MAM0220 - MATHEMATICAL PROBLEMS IN NONLINEAR VISCOELASTICITY

Module Identifier	MAM0220
Module Title	MATHEMATICAL PROBLEMS IN NONLINEAR VISCOELASTICITY
Academic Year	2001/2002
Co-ordinator	Dr Robert Douglas
Semester	Semester 1
Other staff	Professor Arthur Davies
Course delivery	Lecture	16 x 1 hour lectures
	Seminars / Tutorials	4 x 1 hour example classes
Assessment	Course work		100%
	Resit assessment	Coursework	100%

General description

This module develops techniques for the analysis of mathematical problems in nonlinear viscoelasticity. The systems of governing partial differential equations will be analysed to provide information on existence and uniqueness of solutions, the classification of the system and possible change of type. In addition, topics such as the formation of elastic boundary layers, the flow near a reentrant corner, the stability of viscoelastic flows, material instability and melt fracture will be examined in some detail.

Aims

This module will examine a number of mathematical problems in nonlinear viscoelasticity including existence and uniqueness of solutions to the governing sets of partial differential equations, change of type, flow stabilities, corner singularities and stress boundary layers.

Learning outcomes

On completion of this module, students should be able to:

Classify the set of partial differential equations arising from a range of differential constitutive equations.
Explore and describe the stability of a number of viscoelastic flows.
Explain possible causes of material instability and melt fracture.
Examine and describe the formation of elastic boundary layers.
Analyse the nature of the singular behaviour of solutions in regions of the flow near reentrant corners.

Reading Lists

Books
** Recommended Text
D.D.Joseph. (1990) Fluid dynamics of viscoelastic liquids. Springer-Verlag 0387971556
M Renardy. (2000) Mathematical analysis of viscoelastic flows. SIAM