A Locking-free Shell Finite Element And a Micromorphic Theory To Study Architected Structures

The lecture will present the speaker’s recent research in: (1) the development of higher-order, locking-free shell finite elements for large deformation of laminated and functionally graded plate and shell structures [1] and (2) nonlocal approaches for modeling architected materials and structures [2]. The seven-, eight-, and twelve-parameter shell elements developed are based on modified first-order and third-order thickness stretch kinematics, and they require the use of fully three-dimensional constitutive equations. Through the numerical simulation of carefully chosen benchmark problems, it is shown that the developed shell elements are insensitive to all forms of numerical locking and are the best alternative to 3-D finite elements in saving computational resources while predicting accurate stresses. The graph-based finite element approach with nonlocal criterion (called GraFEA) to study fracture in solids is found to be very robust and accurate in predicting fracture. The approach has the ability to model discrete microcracking with random crack orientations. The computational technique also incorporates a probabilistic approach to damage growth by using a measure of “microcrack survival probability” and its evolution. The approach will be demonstrated using several examples.

Dr. Reddy is a Distinguished Professor, Regents’ Professor, and inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University, College Station, Texas. Dr. Reddy, an ISI highly-cited researcher, is known for his significant contributions to the field of applied mechanics through the authorship of 25 textbooks and over 800 journal papers. His pioneering works on the development of shear deformation theories (that bear his name in the literature as the Reddy third-order plate theory and the Reddy layerwise theory) have had a major impact and have led to new research developments and applications.