In this work, we report on the formulation and detailed stability analysis of a dynamic multi-scale scheme involving two different local computational strategies for modeling of elastic wave propagation. The coupled model involves the Local Interaction Simulation Approach and Cellular Automata for Elastodynamics, however the presented analysis approach is general and applies to other numerical techniques. This scheme is capable of coupling two numerical models with possibly dissimilar spatial discretization lengths and material properties, hence it is appealing for a multi-scale and/or multi-resolution analysis. The method developed in this paper employs an interface force–displacement coupling to yield the multi-scale model equations. It is shown that the governing equations contain a self-coupling term that affects the stability of the system, as it contributes to additional stiffness at the interface. Stability analysis is presented in terms of rotations of two vectors in [Formula: see text] space, where each vector represents individual model’s stability. Three model configurations of practical interest were investigated, analytical formulae derived and used to analyze stability. These analytical formulae were compared against results from numerical simulations and perfect agreement was observed.
The spatial grid of numerical models of acoustic emission (AE) sources acts as a spatial filter for elastic wave signals. The filtering effects are particularly prominent for short-time, broadband signals -typical for AE. In this paper, we investigate the filtering influence of spatial discretization (meshing) on broadband AE source modeling. The AE source -generating AEs propagating as elastic waves -was modeled using cohesive zone approach, and the numerical simulations were performed in commercial FEM software COMSOL Multiphysics. Results were processed using Fast Fourier Transform, filtered, and subsequently analyzed in terms of the filtering effects of spatial discretization on AE source modeling. In this paper, it is shown that spatial grids in numerical models effectively work like low-pass filters with the cut-off frequency corresponding to the numerical Brillouin zone. The latter induces short wavelength limitation, and the frequency components near (below) the zone edge are amplified in magnitude. It was found that the amplified frequencies represent numerical errors. Also, it was inferred that the filtering effect of spatial discretization can mask the AE source characteristics and affect the quality of the results.
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