###### Learning Outcomes:

At the completion of the module, the students should be able to:

1. Demonstrate knowledge and understanding of basic concepts of continuum, field theory, and conservation and constitutive laws.

2. Formulate and solve simple Continuum Mechanics problems, i.e. problems involving field theory, stresses, deformation and flow, conservation and constitutive laws.

3. Demonstrate understanding of fundamental basics of FV discretisation procedure; Define and set-up within the FV framework a variety of steady and unsteady continuum mechanics problems.

4. Demonstrate understanding of fundamental basics of FE discretisation procedure; Define and set-up within the FE framework a variety of steady and unsteady continuum mechanics problems.

5. Identify main differences between FV and FV methods, their advantages and disadvantages, and hence decide which of the method will best suit a particular problem.

6. Present and justify the main assumptions and findings in formulating and solving a CCM problem.

###### Indicative Module Content:

1. Basic concepts and definitions: Concept of continuum; Continuity, Homogeneity and isotropy; Mathematical basis; Elements of matrix algebra.

2. Stresses: Body and surface forces; Stress tensor; Principal stresses. Stress tensor's invariants; Spherical and deviatoric stresses.

3. Deformation and flow: Material and spatial description; Deformation; Motion and flow.

4. Fundamental laws of Continuum Mechanics: Mass conservation; Conservation of linear momentum; Conservation of angular momentum; Conservation of energy; Law of entropy production.

5. Constitutive relations: Ideal materials; Classical constitutive relations and equations of state; Elastic solids; Ideal and Newtonian fluids.

6. Mathematical models: Linear elastic solids; Newtonian fluids; Initial and boundary conditions; Generic transport equation.

7. Finite volume disretisation: Main concepts and ideas of the Finite Volume method; Time and space discretisation, equation discretisation, conservativness, boundedness, stability, accuracy, consistency, convergence; Discretisation for 2D Cartesian mesh: u-momentum, v-momentum, energy; Initial and boundary conditions: Dirichlet boundary condition, Neumann boundary condition, mixed boundary condition, symmetry boundary condition; 3D problems in domains of arbitrary shapes.

8. Finite element discretisation: Principle of virtual work; Finite element discretisation; Linear elastic finite element model; Assembly of element and global stiffness matrix; Shape functions; Numerical quadrature; Mapping of elements; Solution of the finite element equations.

Tutorials:Tutorials are integral part of this module and students are strongly advised to attend all tutorial sessions. Tutorials are also the main component of the continuous assessment. There will be five tutorial assignements, and the solutions are to be handed in within one week after the corresponding tutorial session.