Continuum mechanics and thermodynamics of living matter

Objectives

To provide a thermodynamical framework for the constitutive behaviour of active biological materials.

Keywords: Continuum mechanics, thermodynamics, visco-elasticity, living matter, morphogenesis, growth.

Prerequisites:

• Framework of continuum mechanics (kinematics and balance laws)
• Basic knowledge of thermodynamics laws and quantities (first and second principle, energy, entropy, free energy)
• Derivatives of tensor fields

Registration on the ADUM platform

Programme

Dates are for 2025, 1.30pm–3.30pm. The course will take place on University campus, Phitem A building.

1. Thu 6/2, room A120 – Introduction: active stresses in living systems. Discussion of length scales. Define the scope of the course: give a framework that is thermodynamically sound on how to include these active stresses in mechanical models (but not on their origin) and provide examples of the complex behaviours that can result. Thermodynamics of molecular motors.
Slides for lecture 1 (videos included, use a compatible PDF reader such as okular or evince to see them)

2. Thu 13/2, room A103 – Fundamental balance laws: kinematics - mass balance - force balance - energy balance - entropy production
Notes for lecture 2

3. Thu 20/2, room A120 – Microstructure: Derivation of a constitutive equation from the dynamics of the microstructure.
Slides for lecture 3 and additional details

4. Thu 27/2, room A120 – Thermodynamics: Entropy production, close-to-equilibrium dynamics, Onsager approach. Dynamical equations / limiting behaviours

(no course on 6/3 – university break)

5. Thu 13/3, room A120 – Motility: initiation of self-propulsion by interaction with a substrate.

6. Thu 20/3, room A119 – Complements and conclusions.

Bibliography

General references:

• Gurtin, M.E., Fried, E. and Anand, L., 2010. The mechanics and thermodynamics of continua. Cambridge University Press.
• Gonzalez, O. and Stuart, A.M., 2008. A first course in continuum mechanics (Vol. 42). Cambridge University Press.
• Larson, 1988. Constitutive equations for polymer melts and solutions. Butterworth.

Lecture 1:

• Erlich et al. How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale, Interface Focus., 2022, 12(6):058101, 10.1098/rsfs.2022.0038
• Jülicher, Ajdari and Prost. Modeling molecular motors, Rev. Mod. Phys., 1997, 69(4):1269--1282, 10.1103/RevModPhys.69.1269 (access via UGA)

Lecture 3: link provided in the slides.

2023 programme

Alexander Erlich, Jocelyn Etienne and Pierre Recho

1. Thu 6/4 – Introduction: active stresses in living systems, with an emphasis on tissues. Discussion of length scales. Define the scope of the course: give a framework that is thermodynamically sound on how to include these active stresses in mechanical models (but not on their origin) and provide examples of the complex behaviours that can result.
2. Thu 20/4 – Fundamental balance laws: kinematics - mass balance - force balance - energy balance - entropy production
3. Thu 27/4 – Thermodynamics: Entropy production, close-to-equilibrium dynamics, Onsager approach. Dynamical equations / limiting behaviours
4. Thu 4/5 – 1D growth of bars: single bar, assembly of bars, seashell. Main physical ingredient: differential growth.
5. Thu 11/5 – 2D growth of cylindrical structures: onion-like layering (stability, example: arteries). Cylinders stacked on top of each other, example: Drosophila wing disk.
6. Thu 25/5 – Contractility of living tissue: viscoelasticity with an active term. Timescales, morpho-elastic view. Elastic limit and a buckling example: ventral furrow formation of Drosophila embryo. Tissue flow at long timescales.

Dates are for 2023, 10.30am–12.30am.