Proceedings Article | 9 March 2014
KEYWORDS: Copper, Chlorine, Matrices, Finite element methods, Monte Carlo methods, Optimization (mathematics), Stochastic processes, Mechanics, Statistical analysis, Binary data
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.
