Mechanics of deformable bodies

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 measures. Deformation tensors. Basic types of deformation. Compatibility conditions. Geometric linearization. Small strain theory. Material derivative. Transport theorems

Balance laws. Basic physical principles. Stress tensors. Thermodynamics. Material and space form of governing equations. Constitutive relations. Material frame indifference.

Elasticity. Elastic symmetries. Isotropic elasticity. Hyperelasticity. Basic models of hyperelasticity. Variational principles. Infinitesimal elasticity. Navier equation. Green function. Plane problems. Basic examples of three dimensional problems. Elastic waves. Linear fracture mechanics.

Inelasticity; thermoelasticity, viscoelasticity, plasticity.

Introduction to mechanics of materials. Equivalent eigenstrain principle. Effective material properties. Homogenization.

Readings

Bertram A. Elasticity and Plasticity of Large Deformations, Springer, 2008.
Bigoni D. Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability, Cambridge, 2012.
Holzapfel G.A. Nonlinear Solid Mechanics: A Continuum approach for Engineering, Wiley, 2000.
Gross D., Seelig T. Fracture Mechanics: With an Introduction to Micromechanics. Springer, 2011
Slaughter W.S. The Linearized Theory of Elasticity. Birkhäuser, 2002.

Objectives and competences

An overview of fundamental facts and ingredients of mechanics of deformable bodies 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 mechanics of deformable bodies.

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]