Abstract
A general description of the nonlinear mechanical behavior of quasi-periodic alloys is presented: It accounts for the rearrangements of atomic clusters (phason activity) and is based on a Lagrange-d'Alambert-type principle where phason dissipative effects are included. We find the covariance of the balance of phason interactions in the presence of phason friction, discuss the formulation of appropriate conservative and dissipative brackets, and recognize for quasicrystals the universality of affine deformations and affine phason activity at equilibrium for vanishing phason friction. Moreover, we investigate the nature of the influence of phason activity on a macroscopic discontinuity surface endowed with its own surface energy and find covariant interface balances describing its evolution. Finally, we investigate the nature of the balance of phason interactions in the bulk material and relate it to SO(3) invariance.
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Mariano, P. Mechanics of Quasi-Periodic Alloys. J Nonlinear Sci 16, 45–77 (2006). https://doi.org/10.1007/s00332-005-0654-5
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DOI: https://doi.org/10.1007/s00332-005-0654-5