Robust Shell Element & Nonlocal Approaches to Modeling Architected Structure and Fracture in Solids

In this Warren Distinguished Lecture, Professor J.N. Reddy presents his recent research on two main topics: a robust shell finite element formulation and nonlocal approaches for modeling architected materials and fracture. The shell element incorporates a seventh parameter for thickness stretch, based on modified first-order and third-order kinematics, and uses spectral interpolation functions to avoid locking. It employs fully three-dimensional constitutive equations, eliminating the need for plane stress assumptions. The formulation is shown to be free from shear, membrane, and thickness locking, and is computationally efficient through static condensation of internal nodes. The second part introduces Graph-based Finite Element Analysis (GraFEA) for modeling fracture in brittle and quasi-brittle solids, including concrete and glass. This method uses a probabilistic description of crack planes and can simulate crack initiation, propagation, and closure. Reddy also presents a plate formulation based on GraFEA with first-order shear deformation theory, which compares well with 3D simulations and experimental data. The lecture emphasizes the importance of foundational mechanics knowledge and the incremental nature of research, and highlights the need for numerical simulations to be validated against experiments.