Prerequisites:

Familiarity with classical mechanics (a6) and with complex variable theory (a2) and simple perturbation theory (as in the Section c course) will be useful.

Aims

This course introduces the basic concepts and mathematical models for solid mechanics at the continuum level. Both elastic and plastic materials are discussed, together with elastic wave propagation. It is also shown how these ideas can be used as a basis for practically useful models, with reference to

i	Rods, beams, plates, shells
ii	Buckling
iii	Contact and fracture
iv	Composite materials

All these applications use perturbation theory to some extent; (iii) uses complex analysis and elementary calculus of variations.

Synopsis

Tensors, conservation laws, Navier equations. Yield criteria. Simple static solutions in one and two dimensions. Elastic wave propagation, Rayleigh waves.

Ad hoc approximations for thin materials; simple bifurcation theory and buckling; mixed boundary value problems, brittle fracture and smooth contact; simple ideas about homogenization and composite materials.

Reading List

Background material can be found in:

• R M Hill, Mathematical Theory of Plasticity, Oxford Clarendon Press, 1998

• A E H Love, A Treatise on the Mathematical Theory of Elasticity, Dover, 1944