A One-Day Pre-Conference Short Course on

RECENT DEVELOPMENTS IN NON-LOCAL MATERIAL AND STRUCTURAL MODELS

Prof. J.N. Reddy, Texas A&M University

Course Objective:

The aim of the course is to give the participants an exposure to a currently hot topic, namely, non local and non-classical continuum mechanics models. There is experimental evidence that the classical continuum mechanics breaks down because the material (infinitesimal) and structural length scales are of the same order. This length scale problem arises, for example, in the design of beam-like micro and nanoelectromechanical (MEMS and NEMS) components, and in the modeling of foams and man-made lightweight lattice materials. Practical engineering applications for lattice materials include sandwich panels that are used in ship and bridge engineering.

Course Description:

The course will have an overview on materials and structures that are best modeled using non-classical continuum mechanics theories which, unlike the classical theory, employ material models that include intrinsic length scales. To familiarize with the topics prior to the course, selected course material will be sent to the participants. The course encompasses Eringen’s nonlocal elasticity theory and the modified couple-stress and micropolar continuum theories. The focus will be on the couple-stress and micropolar theories and the related beam and plate models including associated finite elements models. In general, accurate modeling of such materials requires the use of non-classical continuum mechanics theories.

The course will consist of lectures, reviewing the scientific literature and applications to beam and plate structures. Lecture notes and other material will be provided in electronic form. After the course, the participants will

1) understand the fundamental features of non-classical continuum mechanics and the differences between various existing theories,

2) can identify size effects in practical applications,

3) understand the main modeling principles of non-classical beams and plates, and

4) can apply the beam and plate models and finite elements in structural design problems.

Prerequisites:

Basic understanding of solid mechanics and some knowledge of the finite element method. The course is aimed for Master’s and PhD level students in aerospace, mechanical, and civil engineering, but all other students (e.g., mathematics, physics, and materials science), as well as faculty and industry persons with a suitable background may participate in the course.

Schedule:

09:00-10:15: Introduction & Motivation - Why do we need non-classical continuum mechanics? Eringen’s model: kinematics, stress, equilibrium

10:15-10:45: Coffee and tea break

10:45-10:15: Applications to beams and plates to bring out the length scale effects

12:00-13:00: Lunch break

13:00-14:15: Modified couple-stress theory: kinematics, stress, equilibrium

14:15-14:45: Coffee and tea break

14:45-16:00: Beam and plate models and finite elements with applications

16:00-16.30: Summary of the Course and Questions and Answers

Registration Fee: $75 (AED 275)

Interested candidates may write to Conveners for more details