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Course, academic year 2019/2020
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Mathematical Methods in Mechanics of Solids - NMMO535
Title in English: Matematické metody v mechanice pevných látek
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2014 to 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Martin Kružík, Ph.D., DSc.
Class: M Mgr. MOD
M Mgr. MOD > Povinně volitelné
M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Mathematical Modeling in Physics
Incompatibility : NMOD044
Interchangeability : NMOD044
Annotation -
Last update: T_MUUK (14.05.2013)
Basic mathematical methods for analysis of boundary-initial-value problems arising in mechanics and thermomechanics of solids.
Aim of the course -
Last update: T_MUUK (14.05.2013)

To present at least a bit from Mathematical Methods in Solid State Continuum Mechanics

Course completion requirements -
Last update: Mgr. Dalibor Šmíd, Ph.D. (14.06.2019)

The exam is oral and the students are granted time for preparation.

Literature -
Last update: T_MUUK (28.04.2016)

Mielke, A. and T. Roubíček (2015). Rate-independent systems, Volume

193 of Applied Mathematical Sciences. Springer, New York. Theory and

application.

Roubíček, T. (2013). Nonlinear partial differential equations with

applications (Second ed.), Volume 153 of International Series of

Numerical Mathematics. Birkhäuser/Springer Basel AG, Basel.

Nečas, J. and I. Hlaváček (1980). Mathematical theory of elastic and

elasto-plastic bodies: an introduction, Volume 3 of Studies in Applied

Mechanics. Amsterdam: Elsevier Scientific Publishing Co.

Teaching methods -
Last update: T_MUUK (14.05.2013)

Lectures

Syllabus -
Last update: T_MUUK (14.05.2013)

Evolution problems at small deformations, viscous materials with rheology of Kelvin, Maxwell, or Poynting-Thompson type, materials with internal parameters (Halphen-Nguyen generalized standard materials), activated inelastic processes, a-priori estimates and existence of weak solutions, quasi-static activated rate-independent processes (plasiticity, martensitic transformation, damage, etc.), definition and existence of energetic solutions. Special evolution problems at large strains. Thermodynamics of viscoelastic matarials and selected inelastic processes, a-priori estimates of thermally coupled systems.

 
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