ENGINEERING TRIPOS PART IIB - 2012/2013

Module 4C9 - Continuum Mechanics

AIMS

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.

LECTURE SYLLABUS

Preliminaries (3L, Prof V.S. Deshpande)

• Introduction to reduced subscript notation
• Stress and equilibrium, strain and compatibility and constitutive relationships

Elasticity (5L, Prof V.S. Deshpande)

• The applications of the principles of elastic analysis will be illustrated by reference to a variety of structural and mechanical elements such as mixed boundary value problems, cracked bodies, contact problems and bodies containing circular or spherical inhomogeneities.

Plasticity (8L, Prof N.A. Fleck)

• 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.

OBJECTIVES

On completion of the module students should:

• have a working knowledge of Cartesian tensor notation;
• be able top determine the relations between loads, deflections and stresses and strains within elastic bodies subjected to a variety of boundary conditions.
• know Drucker's stability postulate and understand the implications of convexity and normality;
• understand the difference between deformation and flow theories of plasticity;
• understand and be able to apply slip line field theory as well as upper and lower bound theorems for perfectly plastic solids.

REFERENCES

Please see the Booklist for Group C Courses for references for this module.

Last updated: June 2012