On accurate measurement of non-uniform displacement gradient

Commonly, the displacement gradient is measured, assuming its variation to be uniform. Systematic error arising due to local uniform approximation of non-uniform displacement gradient is investigated for in-plane periodical varying displacement gradient through the Taylor method. The Taylor method's calculated bound is loose and at variance with the experimental observations. Consequently, an alternate error bound, based on Fourier representation, is proposed, which yields a tighter bound and provides the explanation for the experimental observations. The analytical results are verified through experimental investigation on a plain concrete cylinder subjected to uniaxial compression. The most significant findings are (1) for a body exhibiting periodically varying displacement gradient, the strain measurement would be repeatable for gauge length at least twice the displacement gradient periodicity but would have significant error, and (2) orthogonal gauge orientation (0–45–90 rosette) renders more accurate strain measurement than skewed arrangement (0–60–120 rosette).