Geometric Elasticity and Anelasticity
Speaker: Arash Yavari, The School of Civil and Environmental Engineering, Georgia Tech
Abstract: In this seminar we present some applications of modern differential geometry in solid mechanics. Traditionally, mechanics has been formulated in Euclidean space, mainly for convenience and simplicity as in the early days of modern mechanics, engineering scientists were interested in the simplest possible models. Working with the simplest possible models for the practical problems of the time laid the foundations of continuum mechanics. However, experience in physics shows that, in general, configuration space of a physical system is not globally Euclidean; physical theories should be formulated on manifolds. We first motivate the recent geometric studies in continuum and discrete mechanics by some important applications of geometric ideas, e.g. systematic discritizations of elasticity and mechanics of defects. We review some previous attempts in geometrization of different solid mechanics problems, e.g. continua with distributed defects, etc. We then discuss several applications of geometric techniques in solid mechanics, namely, covariant formulation of elasticity, material evolutions and their role in continuum mechanics, geometric linearization of elasticity, thermal stresses, kinematics of defect mechanics, geometric ideas in growth mechanics, and geometric discretization of elasticity.
Room Reservation Information
Room Number: 216 McAllister
Time: 3:35pm - 4:25pm