(Created 2009-08-11.)

CONTINUUM MECHANICS | FMEN20 |

**Aim**

The purpose of this course is to presents the classical theory of the mechanics of deformable bodies, i.e. continuum mechanics for solid, fluid and gaseous material bodies. The general concepts and principles of continuum mechanics are presented in the formulation of the conservation and balance equations combined with constitutive relations for material bodies. The course also gives an introduction to the algebra and analysis of Cartesian tensors.

*Knowledge and understanding*

For a passing grade the student must

- be able to explain and apply fundamental conception as the deformation gradient, displacement gradient, material and local time derivatives, rate of deformation and stress tensor
- describe the fundamental balance equations and conservation laws for a deformable body
- be able to explain the fundamental results in the general theory of constitutive relations
- describe and apply the general equations for some kind of fluid and elastic bodies and be familiar with some advanced constitutive relations

*Skills and abilities*

For a passing grade the student must

- be able to describe the motion of a deformable body and solve simple dynamic problems of deformable bodies using the fundamental balance equations and conservation laws
- apply and analyze different kind of constitutive relations.
- be able to formulate and solve some simple cases of flow and elastic problems
- be able to present a solution of a continuum mechanical problem in a technical report

*Judgement and approach*

For a passing grade the student must

- be able to evaluate the physical consistence of the obtained results
- be able to evaluate constitutive relations by calibrating and validating to experimental data

**Contents**

Deformation and the kinetics of the deformation of bodies, force and stresses in deformable bodies. General equations of conservation and balance for mass, momentum, linear momentum, force, energy and entropy.The relationship between global and local equations of balance. The theory of constitutive equations. Elastic solids and viscous fluids. Mixture theory. Examples of practical applications.

**Literature**

A.Ahadi, Lecture notes, E.Lundgren, Kontinuumsmekanik.

Mase & Mase: Continuum Mechanics for Engineers.