Structural optimization of biomorphic cellular silicon carbide ceramics with microstructures by homogenization modeling

通过均质化建模优化生物形态多孔碳化硅陶瓷的微观结构

• 批准号: 5276388
• 负责人: Professor Dr. Ronald H.W. Hoppe, since 8/2005
• 金额: --
• 依托单位: Department Werkstoffwissenschaften
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2006-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5276388?language=en
• 关键词: Structural; optimization; biomorphic; cellular; silicon

The project aims to develop efficient tools for the structural optimization of biomorphic microcellular ceramics based on homogenization modeling. The mathematical work will be supported by experimental investigations that provide both realistic model parameters as well as data for the purpose of model validation. The research is intended to be done on the basis of an interdisciplinary co-operation of applied mathematicians and materials scientists. The biomorphic ceramics were prepared by the biotemplating technique, where natural grown materials like wood, cellulose fibres, paper and cardboard structures are used as bulk templates for fast high-temperature conversion into high-strength or light-weight, microcellular ceramics and ceramic composites. Hereby, the engineering design can be significantly facilitated by the application of advanced optimization strategies and numerical solution techniques based on a physically consistent and transparent mathematical modeling taking into account the fine properties of the microstructures but on a much larger scale than that considered in the microscopic regime. Such a model can be established by the mathematical theory of homogenization. We attempt to optimize mechanical performances of the ceramic composites such as the compliance or the bending strength taking into account technological and problem specific constraints on the state variables and design parameters. This leads to a constrained nonconvex, nonlinear optimization problem which will be solved by primal-dual damped Newton-type interior-point methods involving the use of appropriately chosen merit functions for convergence monitoring. In the course of the optimization process, the inelastic deformation of the biomorphic microcellular ceramics has to be computed. This will be taken care of by fully adaptive temporal and spatial discretizations applied to a macroscale model obtained by homogenization from the dynamic and constitutive equations describing the evolving microstructure that features an interface between the organic and inorganic phase.

该项目旨在开发基于均质化模型的生物形态微孔陶瓷结构优化的有效工具。数学工作将得到实验研究的支持，实验研究提供现实的模型参数以及用于模型验证的数据。该研究旨在在应用数学家和材料科学家的跨学科合作的基础上完成。生物形态陶瓷是通过生物模板技术制备的，其中木材、纤维素纤维、纸张和纸板结构等天然材料被用作块状模板，可在高温下快速转化为高强度或轻质的微孔陶瓷和陶瓷复合材料。因此，通过应用基于物理一致和透明的数学模型的先进优化策略和数值求解技术，可以显着促进工程设计，同时考虑到微观结构的精细特性，但其规模比微观领域所考虑的规模大得多。这样的模型可以通过均质化的数学理论来建立。我们尝试优化陶瓷复合材料的机械性能，例如顺应性或弯曲强度，同时考虑到状态变量和设计参数的技术和问题特定约束。这导致了受约束的非凸非线性优化问题，该问题将通过原始双阻尼牛顿型内点方法来解决，该方法涉及使用适当选择的评价函数来进行收敛监控。在优化过程中，必须计算生物微孔陶瓷的非弹性变形。这将通过应用于宏观模型的完全自适应时间和空间离散化来解决，该宏观模型是通过动态和本构方程的均质化获得的，该方程描述了以有机相和无机相之间的界面为特征的演化微观结构。