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2016/2017
Civil Engineering and Geosciences
Master Civiele Techniek
CIE4353
Continuum Mechanics
ECTS: 6
Course Coordinator
Name
E-mail
Ir. C. Kasbergen
C.Kasbergen@tudelft.nl
Instructor
Name
E-mail
Prof.dr. M.A. Hicks
M.A.Hicks@tudelft.nl
Dr. A. Scarpas
A.Scarpas@tudelft.nl
Contact Hours / Week x/x/x/x
4/4/0/0
Education Period
1
2
Start Education
1
Exam Period
2
3
Course Language
English
Course Contents
The course starts with the basics of tensor algebra. Various orders of tensors and their associated tensorial operators (like dyadic product, (double) dot product, cross product) are explained in 3 different tensor notation styles: direct, base and index notation. With this knowledge, tensor expressions are judged on their correctness, and simple proofs for tensor equalities are discussed.
The next topic concerns motion and deformation. Deformation will be the basis for the derivation of small and large/ finite strain tensors in the reference and the current configuration. This is followed by the polar decomposition of the deformation gradient tensor and the spectral decomposition into the principal stretches and their corresponding directions.
Furthermore the stress tensor is introduced, including traction and stress components, principal stresses and their directions, and isotropic and deviatoric stress tensors. Material time derivatives of vector and tensor fields are described and their physical significance is clarified.
The core part of the course is related to mechanical balance laws and several basic continuum theories like hyperelasticity, plasticity and viscoelasticity, all setup in a thermodynamic large deformation framework. Several material models based on combinations of the before mentioned theories are discussed, for example the Generalized Maxwell model.
Finally the basic laws of physics for multi-phase materials are formulated. The same physical laws are deployed for each phase of the multi-phase continuum, inclusive of interaction terms. Then constitutive laws for each of the phases and their interactions are discussed. Also, as a special topic , a constitutive framework for materials with strong discontinuities is presented.
Study Goals
1. To master three notation conventions (direct, base and index notation) commonly used in tensor algebra to perform calculus on tensor-based mathematical expressions.
2. To reproduce several notions in continuum mechanics, like deformation, strain and stress, all in a large deformation framework; using these notions in the application of mechanical balance laws and deformation decompositions.
3. To explain the important continuum theories like hyperelasticity, plasticity and viscoelasticity setup in a thermodynamics large deformation framework, and to apply these theories to develop and interpret elasto-visco-plastic models (e.g. the generalized Maxwell model) ; to reproduce the mechanics and physics of strong discontinuities and multi-phase continuum materials in large deformation and flow.
Education Method
Lectures and homework exercises
Course Relations
CIE4353 uses CTB1001, CTB1002, CTB1110, CTB1310, CTB2210, CTB2400, WI1030WBMT, WI1031WBMT, WI2031WBMT, WB1630, WB1631, WB2630
Literature and Study Materials
Additional reading material:
- Eglit, M.E., Hodges, D.H., "Continuum Mechanics via problems and exercises", Part 1: Theory and Problems, World Scientific Publishing Co. Pte. Ltd, 1996, ISBN: 981-02-2962-3. Part 2: Answer and Solutions, World Scientific Publishing Co. Pte. Ltd, 1996, ISBN: 981-02-2963-1.
- Haupt, P., "Continuum Mechanics and theory of materials", Springer-Verlag, 2000, ISBN: 3-540-66114-x.
Assessment
Written exam (open book) and assignments
Expected prior Knowledge
Basic knowledge of mechanics and linear algebra
Academic Skills
Thinking, interpreting and application skills in mathematics and mechanics, problem solving
Literature & Study Materials
Lecture slides, literature provided during lectures and the books mentioned above as additional reading material
Judgement
Final mark consists for 50% of the mark of the examination and 50% of the mark of the homework assignments
Permitted Materials during Exam
Lecture slides, worked out assignments and notes written in class
Collegerama
No