Aims

The aims of the course are to:

• develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
• understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.

Objectives

As specific objectives, by the end of the course students should be able to:

• show a working knowledge of tensor notation
• define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
• use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
• solve linear viscoelastic problems for arbitrary loading time-histories
• understand numerical solution methods for nonlinear continuum mechanics problems.

Content

This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.

Preliminaries (2L, Dr GJ McShane)

• Introduction to indicial notation.
• Vectors, tensors and their manipulation.

Linearised Continuum Mechanics (6L, Dr GJ McShane)

• Kinematics: infinitesimal strains, compatibility.
• Conservation laws; stress and equilibrium.
• Linear elasticity: method of stationary potential energy.
• Linear viscoelasticity: constitutive equations;  solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.

Nonlinear Continuum Mechanics (8L, Prof GN Wells)

• Nonlinear kinematics.
• Strain rates and stress measures.
• Nonlinear elasticity:  stationary potential energy and hyper-elasticity.
• Numerical solution methods.

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 31/05/2024 10:02