A hybrid Fuzzy-Stochastic-Finite-Element-Method for polymorphic, microstructural uncertainties in heterogeneous materials

用于异质材料中多态性、微观结构不确定性的混合模糊随机有限元方法

• 批准号: 312930871
• 负责人: Professor Dr.-Ing. Paul Steinmann
• 金额: --
• 依托单位: Lehrstuhl für Technische Mechanik (LTM)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/312930871?language=en
• 关键词: hybrid; Fuzzy; Stochastic; Finite; Element

Computational homogenization requires two separate finite element models: a model at the macroscale and a model of the materials’ underlying structure at the microscale. Computational homogenization involves two main ingredients: the transfer of the macroscopic loading to the microscale and averaging the corresponding response of the microstructure to obtain the effective macroscopic properties. A challenging aspect for computational homogenization is the proper modelling of material with uncertainty in the microstructure, as considered in this project. Uncertainties in the macroscopic response of heterogeneous materials result from various sources: the natural variability in the microstructure’s geometry and its constituent’s material properties and the lack of sufficient knowledge regarding the microstructure. The first type of uncertainty is denoted as aleatoric uncertainty and may be characterized by probabilistic approaches. The second type of uncertainty is denoted as epistemic uncertainty and may be described using fuzzy arithmetic. Models considering both sources of uncertainty are denoted polymorphic, requiring some combination of stochastic and fuzzy methods.In Phase I we developed methods for the accurate and efficient propagation of polymorphic uncertainty through the material’s microstructure and applied all proposed approaches to a benchmark problem. The objectives of the Phase II are further development of modelling techniques and their application to the engineering design of structures. The outcome of Phase II will be an accomplished methodology allowing the uncertainty propagation from the lowest level of a material microstructure through the macroscopic structure simulation to the engineering design and decision making. More precisely in Phase II the following challenges are considered:- We continue the development of advanced fuzzy-stochastic benchmark RVE for the microstructure of heterogeneous materials, resulting thus in a more realistic and precise description of polymorphic uncertainty in the material’s microstructure. - Modelling techniques for spectral non-deterministic finite element analysis will be enriched to non-deterministic eXtended Isogeometric Analysis.- The computational cost of full-order large scale simulations of systems in the presence of uncertainty is unacceptably high, in particular considering many-query or real-time applications. Thus, reduced order modeling is an essential tool which allows a speed up microscale simulations. - Reduced order models and metamodels provide a necessary bridge to the final stage of the project, in which a suitable metamodel will be used on the macroscale to run large size simulations of engineering structures. - Finally, the influence of uncertainty in the macrostructure on the static and the dynamic behavior of engineering structures under random loading will be analyzed.

计算均质化需要两个单独的有限元模型：宏观上的模型和微观材料基础结构的模型。计算均质化涉及两个主要的插入物：宏观载荷向显微镜的转移，并平均微结构的相应响应以获得有效的宏观特性。如本项目所考虑的那样，用于计算均质化的挑战者是对微观结构的不确定性的适当建模。异质材料的宏观响应中的不确定性来自各种来源：微观结构的几何形状及其构造材料的自然变异性以及对微结构缺乏足够的知识。第一种不确定性表示为质量不确定性，可能以概率方法为特征。不确定性，可以使用模糊算术来描述。模型考虑了两种不确定性的来源都是表示多态性的，需要某种结合随机和模糊的方法。在第一阶段，我们开发了通过材料的显微结构来准确有效地传播多态性不确定性的方法，并将所有建议的方法应用于基准标准问题。第二阶段的目标是建模技术的进一步发展，第二阶段的结果将是一种实现的方法，可以通过宏观结构模拟到工程设计和决策制定的材料微观结构的最低水平的不确定性传播。更准确地说，在第二阶段中考虑了以下挑战： - 我们继续开发用于异质材料微观结构的先进模糊基准rve，从而导致对材料微观结构中多态性不确定性的更现实和精确描述。 - 光谱非确定性有限元分析的建模技术将富集到非确定性扩展的同几何分析中。-在不确定性存在下，全阶大规模模拟系统的计算成本较高，特别是考虑多个频率或实时应用。那就是降低的订单建模是一种必不可少的工具，可以加快微观模拟。 - 减少的订单模型和元模型为项目的最后阶段提供了必要的桥梁，其中将在宏观上使用合适的元模型来运行工程结构的大尺寸模拟。 - 最后，将分析宏观结构中不确定性对静态的影响以及在随机加载下的工程结构的动态行为。