.. _fundamentals:

Section 1: Fundamentals (Weeks 1-2)
====================================

**Foundation in rheological concepts and terminology**

.. admonition:: Section Overview
   :class: note

   This section builds your foundational understanding of rheology from first principles.
   You will learn core concepts, material classification, experimental techniques, and
   how to interpret rheological parameters physically.

   **Timeline**: Weeks 1-2 (8-10 hours)

   **Prerequisites**: Basic physics (stress, strain) and calculus

Learning Objectives
-------------------

By completing this section, you will be able to:

1. Define rheology and explain its importance in materials science
2. Classify materials as liquids, solids, or gels based on rheological behavior
3. Identify and distinguish between four major test modes (SAOS, relaxation, creep, flow)
4. Interpret physical meaning of rheological parameters (:math:`G'`, :math:`G''`, :math:`\eta`, :math:`\tau`, :math:`\alpha`)
5. Recognize viscoelastic behavior in experimental data

Section Contents
----------------

.. toctree::
   :maxdepth: 2

   what_is_rheology
   material_classification
   test_modes
   model_capabilities
   parameter_interpretation

Section Roadmap
---------------

**Week 1: Core Concepts**

- :doc:`what_is_rheology` — What is rheology and why does it matter?
- :doc:`material_classification` — Understanding liquids, solids, and gels

**Week 2: Experimental Methods**

- :doc:`test_modes` — SAOS, relaxation, creep, and flow experiments
- :doc:`parameter_interpretation` — Physical meaning of rheological parameters

Key Concepts Summary
--------------------

**Rheology** is the study of how materials deform and flow under applied forces.
It bridges solid mechanics (elasticity) and fluid mechanics (viscosity).

**Viscoelastic materials** exhibit both:

- **Elastic behavior**: Energy storage, reversible deformation
- **Viscous behavior**: Energy dissipation, irreversible flow

**Test modes** probe different aspects of material response:

- **Small-Amplitude Oscillatory Shear (SAOS)**: Linear viscoelasticity in frequency domain
- **Stress Relaxation**: Decay of stress under constant strain
- **Creep**: Strain increase under constant stress
- **Steady Shear Flow**: Viscosity as a function of shear rate

**Parameters** have physical interpretations:

- :math:`G'`, :math:`G''`: Storage and loss moduli (stiffness and damping)
- :math:`\eta`: Viscosity (resistance to flow)
- :math:`\tau`: Characteristic relaxation time (timescale of response)
- :math:`\alpha`: Fractional order (distribution of relaxation times)

Learning Resources
------------------

**Recommended Textbooks** (for deeper study):

- Ferry, J.D. *Viscoelastic Properties of Polymers* (3rd ed., 1980)
- Macosko, C.W. *Rheology: Principles, Measurements, and Applications* (1994)
- Larson, R.G. *The Structure and Rheology of Complex Fluids* (1999)

**Online Resources**:

- TA Instruments Rheology Basics (application notes)
- Anton Paar Rheology Wiki
- Society of Rheology educational materials

Assessment
----------

.. admonition:: Self-Assessment Checklist
   :class: tip

   After completing this section, you should be able to:

   ☐ Explain the difference between elastic and viscous behavior

   ☐ Classify a material as liquid-like, solid-like, or gel-like from :math:`G'` and :math:`G''` data

   ☐ Choose the appropriate test mode for a given material and question

   ☐ Interpret fitted parameters in terms of material microstructure

   ☐ Recognize common artifacts in experimental data

Next Steps
----------

After mastering fundamentals, proceed to:

**Section 2: Model Usage** (:doc:`../02_model_usage/index`)

Learn to fit rheological models, select appropriate models for your data,
and validate fitting results.