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 secondprinciple, energy, entropy, free energy)
• Derivatives of tensor fields

Programme

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. The course is expected to take place on University campus, Phitem A building, exact room TBA.

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.

Growth and elasticity:

• Goriely, A., 2017. The mathematics and mechanics of biological growth (Vol. 45). Springer.
• Taber, L.A., 2020. Continuum Modeling in Mechanobiology. Springer International Publishing.
• Epstein, M., 2012. The elements of continuum biomechanics. John Wiley & Sons.