Continuum mechanics

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M1
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

Kinematics of deformation. Deformation gradient. Deformation measures. Deformation tensor. Homogeneous deformation, dilatation, shear. Deformation of arc, surface and volume elements. Lagrangian and Euler description. Material time derivative. Transport theorems.

Balance laws. Conservation of mass. Balance of linear momentum. Stress tensor. Balance of angular momentum. Cauchy momentum equation. Thermodynamics. Energy and the first law. Entropy and the second law.

Constitutive relations. Material frame indifference. Material symmetry, isotropy. Representation of constitutive functions. Basic models, elasticity, viscoelasticity, plasticity, fluids

Boundary value problem. Variational principles. Stability of the equilibrium. Universal equilibrium solutions.

Readings

Bertram A. Elasticity and Plasticity of Large Deformations, Springer, 2008.
Chadwick P. Continuum Mechanics : Concise Theory and Problems, Dover, 1999.
Gurtin M.E. An Introduction to Continuum Mechanics, Academic Press, 1981.
Liu I.S. Continuum Mechanics, Springer, 2002.
Tadmor E.B., Miller R.E. Elliot R.S. Continuum Mechanics and Thermodynamics, Cambridge, 2012.

Objectives and competences

An overview of fundamental facts and ingredients of continuum mechanics with emphasis on correct mathematical formulation based on previously mastered mathematical knowledge.

Intended learning outcomes

Knowledge and understanding:
To establish knowledge and understanding of fundamental principles of continuum mechanics.

Application:
Mastered coursework represents a foundation for specialized research in the field of mechanics.

Reflection:
Connecting acquired mathematical knowledge within the course with application of that knowledge in a general field of mechanics.

Transferable skills:
To enhance knowledge and understanding of mathematical methods for solving problems from natural science and technology.

Learning and teaching methods

Lectures, exercises, usage of computer algebra, homework and consultations.

Assessment

Regular homework assignments: 50%.
Oral presentation of homework: 50%.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

MEJAK, George. Variational formulation of the equivalent eigenstrain method with an application to a problem with radial eigenstrains. International journal of solids and structures, ISSN 0020-7683. [Print ed.], 2014, vol. 51, iss. 7-8, str. 1601-1616. [COBISS-SI-ID 17128281]
MEJAK, George. Eshebly tensors for a finite spherical domain with an axisymmetric inclusion. European journal of mechanics. A, Solids, ISSN 0997-7538. [Print ed.], 2011, vol. 30, iss. 4, str. 477-490. [COBISS-SI-ID 16025177]
MEJAK, George. Finite element solution of a model free surface problem by the optimal shape design approach. International journal for numerical methods in engineering, ISSN 0029-5981. [Print ed.], 1997, vol. 40, str. 1525-1550. [COBISS-SI-ID 9983833]