2 Syllabus
2.1 Course information
| Semester | Fall 2025 |
| Lecture time | Mondays, 10:30–13:30 |
| Location | LD Building, Room 440 (Zoom when remote) |
| Instructor | Shmuel Osovski |
| Office | DK Building, Room 404 |
| Office hours | Mondays 15:00–16:00, or by appointment |
| Contact | shmuliko@technion.ac.il |
2.2 Course description
This course provides a comprehensive introduction to the theory and application of constitutive models for describing the mechanical behavior of engineering materials. We cover the essential mathematical and continuum mechanics framework, then explore fundamental models for elasticity (hyperelasticity), plasticity (rate-independent and rate-dependent), and damage mechanics. A significant portion focuses on the numerical implementation of these models, typically in the context of the Finite Element Method (FEM). The course also addresses validation, verification, inverse modeling for parameter identification, and emerging data-driven approaches.
2.3 Prerequisites
- Undergraduate Solid Mechanics (stress, strain, Hooke’s law)
- Multivariable calculus and differential equations
- Linear algebra (vectors, tensors/matrices)
- Basic programming (Python, MATLAB, Julia, or C++) — especially for the implementation part
- Recommended but not required: Introductory Continuum Mechanics, Introductory FEM
2.4 Learning objectives
Upon completion, students will be able to:
- Apply tensor algebra and calculus for constitutive modeling, including eigenvalue problems and objective rates.
- Analyze and implement kinematics, stress measures, conservation laws, and thermodynamic principles.
- Formulate, interpret, and implement constitutive models: elastic, inelastic, rate-dependent, and damage.
- Implement stress update algorithms (e.g., return mapping) and compute consistent tangent operators.
- Design and execute inverse modeling processes to identify material parameters from experimental data.
- Apply verification and validation methods.
- Evaluate and implement data-driven and surrogate modeling approaches.
2.5 Course schedule (13 weeks)
| Weeks | Topic | Lecture |
|---|---|---|
| 1–2 | Mathematical Preliminaries & Tensor Fundamentals | L01, L02 |
| 3 | Continuum Mechanics Fundamentals & Kinematics | L03 |
| 4 | Thermodynamic Framework & FEM Context | L04 |
| 5 | Hyperelasticity & Viscoelasticity | L05, L06 |
| 6–9 | Plasticity (theory, algorithms, rate-dependence) | L07, L08 |
| 10–11 | Damage Mechanics & Coupled Problems | L09 |
| 11–12 | Inverse Modeling & Parameter Identification | L10 |
| 13 | Data-Driven & Surrogate Modeling | L11 |
2.6 Assessment
| Component | Weight |
|---|---|
| Homework (4 sets) | 60% |
| Final project — report | 25% |
| Final project — presentation | 15% |
Late policy: All assignments must be submitted electronically via Moodle by the posted deadline. No credit is given after the end of the semester.
Final project: Topics will be discussed in class. Students may choose from a provided list or propose their own (subject to approval). Presentations are in the last week. Reports are due two weeks after the semester ends.
2.7 Textbooks & references
Primary:
- Simo, J. C. & Hughes, T. J. R. Computational Inelasticity. Springer.
- de Souza Neto, E. A., Peric, D. & Owen, D. R. J. Computational Methods for Plasticity: Theory and Applications. Wiley.
Supplementary: Selected papers and book chapters distributed throughout the semester.
2.8 Academic integrity
All submitted work must be your own. Collaboration on concepts is encouraged; final submissions must be individually prepared.
For programming assignments: you may discuss algorithms with classmates, but your code must be written independently. Cite all external resources.
On LLM/AI tools: Use is permitted, but you take full responsibility for correctness. LLM-generated text left in submissions will be treated as plagiarism. Incorrect citations will also be treated as plagiarism. AI tools help, but they do not replace the learning process.