Microstructure-informed mechanics and fracture behavior of open-porous materials

Understanding how the macroscopic mechanical behavior of open-porous materials is governed by their micro- and nano-structural morphology remains a crucial question in material design. This thesis addresses this challenge by developing a comprehensive, microstructure-informed computational framework to predict the mechanical response of open-porous materials based on realistic representations of their internal architecture. A primary motivation lies in the growing demand for computational models capable of generating heterogeneous microstructures and accurately predicting macroscopic behavior under quasi-static deformation, thereby enabling reverse engineering of such materials. The study initially focuses on a microstructure generation approach based on Laguerre-Voronoi tessellations and the random closed packing of polydisperse spheres. This methodology captures essential morphological features, such as pore size distribution, solid fraction, and pore-wall thickness. The resulting representative volume elements are modeled as beam-frame networks and analyzed using finite element methods with periodic boundary conditions to simulate mechanical responses under different loading conditions. Model validation is performed using experimental data from $\kappa$-carrageenan-based biopolymer aerogels. The excellent agreement between predicted and experimental microstructural characteristics and stress-strain responses highlights the fidelity and robustness of the proposed framework. The framework is then extended to explore structure-property relationships through systematic variations in pore morphology. The results reveal that while solid fraction primarily governs bulk stiffness and yielding behavior, the pore size distribution critically influences post-yield characteristics, including the extent and onset of the plateau regime and the densification phase. Moreover, the ultra-low-density open-porous materials exhibit a pronounced resistance to volumetric expansion under tensile loading. Furthermore, the fracture behavior for different pore morphologies under tensile loading is studied, using principles of linear elastic fracture mechanics. Results show that higher porosity and thinner walls reduce resistance to crack propagation, while certain architectural features can enhance energy dissipation. These findings emphasize the importance of considering pore geometry distributions in addition to density-based models in material design strategies for achieving tailored mechanical performance. The thesis also introduces a data-driven approach to constitutive modeling using deep symbolic regression. Unlike traditional black-box neural networks, deep symbolic regression provides interpretable closed-form mathematical expressions that capture the relationship between microstructural descriptors and macroscopic mechanical response. This method facilitates the derivation of explicit strain energy functions based on microstructural characteristics, offering a novel and physically interpretable predictive constitutive model for complex cellular-like open-porous materials, preserving the continuum mechanics framework.