Course Details

Nonlinear Mechanics

Academic Year 2024/25

NDB023 course is part of 1 study plan

NPC-SIS Winter Semester 2nd year

Course Guarantor


Language of instruction



4 credits



Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site


13 weeks, 2 hours/week, elective


1. Introduction to nonlinear mechanics. Physical and geometrical nonlinearities. Eulerian and Lagrangian nesnes. 2. Strain measures (Green-Lagrange, Euler-Almansi, engineering, logarithmic), their behavior in large strain and large rotation. Stress measures (Cauchy, 1. Piola-Kirchhoff, 2. Piola-Kirchhoff, Biot). Energeticaly conjugate stress and strain measures. 3. Tangent stiffness matrix, Material stiffness, Geometrical stiffness. Influence of nonlinear members of the strain tensor. Newton-Raphson method. Calculation of unbalanced forces. 4. Modified Newton-Raphson method. Postcritical analysis. Deformation control. Arc length method 5. Linear and nonlinear buckling. Von Mises truss, snap through. Physical nonlinearity (supports, beams, concrete, subsoil). 6. Types of materials, introduction into constitutive material models. Linear and nonlinear fracture mechanics. Fracture mechanical material parameters. 7. Problem of strain localization, false sensitivity on the mesh. Restriction of localization. Crack band model. Nonlocal continuum mechanics. 8. Constitutive equations for concrete and other quasi-fragile materials. Fracture-plastic model. Mircroplane model. 9. Influence of size to bearing capacity (size effect). Energetical and statistical causes. Analysis of the influence of size on strength in tension in bending. 10. Presentation of modeling by a software on nonlinear fracture mechanics. Examples of applications. Mechanics of damane.


13 weeks, 2 hours/week, compulsory


1. Demonstration of the differences between linear and nonlinear calculations. 2. Demonstration of the problems with a big rotations. Demonstration of the differences between the 2nd order theory and the large deformations theory. 3. Examples on bending of beams with a big rotations of the order of radians. 4. Examples on calculations of cables and membranes. 5. Examples on calculations of mechanismes. 6. Examples on calculations of stabilioty of beams. 7. Examples on calculations of stability of shells. 8. Comparison of the Newton-Raphson, modified Newton-Raphson and Picard methods. 9. Examples on postcritical analysis of beams and shells. 10. Demostration of the explicit method in nonlinear dynamics.