An approach to quantify non-uniform strains in inhomogeneous bodies

Although it is well known that in inhomogeneous bodies like concrete, the displacement gradient varies spatially, and this variation depends on the specimen microstructure, attempts are seldom made to correlate both of them. Appropriate estimation of this spatially varying strain and its quantification, which distinguishes specimens of different classes but invariant for the same class, is desired. An extreme value statistics-based approach is proposed to quantify spatially varying strain. Using a photogrammetry method, by judiciously choosing marker configurations to bound the error in the estimated strain, it is possible to get numerous estimates of the strain over a region. The parameters in an appropriate extreme value statistics distribution are found using these measured strain estimates and are examined across stress levels, location and specimen classes. Scale parameters of the extreme value distributions remain statistically the same across stress levels and location but vary significantly with specimen classes, suggesting the potential application of extreme value statistics for quantifying spatial strain variation. Thus, a robust methodology for measuring and quantifying non-uniform strain is proposed and experimentally validated. This holds potential applications across diverse fields and in the development of probabilistic constitutive relations that would rationalize the material partial safety factors.