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).

Automated summary

The systematic error arising from the local uniform approximation of a non-uniform displacement gradient in in-plane periodical varying displacement gradient was investigated using the Taylor method. An alternate error bound, based on Fourier representation, was proposed to provide a tighter bound and explanation for experimental observations. Experimental investigation on a plain concrete cylinder subjected to uniaxial compression verified the analytical results. The most important findings are that strain measurement for a body exhibiting periodically varying displacement gradient is repeatable for a gauge length at least twice the displacement gradient periodicity but with significant error, and that orthogonal gauge orientation (0-45-90 rosette) yields more accurate strain measurement than skewed arrangement (0-60-120 rosette).