Predictive Algorithm for Detection of Microcracks from Macroscale Observables

Abstract

A probabilistic multiscale based computational scheme is developed to predict locations of microcracks and to estimate the associated macroscopic constitutive material properties for structural systems. The proposed scheme only requires a single realization of the macroscale response field (e.g., strain field, strain energy density field) that is often typically available in practice. Here, the macroscale is associated with structural systems of size of the order of 10--100 $m$, while microcracks are used to refer to micron-scale cracks of size 10--100 $\mu m$ (depending on materials) that have the potential to cause catastrophic failures when they coalesce and form larger cracks. The analysis of such microcracks, before a macrocrack visibly appears (say, at the size of a few $cms$), is beyond the scope of the classical fracture mechanics. The present work addresses this issue in a certain sense by incorporating the effects of microcracks into macroscopic constitutive material properties within a probabilistic formalism which is based on multiscale mechanics, random matrix theory, and the principles of minimum complementary energy and minimum potential energy. Distinct differences are observed in the probabilistic features (not deterministic features) of macrolevel response variables depending on the presence or absence of microcracks. Relying on this distinctive probabilistic features and using macroscale experimental measurements as available in practice, an optimization scheme, which is similar to cyclic seesaw optimization, is proposed (1) to identify the spatial locations of microcracks in macroscopic structural systems and (2) to estimate the weakened (due to the presence of microcracks) macroscopic material properties. In particular, the spatial field of weakened macroscopic constitutive elasticity matrix is estimated. The positive-definite feature of the constitutive elasticity matrix is exploited in this proposed optimization-based predictive analytics to achieve a better convergence rate and to improve the accuracy. This work will be useful in estimating remaining useful life of the structural systems.