Structural Optimization of Biomorphic Cellular Silicon Carbide Ceramics with Microstructures by Homogenization Modeling

微结构材料的宏观力学行为强烈地依赖于微结构的形状和拓扑，因此必须考虑微结构的形状和拓扑，以进行最优的结构设计。近年来，一类应用广泛的新型材料，即生物形态陶瓷引起了人们的广泛关注。这些陶瓷是由生物有机物通过生物模板技术生产的，包括高温热解和与渗透物质的反应。本项目旨在开发基于均匀化建模的有效工具，用于优化此类生物形态微孔陶瓷的力学性能。这导致了齐化模型的一个非线性优化问题，在离散区域，该问题将用原始-对偶的阻尼牛顿型内点方法来求解。为了进行逼真的建模、仿真和优化，必须进行实验研究，以便提供模型参数和便于模型验证。

The macroscopic mechanical behavior of microstructured materials strongly depends on the shape and topology of the microstructure which thus has to be taken into account for an optimal structural design. A new class of materials, namely biomorphic ceramics, with a broad spectrum of applications has recently attracted a lot of attention. These ceramics are produced from bioorganic substances by biotemplating techniques involving high-temperature pyrolysis and reaction with infiltrated substances. This project aims to develop efficient tools for the optimization of mechanical performances of such biomorphic microcellular ceramics based on homogenization modeling. This leads to a nonlinear optimization problem for the homogenized model which, in the discrete regime, will be solved by primal-dual damped Newton-type interior-point methods. For a realistic modeling, simulation and optimization, experimental investigations have to be carried out in order to provide model parameters and to facilitate model validations.