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In responding to the needs of the material characterization community, the recently developed mesh‐free random grid method (MFRGM) has been exhibiting very promising characteristics of accuracy, adaptability, implementation flexibility and efficiency. To address the design specification of the method according to an intended application, we are presenting a sensitivity analysis that aids into determining the effects of the experimental and computational parameters characterizing the MFRGM in terms of its performance. The performance characteristics of the MFRGM are mainly its accuracy, sensitivity, smoothing properties and efficiency. In this paper, we are presenting a classification of a set of parameters associated with the characteristics of the experimental set‐up and the random grid applied on the specimen under measurement. The applied sensitivity analysis is based on synthetic images produced from analytic solutions of specific isotropic and orthotropic elasticity boundary value problems. This analysis establishes the trends in the performance characteristics of the MFRGM that will enable the selection of the user controlled variables for a desired performance specification.

An exact solution is presented to the problem of the crack-initiation direction by applying the minimum strain-energy density criterion in the case of a slant crack loaded uniaxially. The exact expressions of stresses, obtained from Muskhelishvili’s complex functions, are used in evaluating strain energy. Although the position of direction of the minimum density (ϑm) was accepted as the probable direction of the next kink of a propagating crack, the mean value of the strain-energy density is also introduced, instead of its minimum value, in the role of the critical quantity for crack initiation. Interesting results were derived for the behavior of this quantity concerning the phenomenon of bifurcation. The ratio of the mean-energy densities above and below the expected path of propagation is introduced as a second factor influencing the exact value of angle ϑm of propagation.