ASYMPTOTIC INDEPENDENCE OF MATERIAL FAILURE AT DIFFERENT SCALES – THE ROLE OF SMALL-SCALE FLUCTUATIONS

Abstract eng:
Most materials are heterogeneous and aperiodic at micro and nanoscales; the properties, interaction etc. of the heterogeneities are random functions of space and time. An adequately detailed probabilistic description of the material microstructure is required for modeling material behavior and failure at all scales of interest. While it is possible to observe surfaces of solids down to nanometer resolutions, it remains a challenge to observe internal microstructural evolution in situ at a comparable resolution, and indirect methods are required for modeling small-scale stochastic damage phenomena. It is important to include both the spatial and the temporal aspects of the small-scale fluctuations. This paper proposes a general model of how the random material microstructure, composed of a matrix and embedded defects, evolves in time and space as a specimen is subjected to external actions. Local stationarity, strong mixing and dispersed extremes are assumed and the limiting distributions of the local average and the local maximum response are elicited. The asymptotic independence of extremal processes and hence failure (defined as first passage of a space-time process) at widely different scales is demonstrated.

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