Rheology Short Course

The short course is scheduled for April 13th and 14th, featuring two full days of immersive lectures and hands-on data analysis. Each day will focus on a distinct topic, covering both fondament concepts and the latest developments in the field. This combination of lectures and hands-on practice gives participants a balanced and engaging learning experience.

April 13th 2025 - "Viscoelastic Materials Under External Stimuli"

Instructors:  Prof. Annette M. Schmidt (U. of Cologne, Germany) & Dr. Alain Ponton (UPC-CNRS, France)

   

 

 

April 14th 2025 - "Applications of Fractional Calculus to Viscoelasticity"

Instructors:  Dr. Alessandra Bonfanti (Politecnico-Milano- Italy) & Prof. Gareth H. McKinley (MIT-USA)

 

This one-day short course on applications of fractional calculus to viscoelasticity will first review key concepts of linear viscoelasticity, emphasizing the limitations of classical (spring-dashpot) models in capturing the rheological behavior of soft materials, ranging from gels to biological tissues. Traditional linear models often fall short when applied to systems with complex microstructures or broad (power-law) time-dependent responses. To overcome these challenges, the course introduces the concepts of fractional-order derivatives and fractional constitutive models (based on the concept of a “spring-pot” element) which offer a more flexible and accurate framework for accurately modeling many complex fluids as well as soft solid materials such as hydrogels. It then delves into nonlinear differential and integral fractional models, highlighting their capacity to describe the onset of nonlinear (rate- and strain-dependence) in the rheological response of such materials.  These new families of fractional constitutive models provide deeper insights and connections to the underlying fractal or multiscale microstructures of many real-world and multicomponent materials, as well as enhanced predictive capabilities with fewer model parameters, offering significant practical advantages in several scientific fields. Participants will also explore the integration of these advanced constitutive models into machine-learning algorithms using Julia. Finally, the course provides hands-on guidance in fitting experimental rheological data using both traditional and fractional models, with practical sessions supported by the RHEOS (RHEology Open Source) package in Julia.

 

Course Outline: (4 x 1.5 lectures)

Lecture 1

·        Introduction to fractional calculus (motivation/overview)

·        History of the fractional derivative; Scott-Blair

·        Notation; quasi-properties, powerlaw indices

·        Fractional diffusion

·        Connections to classical Maxwell and Kelvin-Voigt Models

·        Compact descriptions of Experimental Data (parsimonious models, extrapolation)

 

Lecture 2

·        Characteristics of traditional models (the generalized relaxation spectrum)

·        From traditional viscoelastic models to fractional ones (and derivation of their constitutive equations)

·        The Mittag-Leffler function (qualitative behaviour and computation)

·        Heuristic overview and hierarchy of Fractional Maxwell and K-V models

 

Lecture 3

•       Pipkin Diagram and Extension to Nonlinear Deformations

•       The Strain Damping Function

•       Fractional K-BKZ formulations; normal stress differences

 

Lecture 4

•       Fitting rheological experimental data using linear viscoelastic models (including classical multimode models and fractional formulations).

•       Introduction to RHEOS (https://github.com/JuliaRheology/RHEOS.jl)  and its structures (data structure and code)

•       Practical training session on RHEOS