title: Rigidity transition in materials: hardness is driven by weak atomic constraints.
abstract: Understanding the composition dependence of the hardness in materials is of primary importance for infrastructures and handled devices. Stimulated by the need for stronger protective screens, topological constraint theory has recently been used to predict the hardness in glasses. Herein, we report that the concept of rigidity transition can be extended to a broader range of materials than just glass. We show that hardness depends linearly on the number of angular constraints, which, compared to radial interactions, constitute the weaker ones acting between the atoms. This leads to a predictive model for hardness, generally applicable to any crystalline or glassy material.
authors: Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095, USA.
authors: Mathieu
authors: M
authors: Bauchy
authors: Concrete Sustainability Hub, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
authors: Mohammad Javad Abdolhosseini
authors: MJ
authors: Qomi
authors: Centre Interdisciplinaire des Nanosciences de Marseille, CNRS and Aix-Marseille University, Campus de Luminy, Marseille, 13288 Cedex 09, France.
authors: Christophe
authors: C
authors: Bichara
authors: Concrete Sustainability Hub, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.|MIT-CNRS joint laboratory at Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
authors: Franz-Josef
authors: FJ
authors: Ulm
authors: Concrete Sustainability Hub, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.|Centre Interdisciplinaire des Nanosciences de Marseille, CNRS and Aix-Marseille University, Campus de Luminy, Marseille, 13288 Cedex 09, France.|MIT-CNRS joint laboratory at Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
authors: Roland J-M
authors: RJ
authors: Pellenq