ON NON-LOCAL AND NON-CLASSICAL CONTINUUM MECHANICS THEORIES AND APPLICATIONS

J.N. Reddy

Advanced Computational Mechanics Laboratory

Department of Mechanical Engineering

Texas A & M University, College Station, TX 77843-3123

Abstract

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. In the case of structural mechanics, there is a wide range of theories, from higher gradient to truly nonlocal; however, there is a need for physical explanations and experimental observations that systematically corroborate these theories and provide physical interpretations of the parameters introduced in these theories. In this lecture, an overview of the author’s recent research with many colleagues on nonlocal elasticity and couple stress theories in formulating the governing equations of functionally graded material beams and plates will be presented. In addition to Eringen’s nonlocal elasticity (1972), two different nonlinear gradient elasticity theories that account for (a) geometric nonlinearity and (b) microstructure-dependent size effects are revisited to establish the connection between them. The first theory is based on modified couple stress theory of Mindlin (1963) and the second one is based on Srinivasa-Reddy gradient elasticity theory (2013). These two theories are used to derive the governing equations of beams and plates. In addition, the graph-based finite element framework (GraFEA) suitable for the study of damage in brittle materials will be discussed. GraFEA stems from conventional finite element method (FEM) by transforming it to a network representation based on the study by Reddy and Srinivasa (2015) and advanced by Khodabakhshi, Reddy, and Srinivasa (2016).

References

1. A. C. Eringen (1972): Int. J. Engng Sci, 10, p. 1.

2. R. D. Mindlin (1963): Experi. Mech., 3(1), p. 1.

3. A. R. Srinivasa and J. N. Reddy (2013): J. Mech. Phys. Solids, 61(3), p. 873.

4. J. N. Reddy and A. R. Srinivasa (2015): Finite Elements in Anal. Design, 104, 35-40.

5. P. Khodabakhshi, J. N. Reddy, and A. R. Srinivasa (2016): Meccanica, 51(12), 3129—3147.

2