Aims

The aims of the course are to:

• develop a more in-depth understanding of analytical techniques employed in continuum solid mechanics with particular emphasis on the response of elastic, visco-elastic and plastic bodies.

Objectives

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

• show a working knowledge of Cartesian tensor notation
• use the method of minimum potential energy to solve problems in linear elasticity
• understand how to solve viscoelastic problems in 1D and 3D for arbitrary loading time-histories
• know Drucker's stability postulate and understand the implications of convexity and normality
• understand the difference between deformation and flow theories of plasticity
• able to apply slip line field theory as well as upper and lower bound theorems for perfectly plastic solids

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 analytical techniques employed in continuum solid mechanics with particular emphasis on the response of elastic and plastic bodies.

Preliminaries (3L, Dr GJ McShane)

• Introduction to indicial notation
• Vectors, tensors and their manipulation
• Stress and equilibrium, strain and compatibility, constitutive relationships

Elasticity and Viscoelasticity (5L, Dr GJ McShane)

• Method of minimum potential energy
• Examples: application to elastic beams and plates in bending
• Deriving constitutive equations for linear viscoelasticity
• Solving viscoelastic problems in 1D for arbitrary loading time-histories
• Viscoelastic analysis in 3D

Plasticity (8L, Prof VS Deshpande)

• Constitutive relationships - Drucker's stability postulate, normality and convexity conditions, yield criteria, flow rules, strain-hardening materials, flow and deformation theories of plasticity;
• Limit analysis theorems;
• Slip-line field theory; the solution of boundary value problems - metal forming, contact problems, cracked bodies.

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

Toggle display of UK-SPEC areas.

 
Last modified: 31/05/2017 09:12