制造构件往往具有复杂的宏观几何形貌。为构建.能够合理描述增材制造金属材料微观特性并适用于复杂形状构件模拟计算的本构模型，符合增材制造“工艺参数-材料性能-产品性能”模拟计算的要求，本项目针对增材制造本构模型需要在精确性和高效性中取得平衡的难题，确立了微观计算—宏观符号回归的本构建模框架。首先通过Fourier-Galerkin方法实现考虑增材制造材料微观结构的晶体塑性计算，获得代表体积单元（RVE）的大变形应力响应数据；随后通过本项目提出的数据驱动本构建模方法，利用微观计算数据，建立宏观的适用于增材制造复杂结构分析的本构模型。为解决微观计算问题，本项目开发了变形-压强混合Fourier-Galerkin方法，可用于不可压缩固体和具有不可压缩相的固体的微观计算；为解决数据驱动宏观建模问题，本项目开发了基于混合特征选择技术的张量稀疏符号回归方法（TSSR），可以根据微观计算数据建立显式的“白盒子”宏观本构模型。本项目从理论框架、计算方法、程序构建、结构计算应用等方面实现了面向增材制造材料的多尺度本构建模体系，不仅有助于实现增材制造工艺设计与优化，也推动了先进的微观计算方法和基于数据驱动的模型简化方法在先进制造技术中的应用与延伸。