To provide an introduction to the mathematical theory of viscous fluid flows and solid elastic materials. Cartesian tensors are first introduced. This is followed by modelling of the mechanics of continuous media. The module includes particular examples of the flow of a viscous fluid as well as a variety of problems of linear elasticity.

(LO1) To understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations.

(LO2) To apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability

Cartesian tensors. Transformation of components, symmetry and skew symmetry. Isotropic tensors.

Kinematics. Transformation of line elements, deformation gradient, Green strain. Linear strain measure.

Displacement, velocity, strain-rate.

Stress. Cauchy stress. Relation between traction vector and stress tensor.

Global balance laws. Equations of motion, boundary conditions.

Newtonian fluids. The constitutive law, uniform flow, Poiseuille flow, flow between rotating cylinders.

Linear elasticity. Field equations. Young''s modulus, Poisson''s ratio. Strain energy function. Betti''s reciprocal theorem.

Some simple problems of elastostatics. Expansion of a spherical shell, bulk modulus; deformation of a block under gravity; elementary bending solutions.Torsion of cylinders, Prandtl''s stress function.