Emergence of linear isotropic elasticity in amorphous and polycrystalline materials

• Main Authors: Mahajan, Shivam, Chattoraj, Joyjit, Ciamarra, Massimo Pica
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2021
• Subjects: Science::Physics; Elasticity; Glasses
• Online Access: https://hdl.handle.net/10356/151110
• Institution: Nanyang Technological University

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale ξE, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size. The stiffness matrix of systems of finite size L>ξE is obtained, adding to that predicted by linear isotropic elasticity a random one of spectral norm (L/ξE)−3/2 in three spatial dimensions. We further demonstrate that the elastic length scale corresponds to that of structural correlations, which in polycrystals reflect the typical size of the grain boundaries and length scales characterizing correlations in the stress field. We finally demonstrate that the elastic length scale affects the decay of the anisotropic long-range correlations of locally defined shear modulus and shear stress.