Date:
Thu, 26/05/2022 - 11:00 to 12:00
Location:
Los Angeles Bld., Jerusalem, Israel
Abstract:
Topological defects in 2D crystals embedded on curved surfaces [1], quasi-localized plastic deformations in amorphous matter [2] and wrinkles in thin sheets [3] are typical realizations of stress-relaxation mechanisms in different solid-like structures. Correspondingly, understanding defects structure, mechanical response and the emergent wrinkles patterns in these systems remains a formidable task.
In a recent work we developed a unifying screening theory in solids, in which local stress relaxations are
modeled as induced elastic charges, similar to emergent dipoles in dielectric media [4]. Contrary to its
electrostatic analog, the screening theory in solids is richer even in the linear case, with multiple screening
regimes that lead to qualitatively new mechanical response.
The generic form of the screening theory allows us to test it in different physical systems. For example, we
show that mechanical strains in amorphous solids are screened via the formation of plastic events that are
typically quadrupolar in nature. At low densities the screening effect is reminiscent of dielectrics with elastic
moduli being renormalized, while the effect at high density lead to qualitatively new mechanical response
with emergent screening dipoles. We show that high-density screening results in displacement fields that
strictly deviate from elasticity theory thus interpreted as anomalous elasticity. We show that theoretical
analysis, experimental measurements and MD simulations of frictional granular amorphous assemblies are in agreement with each other and provide a strong support for the theory. To test the generality of our screening approach we conclude by receding back to the wrinkles problem in stamped sheets similar to [3] and analyze it from the perspective of screening theory. We derive quantitative predictions for wrinkles pattern and find very good agreement with experimental measurements.
References:
1. Irvine, WTM, Vitelli V., and Chaikin PM., “Pleats in crystals on curved surfaces”, Nature 468, no. 7326
(2010).
2. Dasgupta, R., Hentschel, H. G. E., and Procaccia, I. ”Microscopic mechanism of shear bands in amorphous
solids”. Physical review letters, 109(25), (2012).
3. Hure, J. Roman, B. and Bico, J., “Stamping and Wrinkling of Elastic Plates”, Phys. Rev. E, Vol (109), p.
054302 (2012).
4. Lemaître, A. Mondal, C, Moshe, M. Procaccia, I. Roy, S. and Screiber-Re’em, K., “Anomalous elasticity and
plastic screening in amorphous solids”, Phys. Rev. E, Vol (104), p. 024904 (2021).
Topological defects in 2D crystals embedded on curved surfaces [1], quasi-localized plastic deformations in amorphous matter [2] and wrinkles in thin sheets [3] are typical realizations of stress-relaxation mechanisms in different solid-like structures. Correspondingly, understanding defects structure, mechanical response and the emergent wrinkles patterns in these systems remains a formidable task.
In a recent work we developed a unifying screening theory in solids, in which local stress relaxations are
modeled as induced elastic charges, similar to emergent dipoles in dielectric media [4]. Contrary to its
electrostatic analog, the screening theory in solids is richer even in the linear case, with multiple screening
regimes that lead to qualitatively new mechanical response.
The generic form of the screening theory allows us to test it in different physical systems. For example, we
show that mechanical strains in amorphous solids are screened via the formation of plastic events that are
typically quadrupolar in nature. At low densities the screening effect is reminiscent of dielectrics with elastic
moduli being renormalized, while the effect at high density lead to qualitatively new mechanical response
with emergent screening dipoles. We show that high-density screening results in displacement fields that
strictly deviate from elasticity theory thus interpreted as anomalous elasticity. We show that theoretical
analysis, experimental measurements and MD simulations of frictional granular amorphous assemblies are in agreement with each other and provide a strong support for the theory. To test the generality of our screening approach we conclude by receding back to the wrinkles problem in stamped sheets similar to [3] and analyze it from the perspective of screening theory. We derive quantitative predictions for wrinkles pattern and find very good agreement with experimental measurements.
References:
1. Irvine, WTM, Vitelli V., and Chaikin PM., “Pleats in crystals on curved surfaces”, Nature 468, no. 7326
(2010).
2. Dasgupta, R., Hentschel, H. G. E., and Procaccia, I. ”Microscopic mechanism of shear bands in amorphous
solids”. Physical review letters, 109(25), (2012).
3. Hure, J. Roman, B. and Bico, J., “Stamping and Wrinkling of Elastic Plates”, Phys. Rev. E, Vol (109), p.
054302 (2012).
4. Lemaître, A. Mondal, C, Moshe, M. Procaccia, I. Roy, S. and Screiber-Re’em, K., “Anomalous elasticity and
plastic screening in amorphous solids”, Phys. Rev. E, Vol (104), p. 024904 (2021).