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Proceedings Paper

Reliable prediction of micro-anomalies from macro-observables
Author(s): Sonjoy Das; Sourish Chakravarty
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Paper Abstract

A stochastic multi-scale based approach is presented in this work to detect signatures of micro-anomalies from macrolevel response variables. By micro-anomalies, we primarily refer to micro-cracks of size 10–100 μm (depending on the material), while macro-level response variables imply, e.g., strains, strain energy density of macro-level structures (typical size often varying in the order of 10–100 m). The micro-anomalies referred above are not discernible to the naked eyes. Nevertheless, they can cause catastrophic failures of structural systems due to fatigue cyclic loading that results in initiation of fatigue cracks. Analysis of such precursory state of internal damage evolution, before amacro-crack visibly appears (say, size of a few cms), is beyond the scope of the conventional crack propagation analysis, e.g., classical fracture mechanics. The present work addresses this issue in a certain sense by incorporating the effects of micro-cracks into the macro-scale constitutive material properties (e.g., constitutive elasticity tensors) within a probabilistic formalism based on random matrix theory, maximum entropy principle, and principles of minimum complementary energy and minimum potential energy. Distinct differences are observed in the macro-level response characteristics depending on the presence or absence of micro-cracks. This particular feature can now be used to reliably detect micro-cracks from experimental measurements of macro-observables. The present work, therefore, further proposes an efficient and robust optimization scheme: (1) to identify locations of micro-cracks in macroscopic structural systems, say, in an aircraft wing which is of the size of 10– 100 m, and (2) to determine the weakened (due to the presence of micro-cracks) macroscopic material properties which will be useful in predicting the remaining useful life of structural systems. The proposed optimization scheme achieves better convergence rate and accuracy by exploiting positive-definite structure of the macroscopic constitutive matrices.

Paper Details

Date Published: 9 March 2014
PDF: 15 pages
Proc. SPIE 9064, Health Monitoring of Structural and Biological Systems 2014, 90641E (9 March 2014); doi: 10.1117/12.2045217
Show Author Affiliations
Sonjoy Das, Univ. at Buffalo (United States)
Sourish Chakravarty, Univ. at Buffalo (United States)

Published in SPIE Proceedings Vol. 9064:
Health Monitoring of Structural and Biological Systems 2014
Tribikram Kundu, Editor(s)

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