On Robust Shell Element and Nonlocal Approaches to Modeling Architected Structures and Fracture in Solids

A Warren Distinguished Lecture and 
 J.S. Braun/Braun Intertec Visiting Professor Lecture with
J. N. Reddy

Mechanical Engineering
Texas A&M University

ABSTRACT
This J.S. Braun/Braun Intertec Visiting Professor Lecture consists of Reddy’s recent research on (1) shell finite element with thickness stretches and free of all types of locking and (2) nonlocal approaches for modeling architected materials and structures and fracture in brittle and quasi-brittle solids including concrete and glass. The seven-parameter shell element developed is 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 element is insensitive to all forms of numerical locking and is a best alternative to 3-D finite elements in saving computational resources while predicting accurate stresses. In addition, a thermodynamically consistent fracture model for brittle and quasi-brittle solids based on Graph-based Finite Element Analysis (GraFEA) will be presented. He also develops a computational model based on GraFEA which describes the deformation kinematics of a plate using the first-order shear deformation theory. The fundamental idea of this model is the presence of multiple microcracks traversing through a material point on the top and bottom surfaces of the plate. Crack planes represent these microcracks, oriented at specific angles relative to the x-axis. The state of a crack plane evolves based on the probabilistic description provided in the previous studies. Reddy shows that the proposed plate formulation compares well with the numerical results from the GraFEA 3D simulations and experimental observations from the literature.

SPEAKER
J. N. Reddy is a Distinguished Professor, Regents’ Professor, and the holder of the O’Donnell Foundation Chair IV in Mechanical Engineering at Texas A&M University. He is known for his significant contributions to the field of applied mechanics through the authorship of many textbooks (25) and journal papers (>800). His pioneering works on the development of shear deformation theories have had a major impact and have led to new research developments and applications. In recent years, Reddy's research has focused on the development of locking-free shell finite elements and nonlocal and nonclassical continuum mechanics problems dealing with architected materials and structures and damage and fracture in solids. Reddy has received some of the highest awards, including the Leonardo da Vinci Award from the European Academy of Sciences, the IACM Congress (Gauss-Newton) Medal from the International Association of Computational Mechanics, and the SP Timoshenko Medal from ASME. He is a member of nine academies, including the US National Academy of Engineering, Chinese Academy of Engineering, and the Royal Society (Sciences) of Canada.