Nonlinear Physics Seminar: "Elasticity and plasticity of amorphous solids: towards a topological theory"

Wed, 18/05/202212:00-13:30
Danciger B Building, Seminar room
Lecturer:    Prof. Alessio Zaccone, University of Milan Italy, and University of Cambridge UK

I will start from the microscopic theory of linear elasticity in amorphous which, from first-principles consideration of non-centrosymmetry in the particle contact environment, leads to mathematical predictions of elastic moduli in quantitative parameter-free agreement with numerical simulations of e.g. random jammed packings [1]. This theory fully accounts for the extra non-affine displacements which arise due to the lack of centrosymmetry that leads to force imbalance in the so-called "affine" position, with characteristic negative contributions to the shear modulus entirely due to non-affinity.
I will then show how the theory can be systematically extended to linear viscoelasticity again in excellent parameter-free agreement with mechanical spectroscopy (oscillatory rheology) in simulations of polymer glass rheology [2]. The same non-affine deformation theory is able to mathematically predict and explain the ubiquitous inverse cubic dependence of low-frequency shear modulus on confinement size for confined liquids and amorphous solids [3].

I will then show that non-affinity of particle motions gives rise to well-defined topological defects (dislocation-like topological defects, DTDs) which have recently been discovered in the linear and non-linear deformation of model amorphous solids [4]. The norm of the associated Burgers vector can be used as an accurate predictor of onset of plastic flow and yielding of the amorphous material, and, in combination with Schmid's law, to explain the phenomenon of shear banding via self-organization of DTDs in slip systems at 45 degrees with respect to flow direction [4]. Broader implications of the topological field theory for liquids and the liquid-solid transition will also be discussed [5].

[1] A. Zaccone and E. Scossa-Romano, Phys. Rev. B 83, 184205 (2011)
[2] V. V. Palyulin, C. Ness, R. Milkus, R. M. Elder, T. W. Sirk, A. Zaccone, Soft Matter 14, 8475-8482 (2018)
[3] A. Zaccone and K. Trachenko, PNAS 117, 19653-19655 (2020)
[4] M. Baggioli, I. Kriuchevskyi, T. W. Sirk, A. Zaccone, Phys. Rev. Lett. 127, 015501 (2021)
[5] M. Baggioli, M. Landry, A. Zaccone, Phys. Rev. E 105, 024602 (2022)