After successful completion of the course, students are able to

• solve theoretical problems regarding continuum mechanics of solid bodies by means of mathematical foundations (tensor algebra and analysis)
• apply various strain measures to practical problems and know how to use them properly
• apply displacment-strain relations for large deformations
• compute strains for a given displacement field
• apply various stress measures to practical problems and know how to use them properly
• compute the stresses in a body as a consequence of the external loading by means of balance equations
• apply simple constitutive laws (incompressible hyperelastic isotropic materials) to practical problems
• differentiate between plane stress and plane strain assumptions

Application of theory of continuum mechanics of solid bodies (see VO) on practical problems.

The content of the exercise is split into 7 subchapters:

1) Mathematical foundations

• Linear algebra (only repitition, basics are required, e.g. as matrix multiplications, calculation of the determinante, calculation of the inverse of a matrix, solving an eigenvalue problem etc.)
• Tensor algebra
• Tensor analysis
• Transformation of coordinates

2) Kinematics of continuum I

• Motion, velocity and acceleration in material and spatial description

3) Kinematics of continuum II

• Deformation gradient, displacement gradient
• Stretch tensors, strain tensors, principal stretch tensor etc.

4) Kinetics of continuum

• Traction vectors, stress tensors, principal stress tensors, axes of principal stresses etc.

5) Balance principles

• Conservation of mass and principle of linear momentum

6) Constitutive equations

• Influence of linearization on constitutive equations
• Incompressible hyperelastic isotropic materials

7) Plane stress and plane strain

• Elasticity matrices for plane stress and plane strain

Examples are presented and solved on the blackboard. A short review of the necessary theory (from the VO) is given.

Examples will be provided via TUWEL approx. one week before the particular exercise and should be self-studied beforehand. There are more examples within the collection of examples than it is possible to present on the blackboard within the time frame of the exercise. These examples can be self-studied in order to prepare for the exams.

The exercises are based on the theory lectured on the corresponding VO! The exercises will only be fruitful, if you partcipate in parallel in the VO or you are familiar with basics of continuum mechanics (due to the application of the theoretical methods on practical problems).

Two written exams, duration a 90min, collection of formulas can be used

Basics of matrix calculations

Basics of mechanics