# 8MB00 - Mechanics

### Contents

1. Vector calculus/ vector operations /decomposition with respect to a basis
2. Concepts of Force and Moment / Newton's laws /tensor- en matrix notation / drawing conventions
3. Equilibrium of force and momentum / free body diagrams
4. Analysis of a 1-D-continuum / strain /stress /material behaviour
5. Tensor calculus / vector field /rigid body rotation
6. Stress 3D/ equilibrium equations / principal stresses / Von Mises stresses / Mohr's circles
7. Motion / time as an extra dimension / Lagrange and Eulerian description / spatial and time time derivatives / displacement vector / gradient operator
8. Deformation and rotation/ rektensors /volume change
9. Constitutive behaviour of solids and fluids / (in) compressibel Neo Hookean behaviour, Newtonian fluids.

### Learning objectives

1. Students have to understand the basics of equilibrium of forces and moments.
2. They need to have operational knowledge of vector- and tensor calculus in coordinate free notation as well as matrix notation after introduction of a basis.
3. Solve the one-dimensional equilibrium equation and have basic knowledge on 2- and 3-dimensional equilibrium equations.
4. A good understanding of the definitions and properties of the stress and strain tensors. Interpret and use them.
5. Understand the deformation rate tensor, the spin tensor and the velocity gradient tensor
6. Determine gradients in scalar and velocity fields
7. Describe movement of particles through a field
8. Understand constitutive behaviour of isotropic solids for small and large deformations and Newtonian fluids.