Module Code - Title:

ME6001 - FUNDAMENTALS OF CONTINUUM MECHANICS

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

0

Tutorial

1

Other

0

Private

0

Credits

6

Grading Type:

Prerequisite Modules:

Rationale and Purpose of the Module:

Syllabus:

Basic concepts and definitions: Concept of a continuum, continuity, homogeneity and isotropy; Elements of vector and tensor algebra. Deformation and flow: Length and angle changes: Strain tensor; Material and Eulerian description; Deformation rate tensor Stresses: Body and surface forces; Stress tensor; Principal stresses, Stress invariants, Hydrostatic and deviatoric stresses. Fundamental laws of continuum mechanics: Mass conservation, Newtons laws, Conservation of energy. Constitutive relations: Ideal materials; Constitutive relations and equations of state; Elastic solids; Newtonian fluids Mathematical models: Linear elastic solids; Newtonian fluids; Initial and boundary conditions. Introduction to the Finite Element method: Principle of virtual work; Finite element discretisation; Linear elastic finite-element model; Shape functions; Numerical quadrature; Mapping of elements; Solution of the finite-element equations.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

1. Demonstrate an understanding of the concept of a continuum and the application of physical and constitutive laws Final exam and homework for credit. 2. Given a deformation field, determine appropriate measures of strain, strain rate and stress for a solid or fluid Final exam and homework for credit. 3. Define and solve simple continuum mechanics problems, involving heat transfer, stress analysis, deformation and/or fluid flow Final exam and homework for credit. 4. Demonstrate how continuum mechanics principles can be used to formulate the finite-element (FE) equations Final exam and homework for credit. 5. Demonstrate the use of shape functions and numerical integration in the finite-element method Final exam and homework for credit.

Affective (Attitudes and Values)

N/A

Psychomotor (Physical Skills)

N/A

How the Module will be Taught and what will be the Learning Experiences of the Students:

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

Belytschko T., Liu W.K., and Moran W.K (2000) Non linear finite-elements for continua and structures , Wiley and Sons

Malvern, L.E (1969) Introduction to the mechanics of a continuous medium , Prentice-Hall, Inc.

Zienkiewicz, O.C. and Taylor, R.L. (2000) The finite-element method, Vol. 1: The basis (5e) , Butterworth-Heinemann

Zienkiewicz, O.C. and Taylor, R.L. (2000) The finite-element method, Vol. 2: Solid mechanics (5e) , Butterworth-Heinemann

Jordan, D.W. and Smith, P (2008) Mathematical Techniques (4e) , Oxford University Press

Other Relevant Texts:

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

Harry.VanDenAkker@ul.ie