Supplement: Mesoscale thermo-structural analysis of defects in ablative materials using homogenization # Part A

Low-density ablative materials commonly used for Thermal Protection System (TPS) are com- posed of a porous, fibrous structure. Most recent studies on these materials have been dedicated to the thermal properties and thermochemical behavior. In recent years, new studies have begun to focus on their mechanical behavior. These studies argue that in order to correctly predict failure of TPS, it is essential to model both the thermal and mechanical response of these materials. The current research activity proposes to use micro-CT images to generate 3D maps of current and next generation TPS materials. Initial e?orts will focus on FiberForm or PICA-char, and leverage recent results from the research team. These micro-CT maps will be digitized to yield meshed representative volumes suitable for finite element calculation, allowing FE calculation of the elastic properties of these digital representations of real regions in real materials. Micro-CT structures will be decomposed into geometric primitives (e.g., overlapping cylinders) and statistical distributions of structural parameters that describe the real materials. Exam- ple structural parameters include fiber length and diameter, correlation/distribution of fiber orientation within the material, the contact area between fibers. These will be used to define mathematical rules for the computational generation of synthetic representative volume ele- ments (s-RVEs). Stochastic s-RVE structures will be generated by placing geometric primitives according to the statistical distributions derived from micro-CT-based RVEs. This methodology will generate a statistical distribution of all properties of the material, therefore accounting for the large variabilities inherent to their fabrication. The proposed work will lead to a better understanding the e?ects of inhomogeneities on the structural response of TPS at the mesoscale level by 1) calculating mechanical properties at the microscale (fiber-scale) using micro-CT images, and 2) using synthetic representative elements to obtained statistical distributions of these properties. Upon completion, the proposed work could be readily implemented in NASA production codes for immediate use. This methodology could also directly lead to the development of new TPS materials where the properties are tailored to specific material behavior and can be used to inform additive manufacturing techniques.