Synopsis for C6.1b: Elasticity and Plasticity

Level: M-level Method of Assessment: Written examination.
Weight: Half-unit. OSS paper code 2467.

Recommended Prerequisites

Familiarity will be assumed with Part A Complex Analysis, Differential Equations and Calculus of Variations, as well as B568 Introduction to Applied Mathematics. A basic understanding of stress tensors from either B6a Viscous Flow or C6.2a Solid Mechanics will also be required. The following courses are also helpful: B5a Techniques of Applied Mathematics, B5b Applied Partial Differential Equations, C6.3a Perturbation Methods, C6.3b Applied Complex Variables.

Overview

The course starts with a rapid overview of mathematical models for basic solid mechanics. Benchmark solutions are derived for static problems and wave propagation in linear elastic materials. It is then shown how these results can be used as a basis for practically useful problems involving thin beams and plates. Simple geometrically nonlinear models are then introduced to explain buckling, fracture and contact. Models for yield and plasticity are then discussed, both microscopically and macroscopically.

Synopsis

Review of tensors, conservation laws, Navier equations. Antiplane strain, torsion, plane strain. Elastic wave propagation, Rayleigh waves. Ad hoc approximations for thin materials; simple bifurcation theory and buckling. Simple mixed boundary value problems, brittle fracture and smooth contact. Perfect plasticity theories for granular materials and metals.

1. P. D. Howell, G. Kozyreff and J. R. Ockendon, Applied Solid Mechanics (Cambridge University Press, 2008).
2. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, 1970).
3. L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon Press, 1986).