A Probabilistic Evaluation of the Least Squares Strain Tensor Derived from a Three‐Dimensional Modular Strain Rosette Using the Monte‐Carlo Technique

Abstract

Abstract: Strain gradients give rise to a number of problems in the field of embedded three‐dimensional strain measurement. In order to avoid these problems a modular type three‐dimensional strain rosette was embedded into known strain fields and the data from the individual gauges compared with theoretical predictions. Finally, the least squares strain tensor was predicted from experimental data analysed using the Monte‐Carlo technique and the theoretical results forecast from finite element data taking into account the mechanical properties of the carrier, plug and prismatic bar. Some of the experimental results were found to correlate well with the theoretical values but some values in the least squares strain tensor, in particular under compression and torsional loading, departed considerably from the theoretical values. It was found that the effect of the measurement errors in the individual gauges combined with the matrix operations in the least squares strain tensor were responsible for biasing the resultant tensor data. However, the modular technique provided a solution to the problem of strain gradients.