题 目：Non-local and Non-classical Continuum Models
Dr. Reddy, the Oscar S Wyatt Endowed Chair Professor, Distinguished Professor, and Regents Professor of Mechanical Engineering at Texas A&M University, is a highly-cited researcher, author of 21 textbooks and over 600 journal papers, and a leader in the applied mechanics field for more than 40 years. Dr. Reddy has been a member of Texas A&M faculty since 1992.
Professor Reddy is known worldwide for his significant contributions to the field of applied mechanics through the authorship of widely used textbooks on the linear and nonlinear finite element analysis, variational methods, composite materials and structures, and continuum mechanics. 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.
Recent Honors include: 2016 Prager Medal, Society of Engineering Science, 2016 Thomson Reuters IP and Science’s Web of Science Highly Cited Researchers - Most Influential Minds, and the 2016 ASME Medal from the American Society of Mechanical Engineers, the 2017 John von Neumann Medal from the US Association of Computational Mechanics. He is a member US National Academy of Engineering and foreign fellow of Indian National Academy of Engineering, the Canadian Academy of Engineering, and the Brazilian National Academy of Engineering. A more complete resume with links to journal papers can be found at http://mechanics.tamu.edu
Structural continuum theories require a proper treatment of the kinematic, kinetic, and constitutive issues accounting for possible sources of non-local and non-classical continuum mechanics concepts and solving associated boundary value problems. There is a wide range of theories, from higher gradient to truly nonlocal (e.g., strain gradient theories, couple stress theories, Eringen’s stress gradient theories). In this lecture, an overview of the author’s recent research on nonlocal elasticity and couple stress theories in developing the governing equations of beams and plates will be presented. Two different nonlinear gradient elasticity theories that account for geometric nonlinearity and microstructure-dependent size effects are discussed. The first theory is based on modified couple stress theory of Mindlin  and the second one is based on Srinivasa and Reddy gradient elasticity theory . These two theories are used to derive the governing equations of beams and plates [3, 4]. In addition, a graph-based finite element framework (GraFEA) suitable for the study of damage in brittle materials will be discussed .
References of additional information
1. Mindlin, R.D., “Influence of couple-stresses on stress concentrations,” Exper Mech. 3(1), 1-7, 1963.
2. Srinivasa, A.R. and Reddy, J.N., “A model for a constrained, finitely deforming, elastic solid with rotation gradient dependent strain energy, and its specialization to von Karman plates and beams,” J. Mech Phys Solids, 61(3), 873-885, 2013.
3. Arbind, A., Reddy, J.N., and Srinivasa, A.R., “Nonlinear analysis of beams with rotation gradient dependent potential energy for constrained micro-rotation,” Eur J Mech, A/Solids, 65, 178-194, 2017.
4. Arbind, A., Reddy, J.N., and Srinivasa, A.R., “Nonlinear analysis of plates with rotation gradient dependent potential energy for constrained micro-rotation,” J Engng Mech, 144(2), 2018.
Khodabakhshi, P., Reddy, J.N., and Srinivasa, A.R., “GraFEA: A graph based finite element approach for study of damage and fracture in brittle materials,” Meccanica, 51(12), 3129-3147, 2016.